commit 47dd434af8ccb3a852dd50025154a298e59e6c0a parent 6a567cecd48465e6a00d8dd49e2ef66cf6425be2 Author: Eamon Caddigan <eamon.caddigan@gmail.com> Date: Wed, 19 Jul 2023 20:05:21 -0700 Copied existing posts and assets to new site Assets include my publications and posters (which, as I approach the 10th anniversary of leaving academia, I wonder why I keep online). I made a couple very minor edits to some posts' content, but nothing noteworthy. I do mention the new theme in the "About" page. Most of the work went into taxonomizing everything. I make no guarantee that the Rmd files will render into these particular md files in the latest versions of the packages they use (I'm almost sure that some won't), but I am committing them anyway in case they're useful to somebody else. Diffstat:
74 files changed, 15214 insertions(+), 0 deletions(-)
diff --git a/content/about/index.md b/content/about/index.md @@ -0,0 +1,51 @@ +--- +title: "About" +date: 2023-07-24T20:43:04-07:00 +--- + +I am a [scientist](/categories/science/) living in Southern California. I +work in health [data science](/categories/data-science/), and have +previously done research in aviation human factors, cognitive neuroscience, +and human vision. I write [programs](/categories/programming) for almost all +of my work. + +<!--more--> + +In addition to my [posts]({{< ref "posts" >}}), you can check out my [list +of registered pre-prints and refereed publications]({{< ref "pubs/index.md" +>}}) (they're also listed under [my ORCiD +profile](https://orcid.org/0000-0002-4492-2846)). I also host a few [code +repositories under a separate subdomain](https://git.eamoncaddigan.net/) using +[stagit](https://codemadness.org/stagit.html). + +You can follow me on the Fediverse at +[@eamon@social.coop](https://social.coop/@eamon/), but the best way to +contact me is through email. My address is [my first and last +initial]@eamoncaddigan.net. + +## About This Site + +This site's theme is based on +[hugo-theme-readable](https://github.com/cjtheham/hugo-theme-readable) and +[readable.css](https://readable-css.freedomtowrite.org/). + +Except where noted, text, image, video, and audio files are available for +use under the [CC BY-SA +4.0](https://creativecommons.org/licenses/by-sa/4.0/) license, and source +code is available for use under the +[GPLv3](https://www.gnu.org/licenses/gpl-3.0.en.html) license +([why?]({{< ref "posts/use-the-gpl/index.md" >}})). + +Additionally, I give permission to use all content (text, images, video, +audio, and source code) on +[www.eamoncaddigan.net](https://www.eamoncaddigan.net) and +[git.eamoncaddigan.net](https://git.eamoncaddigan.net) to train statistical +and machine learning models with the following conditions: + +* The entire training set for the model must be made freely available to the + public for inspection and adaptation +* The source code for the model must be available under a license approved by + the [Open Source Initiative](https://opensource.org/licenses/) +* Any work created using the generated model output must be licensed with + either the [CC0](https://creativecommons.org/publicdomain/zero/1.0/) or + [CC-BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/) license diff --git a/content/posts/antivax-attitudes/index.Rmd b/content/posts/antivax-attitudes/index.Rmd @@ -0,0 +1,414 @@ +--- +title: "Bayesian estimation of anti-vaccination belief changes" +author: "Eamon Caddigan" +date: "September 3, 2015" +output: html_document +--- + +```{r global_options, include=FALSE} +knitr::opts_chunk$set(cache=TRUE, echo=FALSE, warning=FALSE, message=FALSE, + fig.width=9, fig.align="center") +``` + +```{r setup_data, results="hide"} +# Required librarys and external files ---------------------------------------- + +library(readxl) +library(tidyr) +library(dplyr) +library(ggplot2) +library(gridExtra) +library(rjags) +library(runjags) +source("DBDA2E-utilities.R") +source("ggPostPlot.R") + +# Clean and process the data -------------------------------------------------- + +# Generates warnings for the Ps who didn't do day 2 +suppressWarnings(expData <- read_excel("Vacc_HPHH_publicDataset.xlsx", sheet = 2)) + +# Exclude Ps who didn't do day 2 and failed the attention checks +expData.clean <- expData %>% + # It's good to add a subject number so we can go back to original data + mutate(subject_number = 1:nrow(.)) %>% + filter(Returned == 1, + `AttentionCheck_PostTest (if = 4 then include)` == 4, + `AttentionChecks_Sum(include if = 4)` == 4, + Paid_Attention == 1) + +# Get all the dependent measures into a DF +questionnaireData <- expData.clean %>% + # Pull out the columns and use consistent names + select(subject_number, + intervention = Condition, + pretest.healthy = Healthy_VaxscalePretest, + posttest.healthy = Healthy_VaxscalePosttest, + pretest.diseases = Diseases_VaxScalePretest, + posttest.diseases = Diseases_VaxScalePosttest, + pretest.doctors = Doctors_VaxScalePreTest, + posttest.doctors = Doctors_VaxScalePostTest, + pretest.side_effects = Sideeffects_VaxScalePreTest, + posttest.side_effects = Sideeffects_VaxScalePostTest, + pretest.plan_to = Planto_VaxScalePreTest, + posttest.plan_to = Planto_VaxScalePostTest) %>% + # Reverse-code the approrpiate columns + mutate(pretest.diseases = 7 - pretest.diseases, + posttest.diseases = 7 - posttest.diseases, + pretest.side_effects = 7 - pretest.side_effects, + posttest.side_effects = 7 - posttest.side_effects) %>% + # Tidy the data + gather("question", "response", -subject_number, -intervention) %>% + separate(question, c("interval", "question"), sep = "\\.") %>% + mutate(intervention = factor(intervention, + c("Control", "Autism Correction", "Disease Risk")), + interval = factor(interval, + c("pretest", "posttest"), ordered = TRUE), + question = factor(question, + c("healthy", "diseases", "doctors", "side_effects", "plan_to"))) +# ----------------------------------------------------------------------------- +``` + +## Introduction + +How easy is it to change people's minds about vaccinating their children? According to a recent study ([Horne, Powell, Hummel & Holyoak, 2015](http://www.pnas.org/content/112/33/10321.abstract)), a simple intervention -- which consisted of showing participants images, an anecdote, and some short warnings about diseases -- made participants more likely to support childhood vaccinations. [Here's a good writeup](https://news.illinois.edu/blog/view/6367/234202) of the article if you're unable to read the original. + +The authors [placed their data online](https://osf.io/nx364/), which comprises pre- and post-intervention survey responses for three groups of participants: + +1. A control group +2. An "autism correction" group that were shown evidence that vaccines don't cause autism. +3. A "disease risk" group that were shown images, an anecdote, and some short warnings about the diseases (such as rubella and measles) that the vaccines prevent. + +I chose to look over this data for a couple reasons. First, I'm friends with two of the authors (University of Illinois Psychologists Zach Horne and John Hummel) and it's good to see them doing cool work. Second, my own research has given me little opportunity to work with survey data, and I wanted more experience with the method. I was excited to try a Bayesian approach because it makes it possible to perform post hoc comparisons without inflating the "type I"" (false positive) error rates (see below). + +Participants were given a surveys with five questions and asked to rate their level of agreement with each on a six-point scale. + +code | question +-------------|------------- +healthy | Vaccinating healthy children helps protect others by stopping the spread of disease. +diseases | Children do not need vaccines for diseases that are not common anymore. *reverse coded* +doctors | Doctors would not recommend vaccines if they were unsafe. +side_effects | The risk of side effects outweighs any protective benefits of vaccines. *reverse coded* +plan_to | I plan to vaccinate my children. + +```{r plot_responses, dependson="setup_data"} +# Calculate the change-in-attitude for each subject on each question +questionnaireData <- questionnaireData %>% + group_by(subject_number, question) %>% + spread(interval, response) %>% mutate(change = posttest-pretest) %>% + gather("interval", "response", pretest, posttest) + +p2 <- ggplot(questionnaireData, aes(x = interval, y = response, group = subject_number, color = change)) + + geom_line(alpha = 0.2, position = position_jitter(w = 0.1, h = 0.1)) + + facet_grid(intervention ~ question) + + scale_color_gradient2(low="red", mid="grey20", high="blue") +print(p2) +``` + +The above figure shows the data. Each line represents represents a single participant's responses before and after the intervention, organized by intervention group and question. Lines are colored by the magnitude of the change in response; blue lines indicate an increase in agreement (toward a more pro-vaccine stance) and red lines indicate a reduction in agreement (a more anti-vaccine stance). + +The JAGS code for the model is part of the source of this document, which is [available on Github](https://github.com/eamoncaddigan/antivax-attitudes). It uses a Bayesian analog to a three-factor ANOVA, with a thresholded cummulative normal distribution serving as a link function. Such models fit ordinal responses (such as those obtained from surveys) well. The thresholds and variance of the link function were fit independently for each question. The mean of the function was estimated for each response using a linear combination of the levels of the question, the interval (pre-test vs. post-test), the intervention group, and all interactions between these factors. + +## Results + +```{r run_model, dependson="setup_data"} +# Get the data ready for JAGS +x1 <- as.numeric(as.factor(questionnaireData[["question"]])) +Nx1Lvl <- max(x1) +x2 <- as.numeric(as.factor(questionnaireData[["intervention"]])) +Nx2Lvl <- max(x2) +x3 <- as.numeric(as.factor(questionnaireData[["interval"]])) +Nx3Lvl <- max(x3) +y <- as.numeric(questionnaireData[["response"]]) +Ntotal <- length(y) +nYlevels <- max(y) + +# Threshold 1 and nYlevels-1 are fixed; other thresholds are estimated. +# This allows all parameters to be interpretable on the response scale. +thresh <- matrix(data = NA, nrow = Nx1Lvl, ncol = nYlevels-1) +thresh[, 1] <- 1 + 0.5 +thresh[, nYlevels-1] <- nYlevels-1 + 0.5 +# Specify the data in a list, for later shipment to JAGS: +dataList <- list( + x1 = x1, + Nx1Lvl = Nx1Lvl, + x2 = x2, + Nx2Lvl = Nx2Lvl, + x3 = x3, + Nx3Lvl = Nx3Lvl, + y = y, + NyLvl = nYlevels, + thresh = thresh, + Ntotal = Ntotal +) + +# Prepare the model for JAGS +modelString <- " + model { + for (i in 1:Ntotal) { + # Thresholded cummulative normal distribution + y[i] ~ dcat(pr[i,1:NyLvl]) + pr[i,1] <- pnorm(thresh[x1[i], 1], mu[i], 1/sigma[x1[i]]^2) + for (k in 2:(NyLvl-1)) { + pr[i,k] <- max(0, pnorm(thresh[x1[i], k] , mu[i] , 1/sigma[x1[i]]^2 ) - + pnorm(thresh[x1[i], k-1] , mu[i] , 1/sigma[x1[i]]^2 )) + } + pr[i,NyLvl] <- 1 - pnorm(thresh[x1[i], NyLvl-1] , mu[i] , 1/sigma[x1[i]]^2) + + # mu ~ x1*x2*x3 + mu[i] <- a0 + a1[x1[i]] + a2[x2[i]] + a3[x3[i]] + + a1a2[x1[i], x2[i]] + a1a3[x1[i], x3[i]] + a2a3[x2[i], x3[i]] + + a1a2a3[x1[i], x2[i], x3[i]] + } + + a0 ~ dnorm((1+NyLvl)/2, 1/(NyLvl)^2) + + for (j1 in 1:Nx1Lvl) { + # Constant sigma for beta1, we're treating all Qs as independent + a1[j1] ~ dnorm(0.0, 1/(NyLvl)^2) + + # Sigma for normal CDF, unique for each x1. + sigma[j1] ~ dunif(NyLvl/1000, NyLvl*10) + + # Threshold distributions. 1 and NyLvl-1 are fixed, not stochastic + for (k in 2:(NyLvl-2)) { + thresh[j1, k] ~ dnorm(k+0.5, 1/2^2) + } + } + + # Constant sigma for beta2, the interventions are independent + for (j2 in 1:Nx2Lvl) { + a2[j2] ~ dnorm(0.0, 1/(NyLvl)^2) + } + + # Constant sigma for beta3 + for (j3 in 1:Nx3Lvl) { + a3[j3] ~ dnorm(0.0, 1/(NyLvl)^2) + } + + # Interaction terms also have homogenous variance + for (j1 in 1:Nx1Lvl) { + for (j2 in 1:Nx2Lvl) { + a1a2[j1, j2] ~ dnorm(0.0, 1/(NyLvl)^2) + } + } + for (j1 in 1:Nx1Lvl) { + for (j3 in 1:Nx3Lvl) { + a1a3[j1, j3] ~ dnorm(0.0, 1/(NyLvl)^2) + } + } + for (j2 in 1:Nx2Lvl) { + for (j3 in 1:Nx3Lvl) { + a2a3[j2, j3] ~ dnorm(0.0, 1/(NyLvl)^2) + } + } + for (j1 in 1:Nx1Lvl) { + for (j2 in 1:Nx2Lvl) { + for (j3 in 1:Nx3Lvl) { + a1a2a3[j1, j2, j3] ~ dnorm(0.0, 1/(NyLvl)^2) + } + } + } + + # Compute cell means + for (j1 in 1:Nx1Lvl) { + for (j2 in 1:Nx2Lvl) { + for (j3 in 1:Nx3Lvl) { + m[j1, j2, j3] <- a0 + a1[j1] + a2[j2] + a3[j3] + + a1a2[j1, j2] + a1a3[j1, j3] + a2a3[j2, j3] + + a1a2a3[j1, j2, j3] + } + } + } + + # Convert a0, a1[], a2[], &c. to sum-to-zero b0, b1[], b2[], &c. + b0 <- mean(m[1:Nx1Lvl, 1:Nx2Lvl, 1:Nx3Lvl]) + for (j1 in 1:Nx1Lvl) { + b1[j1] <- mean(m[j1, 1:Nx2Lvl, 1:Nx3Lvl]) - b0 + } + for (j2 in 1:Nx2Lvl) { + b2[j2] <- mean(m[1:Nx1Lvl, j2, 1:Nx3Lvl]) - b0 + } + for (j3 in 1:Nx3Lvl) { + b3[j3] <- mean(m[1:Nx1Lvl, 1:Nx2Lvl, j3]) - b0 + } + for (j1 in 1:Nx1Lvl) { + for (j2 in 1:Nx2Lvl) { + b1b2[j1, j2] <- mean(m[j1, j2, 1:Nx3Lvl]) - (b0 + b1[j1] + b2[j2]) + } + } + for (j1 in 1:Nx1Lvl) { + for (j3 in 1:Nx3Lvl) { + b1b3[j1, j3] <- mean(m[j1, 1:Nx2Lvl, j3]) - (b0 + b1[j1] + b3[j3]) + } + } + for (j2 in 1:Nx2Lvl) { + for (j3 in 1:Nx3Lvl) { + b2b3[j2, j3] <- mean(m[1:Nx1Lvl, j2, j3]) - (b0 + b2[j2] + b3[j3]) + } + } + for (j1 in 1:Nx1Lvl) { + for (j2 in 1:Nx2Lvl) { + for (j3 in 1:Nx3Lvl) { + b1b2b3[j1, j2, j3] <- m[j1, j2, j3] - (b0 + b1[j1] + b2[j2] + b3[j3] + + b1b2[j1, j2] + b1b3[j1, j3] + b2b3[j2, j3]) + } + } + } + } +" # close quote for modelString +# Write out modelString to a text file +writeLines(modelString , con="TEMPmodel.txt") + +# Tell JAGS which parameters to return +parameters <- c("b0", "b1", "b2", "b3", "b1b2", "b1b3", "b2b3", "b1b2b3", + "sigma", "thresh") + +# JAGS parameters. We'll let it iniaialize itself +initsList <- NULL +adaptSteps <- 500 # Number of steps to "tune" the samplers +burnInSteps <- 1000 +numSavedSteps <- 15000 +thinSteps <- 10 +nChains <- 4 +fileNameRoot <- "antivax-mcmc" + +# Since running JAGS takes forever, we'll skip redoing it every time we knit. +saveName <- paste0(fileNameRoot, "-coda.Rdata") +if (file.exists(saveName)) { + load(saveName) +} else { + runJagsOut <- run.jags(method="parallel", + model="TEMPmodel.txt", + monitor=parameters, + data=dataList, + #inits=initsList, + n.chains=nChains, + adapt=adaptSteps, + burnin=burnInSteps, + sample=ceiling(numSavedSteps/nChains), + thin=thinSteps, + summarise=FALSE, + plots=FALSE) + codaSamples <- as.mcmc.list(runJagsOut) + save(codaSamples, file=saveName) +} +mcmcMat <- as.matrix(codaSamples) +``` + +### A "risk" intervention changes attitudes toward vaccination + +When fitting model parameters using Monte Carlo methods, it's important to inspect the posterior distribution to make sure the samples converged. Here's an example of one parameter, the intercept for the mean of the cummulative normal. + +```{r plot_diag, dependson="run_model", fig.width=5, fig.height=5} +diagMCMC(codaObject = codaSamples, + parName = "b0", + saveName = NULL) +``` + +It's also important to check the predictions made by a model against the data being fit, as "[we cannot really interpret the parameters of the model very meaningfully when the model doesn't describe the data very well](http://doingbayesiandataanalysis.blogspot.com/2015/08/a-case-in-which-metric-data-are-better.html)". Here are response histograms for each question, averaged across the levels of the other factors. Model predictions are superimposed on the histograms, along with the 95% HDI for each response. + +```{r plot_ppc, dependson="run_model", fig.height=6} +plots <- list() +for (x1Level in seq_along(levels(questionnaireData$question))) { + p <- ggPosteriorPredictive(questionnaireData, codaSamples, x1Level = x1Level) + p <- p + ggtitle(levels(questionnaireData$question)[x1Level]) + p <- p + theme_classic() + plots[[length(plots)+1]] <- p +} +do.call(grid.arrange, c(plots, ncol=3)) +``` + +Since the sampling procedure was well-behaved and the model describes the data well, we can use the parameter estimates to judge the size of the effects. Here are is the estimate of the change in attitude (post-test - pre-test) for each intervention group. + +```{r plot_change, dependson="run_model", fig.height=3} +par(mfrow = c(1, 3), mar=c(2, 1, 1, 1), oma=c(0, 0, 4, 0)) +for (x2Level in seq_along(levels(questionnaireData$intervention))) { + plotPost((mcmcMat[, "b3[2]"] + mcmcMat[, paste0("b2b3[", x2Level, ",2]")]) - + (mcmcMat[, "b3[1]"] + mcmcMat[, paste0("b2b3[", x2Level, ",1]")]), + main = "", + compVal = 0.0, ROPE = c(-0.05, 0.05), + xlab = "") + mtext(levels(questionnaireData$intervention)[x2Level], side=3, line=1) +} +title("Attitude change", outer=TRUE) +``` + +These plots highlight the 95% highest density interval (HDI) for the posterior distributions of the parameters. Also highlighted are a comparison value, which in this case is a pre- vs. post-test difference of 0, and a "range of practical equivalence" (ROPE) around the comparison value. The HDI of the posterior distribution of attitude shifts for the "disease risk" group" (but no other group) falls completely outside this ROPE, so we can reasonably conclude that this intervention changes participants' attitudes toward vaccination. + +we can also use the posterior distributions to directly estimate the shifts relative to the control group. Here is the difference between the attitude change observed for both the "autism correction" and "disease risk" groups compared to the attitude change in the control group. + +```{r plot_change_rel, dependson="run_model", fig.width=6, fig.height=3} +controlLevel = which(levels(questionnaireData$intervention) == "Control") + +par(mfrow = c(1, 2), mar=c(2, 1, 1, 1), oma=c(0, 0, 4, 0)) +for (x2Level in which(levels(questionnaireData$intervention) != "Control")) { + plotPost((mcmcMat[, paste0("b2b3[", x2Level, ",2]")] - mcmcMat[, paste0("b2b3[", x2Level, ",1]")]) - + (mcmcMat[, paste0("b2b3[", controlLevel, ",2]")] - mcmcMat[, paste0("b2b3[", controlLevel, ",1]")]), + compVal = 0.0, ROPE = c(-0.05, 0.05), + main = "", + xlab = "") + mtext(levels(questionnaireData$intervention)[x2Level], side=3, line=1) +} +title("Change relative to control", outer=TRUE) +``` + +The posterior distribution above shows that "disease risk" participants shifted their response about half an interval relative to the control group following the intervention. The "autism correction" participants, however, did not show a credible change in vaccination attitudes. Bayesian estimation replicates the conclusions drawn by Horne and colleagues. + +### Post hoc comparisons + +An analysis following the tradition of null-hypothesis significance testing (NHST) attempts to minimize the risk of "type I" errors, which occur when the "null" hypothesis (i.e., there is no effect) is erroneously rejected. The more tests performed in the course of an analysis, the more likely that such an error will occur due to random variation. The [Wikipedia article on the "Multiple Comparisons Problem"](https://en.wikipedia.org/wiki/Multiple_comparisons_problem) is an approachable read on the topic and explains many of the corrections that are applied when making mulitple comparisons in a NHST framework. + +Instead of focusing on type I error, the goal of Bayesian estimation is to estimate values of the parameters of a model of the data. The posterior distribution provides a range of credible values that these parameters can take. Inferences are made on the basis of these estimates; e.g., we see directly that the "disease risk" intervention shifts participants' attitude toward vaccination about one half of an interval. Since a single model was fit to all the data, additional comparisons of parameter distributions don't increase the chance of generating false positives. [Gelman, Hill, and Yajima (2008)](http://www.stat.columbia.edu/~gelman/research/unpublished/multiple2.pdf) is a great resource on this. + +For example, we can look at the size of the shift in attitude toward each question for each group. If we used an NHST approach, these 15 additional comparisons would either seriously inflate the type I error rate (using a p-value of 0.05 on each test would result in an overall error rate of `r round(1 - (1 - 0.05)^15, 2)`), or require much smaller nominal p-values for each test. + +```{r plot_posthoc, dependson="run_model", fig.height=9} + +# 5 x 3 grid of plots. So understandable! +par(mfrow = c(5, 3), mar=c(2, 1, 1, 1), oma=c(0, 0, 2, 4)) +for (x1Level in seq_along(levels(questionnaireData$question))) { + for (x2Level in seq_along(levels(questionnaireData$intervention))) { + plotPost((mcmcMat[, "b3[2]"] + + mcmcMat[, paste0("b1b2[", x1Level, ",", x2Level, "]")] + + mcmcMat[, paste0("b1b3[", x1Level, ",2]")] + + mcmcMat[, paste0("b2b3[", x2Level, ",2]")] + + mcmcMat[, paste0("b1b2b3[", x1Level, ",", x2Level, ",2]")]) - + (mcmcMat[, "b3[1]"] + + mcmcMat[, paste0("b1b2[", x1Level, ",", x2Level, "]")] + + mcmcMat[, paste0("b1b3[", x1Level, ",1]")] + + mcmcMat[, paste0("b2b3[", x2Level, ",1]")] + + mcmcMat[, paste0("b1b2b3[", x1Level, ",", x2Level, ",1]")]), + main = "", + compVal = 0.0, ROPE = c(-0.05, 0.05), + xlab = "") + + # Label the top row with the name of the intervention and the right column + # with the question + if (x1Level == 1) { + mtext(levels(questionnaireData$intervention)[x2Level], side=3, line=1) + } + if (x2Level == length(levels(questionnaireData$intervention))) { + mtext(levels(questionnaireData$question)[x1Level], side=4, line=2) + } + } +} +``` + +The only credible differences for single questions both occur for participants in the "disease risk" group. The "healthy" ("Vaccinating healthy children helps protect others by stopping the spread of disease.") and "diseases" ("Children do not need vaccines for diseases that are not common anymore.") questions show a reliable positive shift, which makes a lot of sense given the nature of the intervention. However, it's important to note that the HDIs are very wide for these posteriors compared to the ones shown earlier. This is driven primarily by the fact that this comparison relies on a three-way interaction, which has greater variance (as is typical in traditional ANOVA models). The posterior mode of the change for the "plan_to" question ("I plan to vaccinate my children") is fairly large for the "disease risk" group, but the wide HDI spans the ROPE around 0. + +### Expanding the models + +My goal was to examine the conclusions made in the original report of these data. However, this is just one way to model the data, and different models are more appropriate for different questions. For instance, the standard deviation and thereshold values were fit separately for each question here, but these could instead be based on a hyperparameter that could iteself be modelled. I also excluded subject effects from the model; there were many subjects (over 300), so a full model with these included would take much longer to fit, but may produce more generalizable results. Bayesian estimation requires an investigator to be intentional about modelling decisions, which I consider to be an advantage of the method. + +### Prior probabilities + +A defining characteristic of Bayesian analyses is that prior information about the model parameters is combined with their likelihood (derived from the data) to produce posterior distributions. In this analysis, I used priors that put weak constraints on the values of the parameters. If an investigator has reason to assume that parameters will take on certain values (e.g., the results of a previous study), this prior information can -- and should -- be incorporated into the analysis. Again, I like that these decisions have to be made deliberately. + +## Conclusions + +Concerns about a possible link between childhood vaccination and autism is causing some parents to skip childhood vaccinations, which is dangerous ([Calandrillo, 2004](http://www.ncbi.nlm.nih.gov/pubmed/15568260)). However, an intervention that exposes people to the consequences of the diseases that vaccinations prevent makes them respond more favorably toward childhood vaccination. A separate group of participants did not change their attitudes after being shown information discrediting the vaccination-autism link, nor did a group of control participants. + +### Acknowledgements + +[Zach Horne](http://www.zacharyhorne.com/) made the data available for analysis (by anyone!), and gave useful feedback on an earlier version of this write-up. Much of the code for Bayesian estimation was cobbled together from programs distributed with Doing Bayesian Data Analysis (2nd ed) by [John K. Kruschke](http://www.indiana.edu/~kruschke/). +\ No newline at end of file diff --git a/content/posts/antivax-attitudes/index.md b/content/posts/antivax-attitudes/index.md @@ -0,0 +1,197 @@ +--- +title: "Bayesian estimation of anti-vaccination belief changes" +description: How easy is it to change people's minds about vaccinating their children? +date: 2015-09-03 +categories: +- Data Science +- Science +tags: +- Statistics +- Psychology +--- + +## Introduction + +How easy is it to change people's minds about vaccinating their children? +According to a recent study ([Horne, Powell, Hummel & Holyoak, +2015](http://www.pnas.org/content/112/33/10321.abstract)), a simple +intervention -- which consisted of showing participants images, an anecdote, +and some short warnings about diseases -- made participants more likely to +support childhood vaccinations. [Here's a good +writeup](https://news.illinois.edu/blog/view/6367/234202) of the article if +you're unable to read the original. + +The authors [placed their data online](https://osf.io/nx364/), which comprises +pre- and post-intervention survey responses for three groups of participants: + +1. A control group +2. An "autism correction" group that were shown evidence that vaccines don't +cause autism. +3. A "disease risk" group that were shown images, an anecdote, and some short +warnings about the diseases (such as rubella and measles) that the vaccines +prevent. + +I chose to look over this data for a couple reasons. First, I'm friends with +two of the authors (University of Illinois Psychologists Zach Horne and John +Hummel) and it's good to see them doing cool work. Second, my own research has +given me little opportunity to work with survey data, and I wanted more +experience with the method. I was excited to try a Bayesian approach because it +makes it possible to perform post hoc comparisons without inflating the "type +I"" (false positive) error rates (see below). + +Participants were given a surveys with five questions and asked to rate their +level of agreement with each on a six-point scale. + +code | question +-------------|------------- +healthy | Vaccinating healthy children helps protect others by stopping the spread of disease. +diseases | Children do not need vaccines for diseases that are not common anymore. *reverse coded* +doctors | Doctors would not recommend vaccines if they were unsafe. +side_effects | The risk of side effects outweighs any protective benefits of vaccines. *reverse coded* +plan_to | I plan to vaccinate my children. + + + +The above figure shows the data. Each line represents a single participant's +responses before and after the intervention, organized by intervention group +and question. Lines are colored by the magnitude of the change in response; +blue lines indicate an increase in agreement (toward a more pro-vaccine stance) +and red lines indicate a reduction in agreement (a more anti-vaccine stance). + +The JAGS code for the model is part of the source of this document, which is +[available on Github](https://github.com/eamoncaddigan/antivax-attitudes). It +uses a Bayesian analog to a three-factor ANOVA, with a thresholded cummulative +normal distribution serving as a link function. Such models fit ordinal +responses (such as those obtained from surveys) well. The thresholds and +variance of the link function were fit independently for each question. The +mean of the function was estimated for each response using a linear combination +of the levels of the question, the interval (pre-test vs. post-test), the +intervention group, and all interactions between these factors. + +## Results + +### A "risk" intervention changes attitudes toward vaccination + +When fitting model parameters using Monte Carlo methods, it's important to +inspect the posterior distribution to make sure the samples converged. Here's +an example of one parameter, the intercept for the mean of the cummulative +normal. + + + +It's also important to check the predictions made by a model against the data +being fit, as "[we cannot really interpret the parameters of the model very +meaningfully when the model doesn't describe the data very +well](http://doingbayesiandataanalysis.blogspot.com/2015/08/a-case-in-which-metric-data-are-better.html)". +Here are response histograms for each question, averaged across the levels of +the other factors. Model predictions are superimposed on the histograms, along +with the 95% HDI for each response. + + + +Since the sampling procedure was well-behaved and the model describes the data +well, we can use the parameter estimates to judge the size of the effects. Here +are is the estimate of the change in attitude (post-test - pre-test) for each +intervention group. + + + +These plots highlight the 95% highest density interval (HDI) for the posterior +distributions of the parameters. Also highlighted are a comparison value, which +in this case is a pre- vs. post-test difference of 0, and a "range of practical +equivalence" (ROPE) around the comparison value. The HDI of the posterior +distribution of attitude shifts for the "disease risk" group" (but no other +group) falls completely outside this ROPE, so we can reasonably conclude that +this intervention changes participants' attitudes toward vaccination. + +We can also use the posterior distributions to directly estimate the shifts +relative to the control group. Here is the difference between the attitude +change observed for both the "autism correction" and "disease risk" groups +compared to the attitude change in the control group. + + + +The posterior distribution above shows that "disease risk" participants shifted +their response about half an interval relative to the control group following +the intervention. The "autism correction" participants, however, did not show a +credible change in vaccination attitudes. Bayesian estimation replicates the +conclusions drawn by Horne and colleagues. + +### Post hoc comparisons + +An analysis following the tradition of null-hypothesis significance testing +(NHST) attempts to minimize the risk of "type I" errors, which occur when the +"null" hypothesis (i.e., there is no effect) is erroneously rejected. The more +tests performed in the course of an analysis, the more likely that such an +error will occur due to random variation. The [Wikipedia article on the +"Multiple Comparisons +Problem"](https://en.wikipedia.org/wiki/Multiple_comparisons_problem) is an +approachable read on the topic and explains many of the corrections that are +applied when making mulitple comparisons in a NHST framework. + +Instead of focusing on type I error, the goal of Bayesian estimation is to estimate values of the parameters of a model of the data. The posterior distribution provides a range of credible values that these parameters can take. Inferences are made on the basis of these estimates; e.g., we see directly that the "disease risk" intervention shifts participants' attitude toward vaccination about one half of an interval. Since a single model was fit to all the data, additional comparisons of parameter distributions don't increase the chance of generating false positives. [Gelman, Hill, and Yajima (2008)](http://www.stat.columbia.edu/~gelman/research/unpublished/multiple2.pdf) is a great resource on this. + +For example, we can look at the size of the shift in attitude toward each +question for each group. If we used an NHST approach, these 15 additional +comparisons would either seriously inflate the type I error rate (using a +p-value of 0.05 on each test would result in an overall error rate of 0.54), or +require much smaller nominal p-values for each test. + + + +The only credible differences for single questions both occur for participants +in the "disease risk" group. The "healthy" ("Vaccinating healthy children helps +protect others by stopping the spread of disease.") and "diseases" ("Children +do not need vaccines for diseases that are not common anymore.") questions show +a reliable positive shift, which makes a lot of sense given the nature of the +intervention. However, it's important to note that the HDIs are very wide for +these posteriors compared to the ones shown earlier. This is driven primarily +by the fact that this comparison relies on a three-way interaction, which has +greater variance (as is typical in traditional ANOVA models). The posterior +mode of the change for the "plan_to" question ("I plan to vaccinate my +children") is fairly large for the "disease risk" group, but the wide HDI spans +the ROPE around 0. + +### Expanding the models + +My goal was to examine the conclusions made in the original report of these +data. However, this is just one way to model the data, and different models are +more appropriate for different questions. For instance, the standard deviation +and thereshold values were fit separately for each question here, but these +could instead be based on a hyperparameter that could iteself be modelled. I +also excluded subject effects from the model; there were many subjects (over +300), so a full model with these included would take much longer to fit, but +may produce more generalizable results. Bayesian estimation requires an +investigator to be intentional about modelling decisions, which I consider to +be an advantage of the method. + +### Prior probabilities + +A defining characteristic of Bayesian analyses is that prior information about +the model parameters is combined with their likelihood (derived from the data) +to produce posterior distributions. In this analysis, I used priors that put +weak constraints on the values of the parameters. If an investigator has reason +to assume that parameters will take on certain values (e.g., the results of a +previous study), this prior information can -- and should -- be incorporated +into the analysis. Again, I like that these decisions have to be made +deliberately. + +## Conclusions + +Concerns about a possible link between childhood vaccination and autism is +causing some parents to skip childhood vaccinations, which is dangerous +([Calandrillo, 2004](http://www.ncbi.nlm.nih.gov/pubmed/15568260)). However, an +intervention that exposes people to the consequences of the diseases that +vaccinations prevent makes them respond more favorably toward childhood +vaccination. A separate group of participants did not change their attitudes +after being shown information discrediting the vaccination-autism link, nor did +a group of control participants. + +### Acknowledgements + +[Zach Horne](http://www.zacharyhorne.com/) made the data available for analysis +(by anyone!), and gave useful feedback on an earlier version of this write-up. +Much of the code for Bayesian estimation was cobbled together from programs +distributed with Doing Bayesian Data Analysis (2nd ed) by [John K. +Kruschke](http://www.indiana.edu/~kruschke/). + diff --git a/content/posts/antivax-attitudes/plot_change-1.png b/content/posts/antivax-attitudes/plot_change-1.png Binary files differ. diff --git a/content/posts/antivax-attitudes/plot_change_rel-1.png b/content/posts/antivax-attitudes/plot_change_rel-1.png Binary files differ. diff --git a/content/posts/antivax-attitudes/plot_diag-1.png b/content/posts/antivax-attitudes/plot_diag-1.png Binary files differ. diff --git a/content/posts/antivax-attitudes/plot_posthoc-1.png b/content/posts/antivax-attitudes/plot_posthoc-1.png Binary files differ. diff --git a/content/posts/antivax-attitudes/plot_ppc-1.png b/content/posts/antivax-attitudes/plot_ppc-1.png Binary files differ. diff --git a/content/posts/antivax-attitudes/plot_responses-1.png b/content/posts/antivax-attitudes/plot_responses-1.png Binary files differ. diff --git a/content/posts/antivax-bootstrap/bayesian_ending_scores.png b/content/posts/antivax-bootstrap/bayesian_ending_scores.png Binary files differ. diff --git a/content/posts/antivax-bootstrap/index.Rmd b/content/posts/antivax-bootstrap/index.Rmd @@ -0,0 +1,238 @@ +--- +layout: post +title: "Bootstrap analysis of anti-vaccination belief changes" +summary: Another way of looking at the antivaccination data of Horne, et al. +author: "Eamon Caddigan" +date: 2015-09-15 +categories: psych R +output: html_document +--- + +```{r global_options, include=FALSE} +knitr::opts_chunk$set(cache=TRUE, echo=FALSE, warning=FALSE, message=FALSE, + fig.width=9, fig.align="center") +``` + +```{r setup_data, results="hide"} +# Required librarys and external files ---------------------------------------- + +library(readxl) +library(tidyr) +library(dplyr) +library(ggplot2) +library(gridExtra) + +# Clean and process the data -------------------------------------------------- + +# Generates warnings for the Ps who didn't do day 2 +suppressWarnings(expData <- read_excel("Vacc_HPHH_publicDataset.xlsx", sheet = 2)) + +# Exclude Ps who didn't do day 2 and failed the attention checks +expData.clean <- expData %>% + # It's good to add a subject number so we can go back to original data + mutate(subject_number = 1:nrow(.)) %>% + filter(Returned == 1, + `AttentionCheck_PostTest (if = 4 then include)` == 4, + `AttentionChecks_Sum(include if = 4)` == 4, + Paid_Attention == 1) + +# Get all the dependent measures into a DF +questionnaireData <- expData.clean %>% + # Pull out the columns and use consistent names + select(subject_number, + intervention = Condition, + pretest.healthy = Healthy_VaxscalePretest, + posttest.healthy = Healthy_VaxscalePosttest, + pretest.diseases = Diseases_VaxScalePretest, + posttest.diseases = Diseases_VaxScalePosttest, + pretest.doctors = Doctors_VaxScalePreTest, + posttest.doctors = Doctors_VaxScalePostTest, + pretest.side_effects = Sideeffects_VaxScalePreTest, + posttest.side_effects = Sideeffects_VaxScalePostTest, + pretest.plan_to = Planto_VaxScalePreTest, + posttest.plan_to = Planto_VaxScalePostTest) %>% + # Reverse-code the approrpiate columns + mutate(pretest.diseases = 7 - pretest.diseases, + posttest.diseases = 7 - posttest.diseases, + pretest.side_effects = 7 - pretest.side_effects, + posttest.side_effects = 7 - posttest.side_effects) %>% + # Tidy the data + gather("question", "response", -subject_number, -intervention) %>% + separate(question, c("interval", "question"), sep = "\\.") %>% + mutate(intervention = factor(intervention, + c("Control", "Autism Correction", "Disease Risk")), + interval = factor(interval, + c("pretest", "posttest"), ordered = TRUE), + question = factor(question, + c("healthy", "diseases", "doctors", "side_effects", "plan_to"))) %>% + # Pre- and post-test get their own columns in these analyses + mutate(interval = paste0(interval, "_response")) %>% + spread(interval, response) +# ----------------------------------------------------------------------------- +``` + +## Introduction + +In a [previous post]({{ site.url }}/psych/bayes/2015/09/03/antivax-attitudes/) (I don't know why I'm linking it -- there are only two), I presented an analysis of data by [Horne, Powell, Hummel & Holyoak, (2015)](http://www.pnas.org/content/112/33/10321.abstract) that investigated changes in attitudes toward childhood vaccinations. The previous analysis used Bayesian estimation to show a credible increase in pro-vaccination attitudes following a "disease risk" intervention, but not an "autism correction" intervention. + +Some of my friends offered insightful comments, and one [pointed out](https://twitter.com/johnclevenger/status/639795727439429632) what appeared to be a failure of random assignment. Participants in the "disease risk" group happened to have lower scores on the pre-intervention survey and therefore had more room for improvement. This is a fair criticism, but a subsequent analysis showed that post-intervention scores were also higher for the "disease risk" group, which addresses this issue. + + + +### Bootstrapping + +Interpreting differences in parameter values isn't always straightforward, so I thought it'd be worthwhile to try a different approach. Instead of fitting a generative model to the sample, we can use bootstrapping to estimate the unobserved population parameters. [Bootstrapping](https://en.wikipedia.org/wiki/Bootstrapping_(statistics)) is conceptually simple; I feel it would have much wider adoption today had computers been around in the early days of statistics. + +Here is code that uses bootstrapping to estimate the probability of each response on the pre-intervention survey (irrespective of survey question or intervention group assignment). The sample mean is already an unbiased estimator of the population mean, so bootstrapping isn't necessary in this first example. However, this provides a simple illustration of how the technique works: sample observations *with replacement* from the data, calculate a statistic on this new data, and repeat. The mean of the observed statistic values provides an estimate of the population statistic, and the distribution of statistic values provides a measure of certainty. + +```{r setup_bootstrap, dependson="setup_data", echo=TRUE} +numBootstraps <- 1e5 # Should be a big number +numObservations <- nrow(questionnaireData) +uniqueResponses <- sort(unique(questionnaireData$pretest_response)) +interventionLevels <- levels(questionnaireData$intervention) + +# The observed proportion of responses at each level +pretestResponseProbs <- as.numeric(table(questionnaireData$pretest_response)) / + numObservations +``` + +```{r pretest_bootstrap, dependson="setup_bootstrap", echo=TRUE} +# Bootstrap to find the probability that each response will be given to pre-test +# questions. +pretestData <- array(data = 0, + dim = c(numBootstraps, + length(uniqueResponses)), + dimnames = list(NULL, + paste(uniqueResponses))) + +# Run the bootstrap +for (ii in seq_len(numBootstraps)) { + bootSamples <- sample(questionnaireData$pretest_response, + numObservations, + replace = TRUE) + bootSamplesTabulated <- table(bootSamples) + pretestData[ii, names(bootSamplesTabulated)] <- bootSamplesTabulated +} + +# Convert the counts to probabilities +pretestData <- pretestData / numObservations +``` + +```{r pretest_plot, dependson="pretest_bootstrap", fig.width=4, fig.height=4} +pretestDF <- data_frame(response = uniqueResponses, + bootstrap_prob = apply(pretestData, 2, mean), + bootstrap_sd = apply(pretestData, 2, sd), + observed_prob = pretestResponseProbs) + +ggplot(pretestDF, aes(x = response)) + + geom_bar(aes(y = observed_prob), stat = "identity", + color="white", fill="skyblue") + + geom_point(aes(y = bootstrap_prob), size = 3, color = "red") + + geom_errorbar(aes(ymin = bootstrap_prob - bootstrap_sd/2, + ymax = bootstrap_prob + bootstrap_sd/2), + size = 2, color = "red", width = 0) + + scale_x_continuous(breaks = 1:length(uniqueResponses)) + + scale_y_continuous(limits = c(0, 1)) + + xlab("Response Level") + + ylab("Proportion") + + theme_classic() +``` + +As expected, the bootstrap estimates for the proportion of responses at each level almost exactly match the observed data. There are supposed to be error-bars around the points, which show the bootstrap estimates, but they're obscured by the points themselves. + +## Changes in vaccination attitudes + +Due to chance alone, the three groups of participants (the control group, the "autism correction" group, and the "disease risk" group) showed different patterns of responses to the pre-intervention survey. To mitigate this issue, the code below estimates the transition probabilities from each response on the pre-intervention survey to each response on the post-intervention survey, and does so separately for the groups. These are conditional probabilities, e.g., P(post-intervention rating = 4 | pre-intervention rating = 3). + +The conditional probabilities are then combined with the observed pre-intervention response probabilities to calculate the joint probability of each response transition (e.g., P(post-intervention rating = 4 AND pre-intervention rating = 3)). Importantly, since the prior is agnostic to subjects' group assignment, these joint probability estimates are less-affected by biases that would follow from a failure of random assignment. + +```{r posttest_bootstrap, dependson="setup_bootstrap", echo=TRUE} +# preintervention responses x intervention groups x bootstraps x postintervention responses +posttestData <- array(data = 0, + dim = c(length(uniqueResponses), + length(interventionLevels), + numBootstraps, + length(uniqueResponses)), + dimnames = list(paste(uniqueResponses), + interventionLevels, + NULL, + paste(uniqueResponses))) + +for (pretestResponse in seq_along(uniqueResponses)) { + for (interventionLevel in seq_along(interventionLevels)) { + # Get the subset of data for each combination of intervention and + # pre-intervention response level. + questionnaireDataSubset <- filter(questionnaireData, + intervention == interventionLevels[interventionLevel], + pretest_response == pretestResponse) + numObservationsSubset <- nrow(questionnaireDataSubset) + + # Run the bootstrap + for (ii in seq_len(numBootstraps)) { + bootSamples <- sample(questionnaireDataSubset$posttest_response, + numObservationsSubset, + replace = TRUE) + bootSamplesTabulated <- table(bootSamples) + posttestData[pretestResponse, + interventionLevel, + ii, + names(bootSamplesTabulated)] <- bootSamplesTabulated + } + + # Convert the counts to probabilities + posttestData[pretestResponse, interventionLevel, , ] <- + posttestData[pretestResponse, interventionLevel, , ] / numObservationsSubset + } + + # Convert the conditional probabilities to joint probabilities using the + # observed priors on each pretest response. + posttestData[pretestResponse, , , ] <- posttestData[pretestResponse, , , ] * + pretestResponseProbs[pretestResponse] +} +``` + +With the transition probabilities sampled, it's possible to test the hypothesis: **"participants are more likely to shift toward a more pro-vaccine attitude following a 'disease risk' intervention than participants in control and 'autism correction' groups."** We'll use the previously-run bootstrap samples to compute the each group's probability of increasing scores. + +```{r posttest_shifts, dependson="posttest_bootstrap", echo=TRUE} +posttestIncrease <- array(data = 0, + dim = c(numBootstraps, + length(interventionLevels)), + dimnames = list(NULL, + interventionLevels)) + +for (interventionLevel in seq_along(interventionLevels)) { + for (pretestResponse in seq_along(uniqueResponses)) { + for (posttestResponse in seq_along(uniqueResponses)) { + if (posttestResponse > pretestResponse) { + posttestIncrease[, interventionLevel] <- posttestIncrease[, interventionLevel] + + posttestData[pretestResponse, interventionLevel, , posttestResponse] + } + } + } +} +``` + +This estimates the probability that post-intervention responses from the "disease risk" group have a greater probability of being higher than their pre-intervention counterparts than responses from the "autism correction" group. + +```{r posttest_stat, dependson="posttest_shifts", echo=TRUE} +sum(posttestIncrease[, which(interventionLevels == "Disease Risk")] > + posttestIncrease[, which(interventionLevels == "Autism Correction")]) / + nrow(posttestIncrease) +``` + +Below is a visualization of the bootstrap distributions. This illustrates the certainty of the estimates of the probability that participants would express stronger pro-vaccination attitudes after the interventions. + +```{r posttest_plot, dependson="posttest_shifts"} +posttestDF <- gather(as.data.frame(posttestIncrease), "intervention", "prob_increase") +ggplot(posttestDF, aes(x = prob_increase, fill = intervention)) + + geom_density(alpha = 0.6) + + scale_fill_brewer(type = "qual", palette = "Dark2") + + ylab("Samples") + xlab("Probability of rating increase") + + theme_minimal() +``` + +## Conclusion + +Bootstrapping shows that a "disease risk" intervention has a stronger effect than others in shifting participants' pro-vaccination attitudes. This analysis collapses across the five survey questions used by Horne and colleagues, but it would be straightforward to extend this code to estimate attitude change probabilities separately for each question. + +Although there are benefits to analyzing data with nonparametric methods, the biggest shortcoming of the approach I've used here is that it can not estimate the size of the attitude changes. Instead, it estimates that probability of pro-vaccination attitude changes occurring, and the difference in these probabilities between the groups. This is a great example of why it's important to keep your question in mind while analyzing data. diff --git a/content/posts/antivax-bootstrap/index.md b/content/posts/antivax-bootstrap/index.md @@ -0,0 +1,216 @@ +--- +title: "Bootstrap analysis of anti-vaccination belief changes" +description: Another way of looking at the antivaccination data of Horne, et al. +date: 2015-09-17 +categories: +- Data Science +- Science +tags: +- Psychology +- Statistics +- R +--- + +## Introduction + +In a [previous post]({{< ref "/posts/antivax-attitudes/index.md" +>}}), I presented an analysis of data by [Horne, Powell, Hummel & Holyoak, +(2015)](http://www.pnas.org/content/112/33/10321.abstract) that investigated +changes in attitudes toward childhood vaccinations. The previous analysis +used Bayesian estimation to show a credible increase in pro-vaccination +attitudes following a "disease risk" intervention, but not an "autism +correction" intervention. + +Some of my friends offered insightful comments, and one [pointed +out](https://twitter.com/johnclevenger/status/639795727439429632) what appeared +to be a failure of random assignment. Participants in the "disease risk" group +happened to have lower scores on the pre-intervention survey and therefore had +more room for improvement. This is a fair criticism, but a subsequent analysis +showed that post-intervention scores were also higher for the "disease risk" +group, which addresses this issue. + + + +### Bootstrapping + +Interpreting differences in parameter values isn't always straightforward, so I +thought it'd be worthwhile to try a different approach. Instead of fitting a +generative model to the sample, we can use bootstrapping to estimate the +unobserved population parameters. +[Bootstrapping](https://en.wikipedia.org/wiki/Bootstrapping_(statistics)) is +conceptually simple; I feel it would have much wider adoption today had +computers been around in the early days of statistics. + +Here is code that uses bootstrapping to estimate the probability of each +response on the pre-intervention survey (irrespective of survey question or +intervention group assignment). The sample mean is already an unbiased +estimator of the population mean, so bootstrapping isn't necessary in this +first example. However, this provides a simple illustration of how the +technique works: sample observations *with replacement* from the data, +calculate a statistic on this new data, and repeat. The mean of the observed +statistic values provides an estimate of the population statistic, and the +distribution of statistic values provides a measure of certainty. + + +```r +numBootstraps <- 1e5 # Should be a big number +numObservations <- nrow(questionnaireData) +uniqueResponses <- sort(unique(questionnaireData$pretest_response)) +interventionLevels <- levels(questionnaireData$intervention) + +# The observed proportion of responses at each level +pretestResponseProbs <- as.numeric(table(questionnaireData$pretest_response)) / + numObservations +``` +```r +# Bootstrap to find the probability that each response will be given to pre-test +# questions. +pretestData <- array(data = 0, + dim = c(numBootstraps, + length(uniqueResponses)), + dimnames = list(NULL, + paste(uniqueResponses))) + +# Run the bootstrap +for (ii in seq_len(numBootstraps)) { + bootSamples <- sample(questionnaireData$pretest_response, + numObservations, + replace = TRUE) + bootSamplesTabulated <- table(bootSamples) + pretestData[ii, names(bootSamplesTabulated)] <- bootSamplesTabulated +} + +# Convert the counts to probabilities +pretestData <- pretestData / numObservations +``` + + + +As expected, the bootstrap estimates for the proportion of responses at each +level almost exactly match the observed data. There are supposed to be +error-bars around the points, which show the bootstrap estimates, but they're +obscured by the points themselves. + +## Changes in vaccination attitudes + +Due to chance alone, the three groups of participants (the control group, the +"autism correction" group, and the "disease risk" group) showed different +patterns of responses to the pre-intervention survey. To mitigate this issue, +the code below estimates the transition probabilities from each response on the +pre-intervention survey to each response on the post-intervention survey, and +does so separately for the groups. These are conditional probabilities, e.g., +`P(post-intervention rating = 4 | pre-intervention rating = 3)`. + +The conditional probabilities are then combined with the observed +pre-intervention response probabilities to calculate the joint probability of +each response transition (e.g., `P(post-intervention rating = 4 ∩ +pre-intervention rating = 3)`). Importantly, since the prior is agnostic to +subjects' group assignment, these joint probability estimates are less-affected +by biases that would follow from a failure of random assignment. + +```r +# preintervention responses x intervention groups x bootstraps x postintervention responses +posttestData <- array(data = 0, + dim = c(length(uniqueResponses), + length(interventionLevels), + numBootstraps, + length(uniqueResponses)), + dimnames = list(paste(uniqueResponses), + interventionLevels, + NULL, + paste(uniqueResponses))) + +for (pretestResponse in seq_along(uniqueResponses)) { + for (interventionLevel in seq_along(interventionLevels)) { + # Get the subset of data for each combination of intervention and + # pre-intervention response level. + questionnaireDataSubset <- filter(questionnaireData, + intervention == interventionLevels[interventionLevel], + pretest_response == pretestResponse) + numObservationsSubset <- nrow(questionnaireDataSubset) + + # Run the bootstrap + for (ii in seq_len(numBootstraps)) { + bootSamples <- sample(questionnaireDataSubset$posttest_response, + numObservationsSubset, + replace = TRUE) + bootSamplesTabulated <- table(bootSamples) + posttestData[pretestResponse, + interventionLevel, + ii, + names(bootSamplesTabulated)] <- bootSamplesTabulated + } + + # Convert the counts to probabilities + posttestData[pretestResponse, interventionLevel, , ] <- + posttestData[pretestResponse, interventionLevel, , ] / numObservationsSubset + } + + # Convert the conditional probabilities to joint probabilities using the + # observed priors on each pretest response. + posttestData[pretestResponse, , , ] <- posttestData[pretestResponse, , , ] * + pretestResponseProbs[pretestResponse] +} +``` + +With the transition probabilities sampled, it's possible to test the +hypothesis: **"participants are more likely to shift toward a more pro-vaccine +attitude following a 'disease risk' intervention than participants in control +and 'autism correction' groups."** We'll use the previously-run bootstrap +samples to compute the each group's probability of increasing scores. + +```r +posttestIncrease <- array(data = 0, + dim = c(numBootstraps, + length(interventionLevels)), + dimnames = list(NULL, + interventionLevels)) + +for (interventionLevel in seq_along(interventionLevels)) { + for (pretestResponse in seq_along(uniqueResponses)) { + for (posttestResponse in seq_along(uniqueResponses)) { + if (posttestResponse > pretestResponse) { + posttestIncrease[, interventionLevel] <- posttestIncrease[, interventionLevel] + + posttestData[pretestResponse, interventionLevel, , posttestResponse] + } + } + } +} +``` + +This estimates the probability that post-intervention responses from the +"disease risk" group have a greater probability of being higher than their +pre-intervention counterparts than responses from the "autism correction" +group. + +```r +sum(posttestIncrease[, which(interventionLevels == "Disease Risk")] > + posttestIncrease[, which(interventionLevels == "Autism Correction")]) / + nrow(posttestIncrease) +``` + +``` +## [1] 0.99992 +``` + +Below is a visualization of the bootstrap distributions. This illustrates the +certainty of the estimates of the probability that participants would express +stronger pro-vaccination attitudes after the interventions. + + + +## Conclusion + +Bootstrapping shows that a "disease risk" intervention has a stronger effect +than others in shifting participants' pro-vaccination attitudes. This analysis +collapses across the five survey questions used by Horne and colleagues, but it +would be straightforward to extend this code to estimate attitude change +probabilities separately for each question. + +Although there are benefits to analyzing data with nonparametric methods, the +biggest shortcoming of the approach I've used here is that it can not estimate +the size of the attitude changes. Instead, it estimates that probability of +pro-vaccination attitude changes occurring, and the difference in these +probabilities between the groups. This is a great example of why it's important +to keep your question in mind while analyzing data. + diff --git a/content/posts/antivax-bootstrap/posttest_plot-1.png b/content/posts/antivax-bootstrap/posttest_plot-1.png Binary files differ. diff --git a/content/posts/antivax-bootstrap/pretest_plot-1.png b/content/posts/antivax-bootstrap/pretest_plot-1.png Binary files differ. diff --git a/content/posts/art-of-data-science/Cnl03.jpg b/content/posts/art-of-data-science/Cnl03.jpg Binary files differ. diff --git a/content/posts/art-of-data-science/index.md b/content/posts/art-of-data-science/index.md @@ -0,0 +1,71 @@ +--- +title: "The Art of Data Science" +description: This book is a great companion to your boring stats class. +date: 2015-09-09 +categories: +- Data Science +--- + +Data Science is hot. Fortunately, the recently released ebook [The Art of Data +Science (A Guide for Anyone Who Works with +Data)](https://leanpub.com/artofdatascience) doesn't waste space on trendy +technologies, and focuses instead on the enduring fundamentals of data +analysis. I can forgive the authors for choosing a topical title, however, +because few people are better qualified to capitalize on the trend as Johns +Hopkins Professors (and expert data-handlers) [Roger +Peng](http://www.biostat.jhsph.edu/~rpeng/) and [Elizabeth +Matsui](https://twitter.com/eliza68). + +No exercises accompany this book, and although there are a few snatches of R +code, it's not meant to be used as a handbook for data analysis. Instead, it +teaches readers how to think like a (productive) data analyst. Peng and Matsui +break the process of analyzing data into a list of core activities, which +begins with defining the question and ends with communicating the results. +Instead of presenting this as a linear process, they describe an "epicycle of +data analysis", a pattern of thinking and acting that is repeated in all of the +core activities. The authors explain that an analyst will often cycle through +this pattern several times during a single activity, and that the process often +sends scientists back to earlier steps. Readers learn that real world data +analysis is like playing Chutes and Ladders on a board with no ladders. + + + +I would recommend this book to any reader who's interested in this year's +sexiest career -- especially those annoyed that anybody would label a career +"sexy". However, I think this book is most valuable as a companion to +introductory statistics classes, as it fills in key gaps left by traditional +statistics curricula. This is particularly true for students, such as those at +the beginning of a postgraduate education, who expect to analyze real data by +the time the course has finished. Stats teachers have to cover a lot of ground +in classes that begin with stories about ball-filled urns (some lucky students +get actual candy) and end with ANOVA tables. In the end, few future scientists +finish the term with much more than a list of specific tests that can be +matched to familiar situations. Although most students gain additional training +during their graduate student apprenticeship, an education in data analysis +competes for time with the acquisition of domain knowledge and more specific +skills. This often leads to a cargo-cult approach to data analysis among people +who are specifically trained to seek out truth. I believe that reading this +book will help counteract these shortcomings. + +My favorite chapters discuss the process of building models of data, and I +really appreciate that the authors describe the difference between modeling for +inference (i.e., statistical modeling) and modeling for prediction (i.e., +machine learning). As a grad student, I had completed my program's required +stats classes before I *really* understood the relationship between "running a +(statistical) test" and "fitting a model"; learning this lesson earlier would +have made me better at both. I also like that the book encourages analysts to +build visualizations of their data early and often. This indispensable process +has become much easier in recent years as new libraries in several programming +languages streamline the process of tidying and plotting complicated data. The +only section that I would like to see expanded is the chapter on communication, +which might have benefitted from a brief discussion on building visualizations +for an audience. I suppose that this omission may have been intentional; there +are so many new developments in dataviz, such as a shift toward dynamic and +interactive visualizations, that it would be difficult to write something that +won’t soon be out of date. + +If you're new to data analysis, or interested in integrating a more formal (but +still flexible) framework into your practice, I think you'll find The Art of +Data Science to be worth a look. It is a quick read and available at a +pay-what-you-like price, so even poor grad students have no excuse not to. + diff --git a/content/posts/design-everyday-programs/index.md b/content/posts/design-everyday-programs/index.md @@ -0,0 +1,92 @@ +--- +title: "The design of everyday programs" +description: Even command-line programmers should think more like designers. +date: 2016-10-22 +categories: +- Programming +- Data Science +--- + +Several fellow researchers at the FAA have backgrounds in cognitive +neuroscience and are new to applied research. We recently started a book club +through the [South Jersey chapter of the Human Factors and Ergonomics +Society](https://southjerseyhfes.wordpress.com/) to learn more about human +factors and user experience research. Our first reading was [The Design of +Everyday +Things](http://www.jnd.org/books/design-of-everyday-things-revised.html) by Don +Norman, and it’s already influenced how I think about design. Norman focuses on +how designers can apply concepts from psychology to the design of “things”, but +these lessons apply to any interaction—such as the use of the popular revision +control system (RCS) [Git](https://git-scm.com/). + +Git was created to meet the needs of programmers working on the Linux operating +system. Other interfaces are available for it, but it primarily exists as a +collection of command-line utilities; this strongly informs its design. People +typically associate design with graphical and physical interfaces (e.g. web +pages and control panels), but good design helps everything. Command-line +arguments and prescribed sequences of separate commands are “design decisions”, +and poor decisions have made Git harder to use. + +In The Design of Everyday Things, Norman stresses the importance of conceptual +models. Norman defines a conceptual model as “an explanation, usually highly +simplified, of how something works.” A “highly simplified” conceptual model +isn’t *exactly right* but it’s good enough to get the job done. People don’t +need to know how the accelerator pedal of a car changes the flow of air and +fuel to the engine; it suffices to understand that pressing the pedal makes the +engine—and therefore the car—go faster. However, bad models cause problems, and +people who are new to Git are likely to have a poor conceptual model of the +program. + +Users who’ve switched to Git from another RCS (e.g., CVS or Subversion) are +accustomed to systems that use a central repository; the repository is “home” +to the code and programmers sync their work to it. In contrast, Git is designed +for decentralized work; each programmer has their own full repository and +merges their code with everybody else’s. While a conceptual model based on a +central repository is inappropriate for Git, users without previous RCS +experience are in even more trouble. Most [follow a sequence of commands +learned by rote](https://explainxkcd.com/wiki/index.php/1597:_Git) with little +intuition about how the system works. In the case of Git, bad mental models +cause users to make mistakes that they can’t fix (see [Oh Shit, +Git!](http://ohshitgit.com/) for common examples). + + + +In the open source community, the solution to bad mental models is tell users +that they need a better understanding of how the system works. When I shared my +frustrations with experienced Git users, they recommended that I read the free +online book [Pro Git](https://git-scm.com/book/en/v2) by Scott Chacon and Ben +Straub. The book did alleviate my frustrations, but I also spent a lot of time +reading about inner workings of Git that aren’t relevant to my work. It was +like learning how internal combustion engines work just to find out which pedal +makes a car go faster. + +The key to bringing good design to command-line programs lies in understanding +users’ mental models. Instead of expecting users to learn the details of how a +program works, developers should focus on helping them build a simple “good +enough” conceptual model. In their book, Chacon and Straub introduce excellent +metaphors for several concepts in Git, but follow these with details about the +system. Good introductory documentation would focus on these metaphors and save +the detail for users who need it; Git’s documentation is notoriously useless +for non-expert users (the [Git man page +generator](https://git-man-page-generator.lokaltog.net/) parodies the +experience of reading Git’s docs). + +Developers should also understand how people learn to use their systems. Norman +calls the signals that tell people how they can interact with things +“signifiers”. A command-line program will necessarily rely on textual +signifiers, and developers should focus on making them easy to find and +understand. For example, the “git-status” command does a good job of explaining +what actions users can perform on files in their working directory, but doesn’t +explain what these actions mean (and this is arguably the most user friendly of +Git’s commands). Git also uses many of the same commands as CVS and Subversion, +but from the perspective of the user they often serve different functions in +each system. We can consider a well-known command such as “checkout” to be a +signifier; it's bad design that it does something different in Git vs. +Subversion. + +Developers must understand that *any* interface they create for their program +is design work, and that good design will make their program easier to use. +Norman warns readers that “designers are not typical users”; developers should +take note. The time users spend learning the intricacies of a program would be +better spent using it. + diff --git a/content/posts/design-everyday-programs/xkcd_git.png b/content/posts/design-everyday-programs/xkcd_git.png Binary files differ. diff --git a/content/posts/headlamp-illusion/index.md b/content/posts/headlamp-illusion/index.md @@ -0,0 +1,69 @@ +--- +title: "Headlamp illusion" +description: A visual illusion for hikers at night. +date: 2015-11-25 +categories: +- Science +tags: +- Psychology +--- + +The shortening days and end of daylight saving time mean that I've been walking +a dog in the dark lately. I bought [a +headlamp](http://www.rei.com/product/875355/black-diamond-cosmo-headlamp) +because my neighborhood has no street lights and I wanted to keep a hand free +and find my way around. Since I'm not used to wearing one, I was surprised that +some textures had a "shimmering" appearance when illuminated by this lamp. + +After a few walks I noticed that this was limited to certain materials, such as +the dog's fur and the abundant pine needles, all of which are made up of fine +strands. I haven’t found a conclusive explanation for the effect yet. The +shimmering goes away when I close either eye, so I assume that the effect is +not caused by optics (e.g., this isn’t due to diffraction), and is also +binocular. + +We live in a 3D environment, and because of this a different image is captured +by each eye. Our brains are used to this, and in the phenomenon “stereopsis” +they take advantage of binocular disparity to make inferences about depth. When +different images are presented to each eye through contrived means, interesting +things can happen. Devices like the +[View-Master](https://en.wikipedia.org/wiki/View-Master) or [Oculus +Rift](https://www.oculus.com/) present different 2D images to each eye; when +the differences correspond to what’s seen when looking at a real scene, +stereopsis occurs and the brain constructs a 3D representation of a single +scene. + +<br> +*Cross your eyes and try to "fuse" these images to create a 3D percept* + +If the differences between the images are weird (in the sense that they aren’t +the result of depth) “[binocular +rivalry](https://en.wikipedia.org/wiki/Binocular_rivalry)” occurs. When +sufficiently different images are presented to each eye, our percept alternates +between what is shown to each. These perceptual fluctuations don’t occur at +once across the visual field; for large stimuli most observers report seeing +one image interspersed with unstable blobs of the other. In areas of different +luminance, the percept can appear to shimmer in effect called “binocular +luster”. Michael Scroggins has [a good blog +post](https://michaelscroggins.wordpress.com/explorations-in-stereoscopic-imaging/retinal-rivalry-and-luster/) +about rivalry that mentions luster and includes some demos. + +<br> +*Even if you cross your eyes, these won't fuse into a single percept* + +When you wear a headlamp at night, the world is illuminated by a light source +that’s roughly between your eyes. Based on shadows and specular highlights, +your visual cortex determines that your left eye is seeing a world illuminated +by a light to its right, while your right eye is seeing a world consistent with +a light to its left. This is an uncommon arrangement, so it’s possible that the +visual system has enough trouble for rivalry to occur. Most of what you see +with a headlamp remains consistent with a familiar 3D world, so stereopsis +still happens and you know what you’re looking at. I suspect that the +unfamiliar arrangement of shadow and specularity can sometimes induce binocular +luster. If binocular luster is responsible for this effect, it’s a rare example +of rivalry occurring under (relatively) natural viewing conditions. + +I did some searching and have yet to see another mention this phenomenon. Have +you experienced the “headlamp illusion”? I’m pretty sure that this is all in my +mind, but is mine the only one? + diff --git a/content/posts/headlamp-illusion/rivalry.png b/content/posts/headlamp-illusion/rivalry.png Binary files differ. diff --git a/content/posts/headlamp-illusion/stereo.png b/content/posts/headlamp-illusion/stereo.png Binary files differ. diff --git a/content/posts/indexing-matrices-r/index.Rmd b/content/posts/indexing-matrices-r/index.Rmd @@ -0,0 +1,98 @@ +--- +title: "Indexing matrix elements in R" +author: "Eamon Caddigan" +date: "2015-10-22" +output: html_document +layout: post +summary: Why I prefer zero-based numbering. +categories: R programming +--- + +```{r global_options, include=FALSE} +knitr::opts_chunk$set(cache=TRUE) +``` + +I came to science with a background in engineering, but most of my scientist friends didn’t. I often have a hard time articulating why I’m so annoyed by one-based indexing--which R and MATLAB use, but most other programming languages don’t. Here’s a recent example that might help. + +For a simulation I’m running, I use the values in several of the columns of a data frame as indexes into separate vectors. Here’s an example of using indexes in one vector (instead of a column from a `data.frame`) to access the elements in another: + +```{r} +valueVector <- c(2, 5, 8, 3, 0) +indexVector <- c(2, 3, 3, 1, 4, 5, 5) +valueVector[indexVector] +``` + +R veterans will point out that you can use factors for this, and that's definitely true here. However, when the values in the small vector are changing often but the indices are relatively stable, I prefer this approach. Either strategy works. + +Unfortunately, things aren't so easy when the data is in a matrix (a 2D vector) and you want to access its elements using two index vectors (i.e., one indexing the matrix’s rows, and the second indexing its columns). R’s default behavior might not be what you expect: + +```{r} +valueMatrix <- matrix(LETTERS[1:15], ncol = 3) +valueMatrix + +rowIndices <- c(4, 2, 2, 4, 4, 4) +colIndices <- c(2, 3, 3, 2, 3, 2) +valueMatrix[rowIndices, colIndices] +``` + +Instead of returning the six values associated with the six row/column pairs, it returns a 6 × 6 matrix with the elements of interest along the diagonal. When the number of elements is this small, it’s easy to wrap this in a call to `diag()`; that approach isn’t appropriate for long index vectors, since memory requirements are squared. + +Readers who’ve done data manipulation in C are probably familiar with pointer arithmetic. Zero-based numbering makes it easy to combine row and column indexes and make a one-dimensional array behave like a matrix: + +``` +/* When the code has to deal with matrices of varying size, you can’t allocate + an array right away. */ +double *valueMatrix; + +/* Stuff happened, and now you know how big your matrix will be (nrow x ncol), + so you allocate memory on the “heap” to store the data. */ +valueMatrix = (double *)malloc(sizeof(double) * nrow * ncol); + +/* This is how you’d access specific elements. */ +oldValueAtRowCol = valueMatrix[row + nrow*col]; +valueMatrix[row + nrow*col] = newValueAtRowCol; + +/* Can’t forget this when you’re done; I don’t miss C. */ +free(valueMatrix); +valueMatrix = 0; + +/* NB: All programs work this way, but most scripting languages take care of + this stuff for you. Progress! */ +``` + +To its credit, R makes this easy too; everything is stored as a one-dimensional vector behind the scenes, and can be accessed as such. R’s use of one-based indexing just makes it look a bit more awkward: + +```{r} +valueMatrix[rowIndices + nrow(valueMatrix) * (colIndices - 1)] +``` + +I hope this is useful for anybody who wants to access matrix elements using index vectors. More importantly, maybe some scientists-turned-programmers can gain a bit of insight into why zero-based numbering make sense to those of us who cut our teeth on C (or languages like it). + +*** + +### Update + +After I posted this, [Andrie de Vries](http://rfordummies.com/) sent [a tweet](https://twitter.com/RevoAndrie/status/657187336833388545) sharing an alternate syntax that's more R-like: + +```{r} +valueMatrix[cbind(rowIndices, colIndices)] +``` + +I definitely agree that it looks better, but there is a slight performance hit due to the call to `cbind()`. If you're repeatedly accessing a matrix with the same pair of indices, it might be worth it store the bound pair as a variable and reuse that. Here's the benchmark performance of each of the approaches I've discussed: + +```{r} +library("microbenchmark") + +rowIndices <- sample(1:5, 1e4, replace=TRUE) +colIndices <- sample(1:3, 1e4, replace=TRUE) +boundIndices <- cbind(rowIndices, colIndices) + +op <- microbenchmark(diag_matrix = diag(valueMatrix[rowIndices, colIndices]), + pointer_math = valueMatrix[rowIndices + nrow(valueMatrix) * (colIndices - 1)], + array_indexing = valueMatrix[cbind(rowIndices, colIndices)], + array_indexing_prebound = valueMatrix[boundIndices], + times = 100) +print(op) +``` + +Indexing with the pre-bound pair is fastest, using arithmetic on the indexes is a close second, and calling `cbind()` inside the brackets is in third place. Creating the n × n matrix and extracting its diagonal is excessively slow (and uses up a lot of RAM), so don't ever do that. diff --git a/content/posts/indexing-matrices-r/index.md b/content/posts/indexing-matrices-r/index.md @@ -0,0 +1,169 @@ +--- +title: "Indexing matrix elements in R" +date: "2015-10-22" +description: Why I prefer zero-based numbering. +categories: +- Programming +- Data Science +tags: +- R +--- + +I came to science with a background in engineering, but most of my scientist +friends didn’t. I often have a hard time articulating why I’m so annoyed by +one-based indexing--which R and MATLAB use, but most other programming +languages don’t. Here’s a recent example that might help. + +For a simulation I’m running, I use the values in several of the columns of a +data frame as indexes into separate vectors. Here’s an example of using indexes +in one vector (instead of a column from a `data.frame`) to access the elements +in another: + +```r +valueVector <- c(2, 5, 8, 3, 0) +indexVector <- c(2, 3, 3, 1, 4, 5, 5) +valueVector[indexVector] +``` +``` +## [1] 5 8 8 2 3 0 0 +``` + +R veterans will point out that you can use factors for this, and that's +definitely true here. However, when the values in the small vector are changing +often but the indices are relatively stable, I prefer this approach. Either +strategy works. + +Unfortunately, things aren't so easy when the data is in a matrix (a 2D vector) +and you want to access its elements using two index vectors (i.e., one indexing +the matrix’s rows, and the second indexing its columns). R’s default behavior +might not be what you expect: + +```r +valueMatrix <- matrix(LETTERS[1:15], ncol = 3) +valueMatrix +``` +``` +## [,1] [,2] [,3] +## [1,] "A" "F" "K" +## [2,] "B" "G" "L" +## [3,] "C" "H" "M" +## [4,] "D" "I" "N" +## [5,] "E" "J" "O" +``` + +```r +rowIndices <- c(4, 2, 2, 4, 4, 4) +colIndices <- c(2, 3, 3, 2, 3, 2) +valueMatrix[rowIndices, colIndices] +``` +``` +## [,1] [,2] [,3] [,4] [,5] [,6] +## [1,] "I" "N" "N" "I" "N" "I" +## [2,] "G" "L" "L" "G" "L" "G" +## [3,] "G" "L" "L" "G" "L" "G" +## [4,] "I" "N" "N" "I" "N" "I" +## [5,] "I" "N" "N" "I" "N" "I" +## [6,] "I" "N" "N" "I" "N" "I" +``` + +Instead of returning the six values associated with the six row/column pairs, +it returns a 6 × 6 matrix with the elements of interest along the diagonal. +When the number of elements is this small, it’s easy to wrap this in a call to +`diag()`; that approach isn’t appropriate for long index vectors, since memory +requirements are squared. + +Readers who’ve done data manipulation in C are probably familiar with pointer +arithmetic. Zero-based numbering makes it easy to combine row and column +indexes and make a one-dimensional array behave like a matrix: + +```c +/* When the code has to deal with matrices of varying size, you can’t allocate + an array right away. */ +double *valueMatrix; + +/* Stuff happened, and now you know how big your matrix will be (nrow x ncol), + so you allocate memory on the “heap” to store the data. */ +valueMatrix = (double *)malloc(sizeof(double) * nrow * ncol); + +/* This is how you’d access specific elements. */ +oldValueAtRowCol = valueMatrix[row + nrow*col]; +valueMatrix[row + nrow*col] = newValueAtRowCol; + +/* Can’t forget this when you’re done; I don’t miss C. */ +free(valueMatrix); +valueMatrix = 0; + +/* NB: All programs work this way, but most scripting languages take care of + this stuff for you. Progress! */ +``` + +To its credit, R makes this easy too; everything is stored as a one-dimensional +vector behind the scenes, and can be accessed as such. R’s use of one-based +indexing just makes it look a bit more awkward: + +```r +valueMatrix[rowIndices + nrow(valueMatrix) * (colIndices - 1)] +``` +``` +## [1] "I" "L" "L" "I" "N" "I" +``` + +I hope this is useful for anybody who wants to access matrix elements using +index vectors. More importantly, maybe some scientists-turned-programmers can +gain a bit of insight into why zero-based numbering make sense to those of us +who cut our teeth on C (or languages like it). + +--- + +### Update + +After I posted this, [Andrie de Vries](http://rfordummies.com/) sent [a +tweet](https://twitter.com/RevoAndrie/status/657187336833388545) sharing an +alternate syntax that's more R-like: + +```r +valueMatrix[cbind(rowIndices, colIndices)] +``` +``` +## [1] "I" "L" "L" "I" "N" "I" +``` + +I definitely agree that it looks better, but there is a slight performance hit +due to the call to `cbind()`. If you're repeatedly accessing a matrix with the +same pair of indices, it might be worth it store the bound pair as a variable +and reuse that. Here's the benchmark performance of each of the approaches I've +discussed: + + +```r +library("microbenchmark") + +rowIndices <- sample(1:5, 1e4, replace=TRUE) +colIndices <- sample(1:3, 1e4, replace=TRUE) +boundIndices <- cbind(rowIndices, colIndices) + +op <- microbenchmark(diag_matrix = diag(valueMatrix[rowIndices, colIndices]), + pointer_math = valueMatrix[rowIndices + nrow(valueMatrix) * (colIndices - 1)], + array_indexing = valueMatrix[cbind(rowIndices, colIndices)], + array_indexing_prebound = valueMatrix[boundIndices], + times = 100) +print(op) +``` +``` +## Unit: microseconds +## expr min lq mean median +## diag_matrix 1692950.428 1984553.2750 2024360.4989 2031899.941 +## pointer_math 243.356 251.9710 265.7848 260.419 +## array_indexing 332.864 352.2625 373.6505 367.539 +## array_indexing_prebound 149.192 154.6295 165.4170 160.201 +## uq max neval +## 2056263.5955 2201740.926 100 +## 272.5130 331.070 100 +## 387.1940 544.230 100 +## 170.5105 277.498 100 +``` + +Indexing with the pre-bound pair is fastest, using arithmetic on the indexes is +a close second, and calling `cbind()` inside the brackets is in third place. +Creating the n × n matrix and extracting its diagonal is excessively slow (and +uses up a lot of RAM), so don't ever do that. diff --git a/content/posts/instagram-sentiment/category_sentiment-1.png b/content/posts/instagram-sentiment/category_sentiment-1.png Binary files differ. diff --git a/content/posts/instagram-sentiment/cumulative_sentiment-1.png b/content/posts/instagram-sentiment/cumulative_sentiment-1.png Binary files differ. diff --git a/content/posts/instagram-sentiment/index.Rmd b/content/posts/instagram-sentiment/index.Rmd @@ -0,0 +1,421 @@ +--- +title: "Post types and sentiment from my Instagram feed" +description: "Does Instagram spark joy? A look at what I'm seeing and how I feel while using this platform." +date: 2022-07-13T12:28:22-04:00 +draft: False +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set( + echo = FALSE, + fig.path = file.path("figs", + sub("\\.Rmd$", "", + basename(rstudioapi::getActiveDocumentContext()$path)), + "") +) +knitr::opts_knit$set( + base.dir = file.path(Sys.getenv("HUGO_ROOT"), "static"), + base.url = "/" +) +``` +```{r packages, include=FALSE} +library(dplyr) +library(ggplot2) +library(forcats) +``` +```{r data} +ig_dat <- tibble::tribble( + ~date, ~medium, ~sentiment, ~poster_category, ~poster_followed, + "2022-07-09", "Video", 1L, "Business (Friend's)", TRUE, + "2022-07-09", "Photo", 2L, "Friend", TRUE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Image", 1L, "Meme account", TRUE, + "2022-07-09", "Photo", 2L, "Friend", TRUE, + "2022-07-09", "Video", -1L, "Suggested post", FALSE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Photo", 1L, "Friend", TRUE, + "2022-07-09", "Video", 0L, "Suggested post", FALSE, + "2022-07-09", "Video", 0L, "Meme account", TRUE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Video", -1L, "Suggested post", FALSE, + "2022-07-09", "Photo", 1L, "Meme account", TRUE, + "2022-07-09", "Video", 1L, "Suggested post", FALSE, + "2022-07-09", "Video", 0L, "Ad", FALSE, + "2022-07-09", "Video", 1L, "Business (Friend's)", TRUE, + "2022-07-09", "Video", 1L, "Suggested post", FALSE, + "2022-07-09", "Image", 1L, "Meme account", TRUE, + "2022-07-09", "Video", -1L, "Ad", FALSE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Image", 0L, "Meme account", TRUE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Photo", -2L, "Ad", FALSE, + "2022-07-09", "Photo", 2L, "Organization", TRUE, + "2022-07-09", "Video", -1L, "Suggested post", FALSE, + "2022-07-09", "Image", 1L, "Business (Friend's)", TRUE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Photo", 0L, "Artist", TRUE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Photo", 2L, "Friend", TRUE, + "2022-07-09", "Video", -1L, "Suggested post", FALSE, + "2022-07-09", "Image", 2L, "Artist", TRUE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Photo", 1L, "Organization", TRUE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Video", -1L, "Ad", FALSE, + "2022-07-09", "Photo", 1L, "Organization", TRUE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Image", 2L, "Artist", TRUE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Video", -1L, "Suggested post", FALSE, + "2022-07-09", "Photo", 0L, "Organization", TRUE, + "2022-07-09", "Video", -1L, "Suggested post", FALSE, + "2022-07-09", "Video", -2L, "Ad", FALSE, + "2022-07-09", "Photo", 2L, "Friend", TRUE, + "2022-07-09", "Video", -2L, "Suggested post", FALSE, + "2022-07-09", "Photo", 1L, "Meme account", TRUE, + "2022-07-10", "Image", 2L, "Artist", TRUE, + "2022-07-10", "Image", 0L, "Meme account", TRUE, + "2022-07-10", "Image", 1L, "Meme account", TRUE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Photo", 1L, "Friend", TRUE, + "2022-07-10", "Video", 1L, "Friend", TRUE, + "2022-07-10", "Video", 0L, "Suggested post", FALSE, + "2022-07-10", "Image", 0L, "Meme account", TRUE, + "2022-07-10", "Video", 1L, "Suggested post", FALSE, + "2022-07-10", "Image", 2L, "Friend", TRUE, + "2022-07-10", "Video", 0L, "Suggested post", FALSE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Photo", 1L, "Friend", TRUE, + "2022-07-10", "Video", -1L, "Suggested post", FALSE, + "2022-07-10", "Image", 1L, "Meme account", TRUE, + "2022-07-10", "Video", -1L, "Ad", FALSE, + "2022-07-10", "Video", -1L, "Suggested post", FALSE, + "2022-07-10", "Image", 1L, "Friend", TRUE, + "2022-07-10", "Video", 1L, "Suggested post", FALSE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Photo", 1L, "Organization", TRUE, + "2022-07-10", "Video", 0L, "Suggested post", FALSE, + "2022-07-10", "Photo", 0L, "Business (Friend's)", TRUE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Video", -2L, "Suggested post", FALSE, + "2022-07-10", "Photo", 1L, "Meme account", TRUE, + "2022-07-10", "Video", -2L, "Suggested post", FALSE, + "2022-07-10", "Image", -1L, "Ad", FALSE, + "2022-07-10", "Image", 1L, "Artist", TRUE, + "2022-07-10", "Video", 0L, "Suggested post", FALSE, + "2022-07-10", "Photo", 2L, "Friend", TRUE, + "2022-07-10", "Image", -1L, "Ad", FALSE, + "2022-07-10", "Video", 1L, "Suggested post", FALSE, + "2022-07-10", "Photo", 1L, "Organization", TRUE, + "2022-07-10", "Video", -2L, "Suggested post", FALSE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Video", -1L, "Organization", TRUE, + "2022-07-10", "Video", -2L, "Suggested post", FALSE, + "2022-07-10", "Photo", 2L, "Friend", TRUE, + "2022-07-10", "Video", -1L, "Ad", FALSE, + "2022-07-10", "Video", -1L, "Suggested post", FALSE, + "2022-07-10", "Image", 1L, "Artist", TRUE, + "2022-07-10", "Video", 1L, "Suggested post", FALSE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Video", 2L, "Friend", TRUE, + "2022-07-10", "Video", -1L, "Suggested post", FALSE, + "2022-07-10", "Video", 1L, "Friend", TRUE, + "2022-07-10", "Video", -2L, "Ad", FALSE, + "2022-07-10", "Video", -1L, "Suggested post", FALSE, + "2022-07-10", "Photo", 2L, "Friend", TRUE, + "2022-07-11", "Photo", 0L, "Friend", TRUE, + "2022-07-11", "Video", -1L, "Ad", FALSE, + "2022-07-11", "Video", 0L, "Business (Friend's)", TRUE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Video", 2L, "Artist", TRUE, + "2022-07-11", "Video", -1L, "Ad", FALSE, + "2022-07-11", "Photo", 0L, "Organization", TRUE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Photo", 1L, "Organization", TRUE, + "2022-07-11", "Photo", 2L, "Friend", TRUE, + "2022-07-11", "Video", -1L, "Suggested post", FALSE, + "2022-07-11", "Photo", 1L, "Friend", TRUE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Photo", 2L, "Organization", TRUE, + "2022-07-11", "Video", -2L, "Ad", FALSE, + "2022-07-11", "Video", -1L, "Suggested post", FALSE, + "2022-07-11", "Image", 2L, "Friend", TRUE, + "2022-07-11", "Image", 2L, "Artist", TRUE, + "2022-07-11", "Video", -2L, "Ad", FALSE, + "2022-07-11", "Video", 0L, "Suggested post", FALSE, + "2022-07-11", "Photo", 2L, "Friend", TRUE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Video", -2L, "Ad", FALSE, + "2022-07-11", "Photo", 0L, "Organization", TRUE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Image", 0L, "Artist", TRUE, + "2022-07-11", "Video", -1L, "Ad", FALSE, + "2022-07-11", "Video", -1L, "Suggested post", FALSE, + "2022-07-11", "Video", -1L, "Friend", TRUE, + "2022-07-11", "Video", -1L, "Suggested post", FALSE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Photo", 1L, "Meme account", TRUE, + "2022-07-11", "Video", -2L, "Suggested post", FALSE, + "2022-07-11", "Photo", 1L, "Friend", TRUE, + "2022-07-11", "Video", -1L, "Ad", FALSE, + "2022-07-11", "Video", -1L, "Suggested post", FALSE, + "2022-07-11", "Photo", 0L, "Organization", TRUE, + "2022-07-11", "Video", 0L, "Suggested post", FALSE, + "2022-07-11", "Video", 0L, "Ad", FALSE, + "2022-07-11", "Photo", 2L, "Friend", TRUE, + "2022-07-11", "Video", 0L, "Suggested post", FALSE, + "2022-07-11", "Photo", 0L, "Meme account", TRUE, + "2022-07-11", "Video", -1L, "Ad", FALSE, + "2022-07-11", "Video", 1L, "Suggested post", FALSE, + "2022-07-11", "Video", 0L, "Suggested post", FALSE, + "2022-07-11", "Image", 0L, "Friend", TRUE, + "2022-07-11", "Video", -1L, "Ad", FALSE, + "2022-07-11", "Video", 0L, "Suggested post", FALSE, + "2022-07-11", "Photo", 2L, "Friend", TRUE, + "2022-07-11", "Video", 0L, "Suggested post", FALSE, + "2022-07-12", "Photo", 2L, "Friend", TRUE, + "2022-07-12", "Photo", 1L, "Meme account", TRUE, + "2022-07-12", "Video", -1L, "Ad", FALSE, + "2022-07-12", "Video", -1L, "Suggested post", FALSE, + "2022-07-12", "Photo", 0L, "Friend", TRUE, + "2022-07-12", "Photo", 1L, "Friend", TRUE, + "2022-07-12", "Image", 0L, "Meme account", TRUE, + "2022-07-12", "Photo", 0L, "Ad", FALSE, + "2022-07-12", "Image", 0L, "Suggested post", FALSE, + "2022-07-12", "Photo", 2L, "Friend", TRUE, + "2022-07-12", "Video", 1L, "Suggested post", FALSE, + "2022-07-12", "Video", -2L, "Ad", FALSE, + "2022-07-12", "Photo", 2L, "Friend", TRUE, + "2022-07-12", "Video", 0L, "Suggested post", FALSE, + "2022-07-12", "Image", 1L, "Organization", TRUE, + "2022-07-12", "Video", -1L, "Ad", FALSE, + "2022-07-12", "Video", -1L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Friend", TRUE, + "2022-07-12", "Video", 0L, "Suggested post", FALSE, + "2022-07-12", "Image", -1L, "Ad", FALSE, + "2022-07-12", "Image", 0L, "Business (Friend's)", TRUE, + "2022-07-12", "Video", -1L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Meme account", TRUE, + "2022-07-12", "Video", 0L, "Ad", FALSE, + "2022-07-12", "Image", 0L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Meme account", TRUE, + "2022-07-12", "Video", 0L, "Suggested post", FALSE, + "2022-07-12", "Video", -2L, "Ad", FALSE, + "2022-07-12", "Image", 0L, "Organization", TRUE, + "2022-07-12", "Video", 0L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Friend", TRUE, + "2022-07-12", "Video", -1L, "Suggested post", FALSE, + "2022-07-12", "Video", -2L, "Ad", FALSE, + "2022-07-12", "Photo", 1L, "Meme account", TRUE, + "2022-07-12", "Video", -1L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Organization", TRUE, + "2022-07-12", "Image", -2L, "Ad", FALSE, + "2022-07-12", "Video", -1L, "Suggested post", FALSE, + "2022-07-12", "Photo", 0L, "Artist", TRUE, + "2022-07-12", "Video", 0L, "Suggested post", FALSE, + "2022-07-12", "Video", 1L, "Ad", FALSE, + "2022-07-12", "Image", 2L, "Artist", TRUE, + "2022-07-12", "Video", -2L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Friend", TRUE, + "2022-07-12", "Video", -2L, "Ad", FALSE, + "2022-07-12", "Image", 0L, "Suggested post", FALSE, + "2022-07-12", "Photo", 1L, "Friend", TRUE, + "2022-07-12", "Video", 1L, "Suggested post", FALSE, + "2022-07-12", "Photo", 0L, "Business (Friend's)", TRUE, + "2022-07-12", "Video", -2L, "Ad", FALSE + ) %>% + mutate(poster_category = sub(" \\(Friend's\\)", "", poster_category)) +``` + +I've been critical of social media platforms (in spite of my continued use of them), but I've traditionally defended Instagram. I knew that it had major problems (most galling, [internal research showed that use of the platform was hurting teenage girls' body image, and Meta suppressed the findings](https://www.wsj.com/articles/facebook-knows-instagram-is-toxic-for-teen-girls-company-documents-show-11631620739?mod=article_inline)), but browsing IG has nevertheless been a pleasant experience for me. Photos of my friends' pets, children, and vacations are _nice things_, and being exposed to them _made me happy_. + +Recently, Instagram instituted changes to the app's main feed, which were [announed by Adam Mosseri, the head of Instagram, on Twitter](https://twitter.com/mosseri/status/1521589403671355392). I feel like Instagram stopped being as fun for me shortly after these changes were rolled out, so I collected a bit of data. + +## Method + +Over the course of four days (July 9–12, 2022), I only opened the app once per day, on my phone. I looked at the first 50 posts on my feed, and logged a couple features, described below, about each one. I also gave each post a subjective "sentiment score" using a five-point scale from -2 (for posts I actively disliked) to 2 (for posts I quite liked), with a score of 0 being neutral. + +## Results + +What does Instagram show me? Let's first look at "poster category" counts, which shows who the posts come from. + +```{r poster_category, fig.height=4, fig.width=7} +caption_text <- "Data from 200 posts viewed over 4 days (50 posts/day)" + +ig_dat %>% + mutate(poster_category = fct_rev(fct_infreq(poster_category))) %>% + ggplot(aes(x = poster_category)) + + geom_bar(aes(fill = !poster_followed)) + + geom_text(aes(label = ..count..), stat = "count", + hjust = 0, nudge_y = 1, size = 6) + + scale_fill_brewer(palette = "Dark2") + + expand_limits(y = 75) + + coord_flip() + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + plot.title.position = "plot", + plot.caption.position = "plot", + legend.position = "none", + axis.line = element_blank(), + axis.ticks = element_blank(), + axis.title = element_blank(), + axis.text.x = element_blank(), + axis.text.y = element_text(size = 16, + margin = margin(r = -16))) + + labs(title = "Poster categories in my Instagram feed", + caption = caption_text) +``` + +Most of the 410 accounts I follow are my friends'. I also follow a few _artists_ (a combination of musicians, visual artists, and authors), _organizations_ (primarily political and community orgs), _businesses_ (all of which are run by friends—a couple bakers, a couple shop owners), and a small handful of _meme accounts_ (e.g., "dnddads"). Subjectively, meme accounts are over-represented on my feed; I follow hundreds of actual people and only around five meme accounts, but the latter account for over half as many posts as the former. + +The biggest issue here is that the majority of posts come from _accounts I don't follow_. I understand that Instagram is an ad-supported business, but I see more ads than posts from friends. Worse still, I see almost twice as many "suggested posts" as I do posts from friends. + +What types of content are represented by these posts? + +```{r medium, fig.height=3, fig.width=7} +ig_dat %>% + mutate(medium = fct_rev(fct_infreq(medium))) %>% + ggplot(aes(x = medium)) + + geom_bar(aes(fill = medium)) + + geom_text(aes(label = ..count..), stat = "count", + hjust = 0, nudge_y = 1, size = 6) + + scale_fill_brewer(palette = "Paired") + + expand_limits(y = 120) + + coord_flip() + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + plot.title.position = "plot", + plot.caption.position = "plot", + legend.position = "none", + axis.line = element_blank(), + axis.ticks = element_blank(), + axis.title = element_blank(), + axis.text.x = element_blank(), + axis.text.y = element_text(size = 20, + margin = margin(r = -20))) + + labs(title = "Media present in my Instagram feed", + caption = caption_text) +``` + +Mosseri announced that Meta wanted to make video a bigger part of the Instagram experience, and they seem to have delivered. Of the 200 posts I logged, the majority were video. Photographs, which the app was originally designed for, account for a little over a quarter of the posts, with other types of image (drawings, illustrations, etc.) accounting for the rest. + +What's the relationship between _poster category_ and _post medium_? + +```{r poster_media, fig.height=4} +ig_dat %>% + mutate(poster_category = fct_rev(fct_infreq(poster_category))) %>% + ggplot(aes(x = poster_category)) + + geom_bar(aes(fill = medium)) + + geom_text(aes(label = ..count..), stat = "count", + hjust = 0, nudge_y = 1, size = 6) + + scale_fill_brewer(palette = "Paired") + + expand_limits(y = 75) + + coord_flip() + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + plot.title.position = "plot", + plot.caption.position = "plot", + legend.title = element_text(size = 12), + legend.text = element_text(size = 12), + legend.position = c(0.8, 0.2), + axis.line = element_blank(), + axis.ticks = element_blank(), + axis.title = element_blank(), + axis.text.x = element_blank(), + axis.text.y = element_text(size = 16, + margin = margin(r = -16))) + + labs(title = "Post medium and poster category in my Instagram feed", + caption = caption_text, + fill = "Post medium") +``` + +There's a tight correspondence between what medium is employed for a post and who's posting it. Videos are being pushed by accounts I don't follow, while my friends continue to prioritize photographs. + +Since post medium and poster category are so tightly linked, I'll focus on looking at the sentiment by poster category—it would be difficult to tease apart how I feel about photos vs. videos and how I feel about posts from accounts I do vs. do not follow. + +```{r category_sentiment} +ig_dat %>% + mutate(poster_category = fct_rev(fct_infreq(poster_category))) %>% + ggplot(aes(poster_category, sentiment)) + + geom_boxplot(aes(fill = !poster_followed)) + + scale_fill_brewer(palette = "Dark2") + + coord_flip() + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + plot.title.position = "plot", + plot.caption.position = "plot", + legend.position = "none", + axis.line = element_blank(), + axis.ticks = element_blank(), + axis.title.x = element_text(size = 16), + axis.title.y = element_blank(), + axis.text.x = element_text(size = 12), + axis.text.y = element_text(size = 16, + margin = margin(r = -16))) + + labs(title = "Instagram sentiment by poster category", + caption = caption_text, + y = "Subjective sentiment") +``` + +These box-and-whisker plots show the distribution of sentiment scores for each post category. The heavy vertical line indicates the median score, and the boxes extend from the first through third quartiles (the "interquartile range", or IQR). The "whiskers" cover the full range of scores, unless any observation is identified as a potential "outlier". Outliers are defined as observations with values more than 150% of the value of the IQR above or below the third or first quartile, respectively. For example, I was bothered by a photo of a dead bird which was posted by a friend, and gave it a score of -1. The first and third quartiles of sentiment scores for posts from friends are 1 and 2, providing an IQR of 1. Since -1 is less than 1 (the first quartile) - 1.5 (150% of 1, the IQR), that score is an outlier. + +I'm not surprised that I like posts from the accounts I follow more than those from accounts I don't. It's disappointing that suggested posts aren't much nicer to see than ads; these are supposed to make the platorm more "immersive" and "engaging" and fail to achieve that. + +In an attempt to quantify the "experience" of browsing Instagram, I looked at the cumulative sentiment scores across each of the four days. There's no doubt that the actual dynamics of my affect, to the extent that it can even be quantified, is more complicated than +2 + -2 = 0. However, this is a good first approximation of what it feels like to scroll through a feed. + +```{r cumulative_sentiment} +ig_sentiment <- ig_dat %>% + group_by(date) %>% + mutate(seq = row_number(date), + cum_sent = cumsum(sentiment)) + +ig_sentiment %>% + ggplot(aes(seq, cum_sent)) + + geom_hline(yintercept = 0, linetype = "dashed") + + geom_step(aes(color = date), size = 1) + + geom_text(aes(label = cum_sent), data = filter(ig_sentiment, seq == 50), + hjust = 0, nudge_x = 0.5, size = 5) + + scale_color_brewer(palette = "Set2") + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + plot.title.position = "plot", + plot.caption.position = "plot", + legend.title = element_text(size = 12), + legend.text = element_text(size = 12), + legend.position = "none", + axis.line.y = element_blank(), + axis.ticks.y = element_blank(), + axis.title = element_blank(), + #axis.text.x = element_blank(), + axis.text.y = element_blank()) + + labs(title = "Cumulative sentiment while browsing Instagram", + caption = caption_text) +``` + +Each of the four days has a negative cumulative sentiment score, which indicates that I see more posts that I dislike than posts that I like. There's also a suggestion of a pattern, in which my sentiment stays relatively flat and positive over the first 20–30 posts, and then drops. + +I wonder if this is the result of an intentional design decision by Instagram. If they have an internal model of what posts I might like, they could certainly time them in such a way to encourage longer stretches of engagement, and they have the data to figure out what the optimal timing would look like. On the other hand, this is a purely subjective score that I didn't attempt to carefully calibrate, so it's worth considering that I might just get tired of my feed after a couple dozen posts. + +## Conclusions + +I don't know if it's worth an attempt to use my experience to formulate suggestions to Instagram (or their would-be competitors). I'm approaching middle age, and I don't spend much money on the internet; Instagram can get stronger engagement and much better ad conversion rates from people who aren't like me. Perhaps I'm an unprofitable user and this is their attempt to nudge me off the platform? + +However, this has been a useful exercise for me, because it suggests a few things I could change right now to improve my experience: + +* Stop following meme accounts and organizations (these posts provide a neutral-to-good experience, but they potentially crowd out posts from friends and artists that I would enjoy more) +* Stop scrolling my feed after the first 20 or so posts (cumulative sentiment appears to begin dropping after this point) + +Most importantly, it calls into question whether I should even continue using the platform at all. The maximum cumulative sentiment that I experienced was only six (which corresponds to seeing just three things that I really like), and that was only achieved on two of the four days that I measured this. As much as I enjoy seeing photos from my friends (and the data show that I really do enjoy this), it's hard to conclude that the experience of using Instagram is joyful. +\ No newline at end of file diff --git a/content/posts/instagram-sentiment/index.md b/content/posts/instagram-sentiment/index.md @@ -0,0 +1,161 @@ +--- +title: "Post types and sentiment from my Instagram feed" +description: "Does Instagram spark joy? A look at what I'm seeing and how I feel while using this platform." +date: 2022-07-13T12:28:22-04:00 +draft: False +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +categories: +- Data Science +- Science +tags: +- Psychology +--- + +I've been critical of social media platforms (in spite of my continued +use of them), but I've traditionally defended Instagram. I knew that it +had major problems (most galling, [internal research showed that use of +the platform was hurting teenage girls' body image, and Meta suppressed +the +findings](https://www.wsj.com/articles/facebook-knows-instagram-is-toxic-for-teen-girls-company-documents-show-11631620739?mod=article_inline)), +but browsing IG has nevertheless been a pleasant experience for me. +Photos of my friends' pets, children, and vacations are *nice things*, +and being exposed to them *made me happy*. + +Recently, Instagram instituted changes to the app's main feed, which +were [announced by Adam Mosseri, the head of Instagram, on +Twitter](https://twitter.com/mosseri/status/1521589403671355392). I feel +like Instagram stopped being as fun for me shortly after these changes +were rolled out, so I collected a bit of data. + +## Method + +Over the course of four days (July 9--12, 2022), I only opened the app +once per day, on my phone. I looked at the first 50 posts on my feed, +and logged a couple features, described below, about each one. I also +gave each post a subjective "sentiment score" using a five-point scale +from -2 (for posts I actively disliked) to 2 (for posts I quite liked), +with a score of 0 being neutral. + +## Results + +What does Instagram show me? Let's first look at "poster category" +counts, which shows who the posts come from. + + + +Most of the 410 accounts I follow are my friends'. I also follow a few +*artists* (a combination of musicians, visual artists, and authors), +*organizations* (primarily political and community orgs), *businesses* +(all of which are run by friends---a couple bakers, a couple shop +owners), and a small handful of *meme accounts* (e.g., "dnddads"). +Subjectively, meme accounts are over-represented on my feed; I follow +hundreds of actual people and only around five meme accounts, but the +latter account for over half as many posts as the former. + +The biggest issue here is that the majority of posts come from *accounts +I don't follow*. I understand that Instagram is an ad-supported +business, but I see more ads than posts from friends. Worse still, I see +almost twice as many "suggested posts" as I do posts from friends. + +What types of content are represented by these posts? + + + +Mosseri announced that Meta wanted to make video a bigger part of the +Instagram experience, and they seem to have delivered. Of the 200 posts +I logged, the majority were video. Photographs, which the app was +originally designed for, account for a little over a quarter of the +posts, with other types of image (drawings, illustrations, etc.) +accounting for the rest. + +What's the relationship between *poster category* and *post medium*? + + + +There's a tight correspondence between what medium is employed for a +post and who's posting it. Videos are being pushed by accounts I don't +follow, while my friends continue to prioritize photographs. + +Since post medium and poster category are so tightly linked, I'll focus +on looking at the sentiment by poster category---it would be difficult +to tease apart how I feel about photos vs. videos and how I feel about +posts from accounts I do vs. do not follow. + + + +These box-and-whisker plots show the distribution of sentiment scores +for each post category. The heavy vertical line indicates the median +score, and the boxes extend from the first through third quartiles (the +"interquartile range", or IQR). The "whiskers" cover the full range of +scores, unless any observation is identified as a potential "outlier". +Outliers are defined as observations with values more than 150% of the +value of the IQR above or below the third or first quartile, +respectively. For example, I was bothered by a photo of a dead bird +which was posted by a friend, and gave it a score of -1. The first and +third quartiles of sentiment scores for posts from friends are 1 and 2, +providing an IQR of 1. Since -1 is less than 1 (the first quartile) - +1.5 (150% of 1, the IQR), that score is an outlier. + +I'm not surprised that I like posts from the accounts I follow more than +those from accounts I don't. It's disappointing that suggested posts +aren't much nicer to see than ads; these are supposed to make the +platform more "immersive" and "engaging" and fail to achieve that. + +In an attempt to quantify the "experience" of browsing Instagram, I +looked at the cumulative sentiment scores across each of the four days. +There's no doubt that the actual dynamics of my affect, to the extent +that it can even be quantified, is more complicated than +2 + -2 = 0. +However, this is a good first approximation of what it feels like to +scroll through a feed. + + + +Each of the four days has a negative cumulative sentiment score, which +indicates that I see more posts that I dislike than posts that I like. +There's also a suggestion of a pattern, in which my sentiment stays +relatively flat and positive over the first 20--30 posts, and then +drops. + +I wonder if this is the result of an intentional design decision by +Instagram. If they have an internal model of what posts I might like, +they could certainly time them in such a way to encourage longer +stretches of engagement, and they have the data to figure out what the +optimal timing would look like. On the other hand, this is a purely +subjective score that I didn't attempt to carefully calibrate, so it's +worth considering that I might just get tired of my feed after a couple +dozen posts. + +## Conclusions + +I don't know if it's worth an attempt to use my experience to formulate +suggestions to Instagram (or their would-be competitors). I'm +approaching middle age, and I don't spend much money on the internet; +Instagram can get stronger engagement and much better ad conversion +rates from people who aren't like me. Perhaps I'm an unprofitable user +and this is their attempt to nudge me off the platform? + +However, this has been a useful exercise for me, because it suggests a +few things I could change right now to improve my experience: + +- Stop following meme accounts and organizations (these posts provide + a neutral-to-good experience, but they potentially crowd out posts + from friends and artists that I would enjoy more) +- Stop scrolling my feed after the first 20 or so posts (cumulative + sentiment appears to begin dropping after this point) + +Most importantly, it calls into question whether I should even continue +using the platform at all. The maximum cumulative sentiment that I +experienced was only six (which corresponds to seeing just three things +that I really like), and that was only achieved on two of the four days +that I measured this. As much as I enjoy seeing photos from my friends +(and the data show that I really do enjoy this), it's hard to conclude +that the experience of using Instagram is joyful. diff --git a/content/posts/instagram-sentiment/medium-1.png b/content/posts/instagram-sentiment/medium-1.png Binary files differ. diff --git a/content/posts/instagram-sentiment/poster_category-1.png b/content/posts/instagram-sentiment/poster_category-1.png Binary files differ. diff --git a/content/posts/instagram-sentiment/poster_media-1.png b/content/posts/instagram-sentiment/poster_media-1.png Binary files differ. diff --git a/content/posts/labeling-ggplots/better_plot-1.png b/content/posts/labeling-ggplots/better_plot-1.png Binary files differ. diff --git a/content/posts/labeling-ggplots/ecdf-1.png b/content/posts/labeling-ggplots/ecdf-1.png Binary files differ. diff --git a/content/posts/labeling-ggplots/index.Rmd b/content/posts/labeling-ggplots/index.Rmd @@ -0,0 +1,92 @@ +--- +title: "Labeling bar charts (and other graphics) in ggplot2" +description: "How to combine stats and geoms to simplify complex plots." +date: 2022-07-08T19:32:57-04:00 +draft: False +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set( + echo = TRUE, + fig.path = file.path("figs", + sub("\\.Rmd$", "", + basename(rstudioapi::getActiveDocumentContext()$path)), + "") +) +knitr::opts_knit$set( + base.dir = file.path(Sys.getenv("HUGO_ROOT"), "static"), + base.url = "/" +) +``` + +Bar charts are [rightfully criticized for being potentially misleading](https://www.kickstarter.com/projects/1474588473/barbarplots), but they're still useful for some data graphics. They're a great way to display counts, for example, and non-technical audiences are comfortable interpreting them. + +One way that a typical bar plot can be improved is by removing unnecessary axis labels and directly labeling the bars themselves. For example, if we wanted to see how many counties are in some of the states comprising the Midwestern US, we could use the `midwest` data set that's packaged with ggplot2 and draw a simple bar plot. + +```{r simple_bar} +library(ggplot2) + +ggplot(midwest, aes(x = state)) + + geom_bar() + + labs(x = "", y = "Number of counties") + + theme_minimal() + + theme(axis.text.x = element_text(size = 16), + axis.title.y = element_text(size = 14)) +``` + +This is fine (provided that you can accept that Ohio is part of the Midwest and Iowa isn't). However, we can easily strip away some of the "chart junk" by removing unnecessary theme elements and labeling the bars using `geom_text`. + +```{r better_plot} +ggplot(midwest, aes(state)) + + geom_bar() + + geom_text(aes(y = ..count.., label = ..count..), stat = "count", + vjust = 0, nudge_y = 2, size = 8) + + expand_limits(y = 110) + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + axis.line = element_blank(), + axis.ticks = element_blank(), + axis.title = element_blank(), + axis.text.y = element_blank(), + axis.text.x = element_text(size = 16)) + + labs(title = "Number of counties in Midwestern states") +``` + +There's still room for improvement—I'd consider rearranging the bars based on something more meaningful than alphabetic order, and possibly coloring them—but this simultaneously conveys more information than the previous plot (objectively) and is less "cluttered" (subjectively). + +## How this works + +I'm surprised I'm still writing blog posts about ggplot2 after seven years, but I continue to learn new things about it even after regular use. Recently, I decided that it bothered me that there were "stats" (like `stat_ecdf`) and "geoms" (like `geom_bar`), and I really didn't understand the difference between them—they seemed interchange but not identical. I finally looked into it and came across [this response on StackOverflow](https://stackoverflow.com/a/44226841), which contained the following quote from the [ggplot2 book](https://ggplot2-book.org/): + +> You only need to set one of stat and geom: every geom has a default stat, and every stat has a default geom. + +It turns out that "stats" and "geoms" _are_ largely interchangeable, because they're both wrappers around `layer()`, with different ways of handling defaults. The code above works because I changed the `stat` parameter of `geom_text` (which, according to [the documentation](https://ggplot2.tidyverse.org/reference/geom_text.html), defaults to `"identity"`) to `"count"`, which is the default `stat` of `geom_bar`. Looking at [the documentation for `stat_count`](https://ggplot2.tidyverse.org/reference/geom_bar.html), we see that it provides two _computed variables_, and we use use the computed `count` variable in our aesthetics for `geom_text` to provide both the vertical position and label. + +Getting my head around this has helped me iterate through analyses more quickly. For instance, I frequently use `stat_ecdf` to get a handle on distributions, and now I can label these plots easily. Sticking with data about the Midwest, here's the ECDF of population density for Midwestern counties, with a few values highlighted. + +```{r ecdf} +ggplot(midwest, aes(popdensity)) + + stat_ecdf() + # This could also be `geom_step(stat = "ecdf")` + geom_text(aes(label = sprintf("(%.0f: %.0f%%)", ..x.., floor(100 * ..y..))), + stat = "ecdf", hjust = 1, vjust = 0, check_overlap = TRUE, size = 5) + + expand_limits(x = -15000) + + scale_y_continuous(labels = scales::label_percent()) + + theme_minimal() + + labs(x = "Population density", y = "CDF") +``` + +I wouldn't call this a _beautiful_ graphic, but visualizations like this are often _useful_, especially when getting a handle on a new data set. Here we see that over a third of Midwestern counties have population densities fully two orders of magnitude smaller than the most densely populated county, and we've only had to draw a single plot. + +It's hard to justify putting much effort into producing plots that aren't meant to be shared, and a typical data analysis will involve creating dozens of plots that are only useful for the person analyzing the data. Without understanding stats and geoms, I would never have bothered labeling an ECDF plot; "quick and dirty" needs to be quick after all. On the other hand, labeling the values in a bar chart is something that one should do when preparing publication-quality graphics. ggplot2 is useful in both phases of a project. + +In the words of Alan Kay, ["simple things should be simple, complex things should be possible."](https://www.quora.com/What-is-the-story-behind-Alan-Kay-s-adage-Simple-things-should-be-simple-complex-things-should-be-possible) ggplot2 does both of these consistently. Occasionally, it even makes complex things simple. +\ No newline at end of file diff --git a/content/posts/labeling-ggplots/index.md b/content/posts/labeling-ggplots/index.md @@ -0,0 +1,141 @@ +--- +title: "Labeling bar charts (and other graphics) in ggplot2" +description: "How to combine stats and geoms to simplify complex plots." +date: 2022-07-08T19:32:57-04:00 +draft: False +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +categories: +- Data Science +tags: +- R +- Dataviz +--- + +Bar charts are [rightfully criticized for being potentially +misleading](https://www.kickstarter.com/projects/1474588473/barbarplots), +but they're still useful for some data graphics. They're a great way to +display counts, for example, and non-technical audiences are comfortable +interpreting them. + +One way that a typical bar plot can be improved is by removing +unnecessary axis labels and directly labeling the bars themselves. For +example, if we wanted to see how many counties are in some of the states +comprising the Midwestern US, we could use the `midwest` data set that's +packaged with ggplot2 and draw a simple bar plot. + +``` r +library(ggplot2) + +ggplot(midwest, aes(x = state)) + + geom_bar() + + labs(x = "", y = "Number of counties") + + theme_minimal() + + theme(axis.text.x = element_text(size = 16), + axis.title.y = element_text(size = 14)) +``` + + + +This is fine (provided that you can accept that Ohio is part of the +Midwest and Iowa isn't). However, we can easily strip away some of the +"chart junk" by removing unnecessary theme elements and labeling the +bars using `geom_text`. + +``` r +ggplot(midwest, aes(state)) + + geom_bar() + + geom_text(aes(y = ..count.., label = ..count..), stat = "count", + vjust = 0, nudge_y = 2, size = 8) + + expand_limits(y = 110) + + theme(panel.background = element_blank(), + panel.grid = element_blank(), + axis.line = element_blank(), + axis.ticks = element_blank(), + axis.title = element_blank(), + axis.text.y = element_blank(), + axis.text.x = element_text(size = 16)) + + labs(title = "Number of counties in Midwestern states") +``` + + + +There's still room for improvement---I'd consider rearranging the bars +based on something more meaningful than alphabetic order, and possibly +coloring them---but this simultaneously conveys more information than +the previous plot (objectively) and is less "cluttered" (subjectively). + +## How this works + +I'm surprised I'm still writing blog posts about ggplot2 after seven +years, but I continue to learn new things about it even after regular +use. Recently, I decided that it bothered me that there were "stats" +(like `stat_ecdf`) and "geoms" (like `geom_bar`), and I really didn't +understand the difference between them---they seemed interchange but not +identical. I finally looked into it and came across [this response on +StackOverflow](https://stackoverflow.com/a/44226841), which contained +the following quote from the [ggplot2 book](https://ggplot2-book.org/): + +> You only need to set one of stat and geom: every geom has a default +> stat, and every stat has a default geom. + +It turns out that "stats" and "geoms" *are* largely interchangeable, +because they're both wrappers around `layer()`, with different ways of +handling defaults. The code above works because I changed the `stat` +parameter of `geom_text` (which, according to [the +documentation](https://ggplot2.tidyverse.org/reference/geom_text.html), +defaults to `"identity"`) to `"count"`, which is the default `stat` of +`geom_bar`. Looking at [the documentation for +`stat_count`](https://ggplot2.tidyverse.org/reference/geom_bar.html), we +see that it provides two *computed variables*, and we use use the +computed `count` variable in our aesthetics for `geom_text` to provide +both the vertical position and label. + +Getting my head around this has helped me iterate through analyses more +quickly. For instance, I frequently use `stat_ecdf` to get a handle on +distributions, and now I can label these plots easily. Sticking with +data about the Midwest, here's the ECDF of population density for +Midwestern counties, with a few values highlighted. + +``` r +ggplot(midwest, aes(popdensity)) + + stat_ecdf() + # This could also be `geom_step(stat = "ecdf")` + geom_text(aes(label = sprintf("(%.0f: %.0f%%)", ..x.., floor(100 * ..y..))), + stat = "ecdf", hjust = 1, vjust = 0, check_overlap = TRUE, size = 5) + + expand_limits(x = -15000) + + scale_y_continuous(labels = scales::label_percent()) + + theme_minimal() + + labs(x = "Population density", y = "CDF") +``` + + + +I wouldn't call this a *beautiful* graphic, but visualizations like this are +often *useful*, [especially when getting a handle on a new data set]({{< ref +"/posts/tufte-plot/index.md" >}}). Here we see that over a third of +Midwestern counties have population densities fully two orders of magnitude +smaller than the most densely populated county, and we've only had to draw a +single plot. + +It's hard to justify putting much effort into producing plots that +aren't meant to be shared, and a typical data analysis will involve +creating dozens of plots that are only useful for the person analyzing +the data. Without understanding stats and geoms, I would never have +bothered labeling an ECDF plot; "quick and dirty" needs to be quick +after all. On the other hand, labeling the values in a bar chart is +something that one should do when preparing publication-quality +graphics. GGplot2 is useful in both phases of a project. + +In the words of Alan Kay, ["simple things should be simple, complex +things should be +possible."](https://www.quora.com/What-is-the-story-behind-Alan-Kay-s-adage-Simple-things-should-be-simple-complex-things-should-be-possible) +GGplot2 does both of these consistently. Occasionally, it even makes +complex things simple. diff --git a/content/posts/labeling-ggplots/simple_bar-1.png b/content/posts/labeling-ggplots/simple_bar-1.png Binary files differ. diff --git a/content/posts/reproducible-research/index.md b/content/posts/reproducible-research/index.md @@ -0,0 +1,104 @@ +--- +title: "Reproducible research fail" +description: One of the mistakes I made in data collection. +date: 2015-10-01 +categories: +- Data Science +- Science +tags: +- Psychology +--- + +In most of the psychology subdisciplines under the umbrella of “cognitive +psychology” (e.g., language, memory, perception, etc.), researchers use +programs to collect data from participants (c.f. social psychology, which often +uses surveys instead). These are usually simple programs that display words or +pictures and record responses; if you’ve ever taken an introductory psychology +course, you were surely made to sit through a few of these. Although there are +a few tools that allow psychologists to create experiments without writing +their own code, most of us (at least in the departments with which I’ve been +affiliated) program their own studies. + +The majority of psych grad students start their Ph.D.s with little programming +experience, so it’s not surprising that coding errors sometimes affect +research. As a first year grad student who’d previously worked as a programmer, +I was determined to do better. Naturally, I made a ton of mistakes, and I want +to talk about one of them: a five-year-old mistake I’m dealing with *today*. + +Like many mistakes, I made this one while trying to avoid another. I noticed +that it was common for experiments to fail to record details about trials which +later turned out to be important. For instance, a researcher could run a +[visual search](http://www.scholarpedia.org/article/Visual_search) experiment +and not save the locations and identities of the randomly-selected +“distractors”, but later be unable to see if there was an effect of +[crowding](http://www.scholarpedia.org/article/Visual_search#Spatial_layout.2C_density.2C_crowding). +It was fairly common to fail to record response times while looking for an +effect on task accuracy, but then be unable to show that the observed effect +was not due to a speed-accuracy tradeoff. + +I decided that I’d definitely record everything. This wasn’t itself a mistake. + +Since I program my experiments in Python and using an object-oriented design -- +all of the data necessary to display a trial was encapsulated in instances of +the Trial class -- I decided that the best way to save *everything* was to +serialize these objects using Python’s pickle module. This way, if I added +additional members to Trial, I didn’t have to remember to explicitly include +them in the experiment’s output. I also smugly knew that I didn’t have to worry +about rounding errors since everything was stored in machine precision (because +*that* matters). + +That’s not quite where I went wrong. + +The big mistake was using this approach but failing to follow best practices +for reproducible research. It’s now incredibly difficult to unpickle the data +from my studies because the half dozen modules necessary to run my code have +all been updated since I wrote these programs. I didn’t even record the version +numbers of anything. I’ve had to write a bunch of hacks and manually install a +few old modules just to get my data back. + +Today it’s a lot easier to do things the right way. If you’re programming in +Python, you can use the [Anaconda +distribution](https://www.continuum.io/why-anaconda) to create environments +that keep their own copies of your code’s dependencies. These won’t get updated +with the rest of the system, so you should be able to go back and run things +later. A language-agnostic approach could utilize [Docker +images](https://www.docker.com/), or go a step further and run each experiment +in its own virtual machine (although care should be taken to ensure adequate +system performance). + +I do feel like I took things too far by pickling my Python objects. Even if I +had used anaconda, I’d have been committing myself to either performing all my +analyses in Python, or performing the intermediate step of writing a script to +export my output (giving myself another chance to introduce a coding error). +Using a generic output file format (e.g., a simple CSV file) affords more +flexibility in choosing analysis tools, and also better supports data-sharing. + +I still think it’s important to record “everything”, but there are better ways +to do it. An approach I began to use later was to write separate programs for +generating trials and displaying them. The first program handles +counterbalancing and all the logic supporting randomness; it then creates a CSV +for each participant. The second program simply reads these CSVs and dutifully +displays trials based *only* on the information they contain, ensuring that no +aspect of a trial (e.g., the color of a distractor item) could be forgotten. + +The display program records responses from participants and combines them with +trial info to create simple output files for analysis. To further protect +against data loss, it also records, with timestamps, a simple log of every +event that occurs during the experiment. The log file includes the experiment +start time, keypresses and input events, changes to the display, and anything +else that could happen. Between the input CSVs and this log file, it’s possible +to recreate exactly what happened during the course of the study -- even if the +information wasn’t in the “simple” output files. I make sure that the output is +written to disk frequently to ensure that nothing is lost in case of a system +crash. This approach also makes it easy to restart at a specific point, which +is useful for long studies and projects using fMRI (the scanner makes it easy +to have false-starts). + +My position at the FAA doesn’t involve programming a lot of studies. We do most +of our work on fairly complicated simulator configurations (I have yet to do a +study that didn’t include a diagram describing the servers involved), and there +are a lot of good programmers around who are here specifically to keep these +running. I hope this lesson is useful for anybody else who might be collecting +data from people, whether it’s in the context of a psychology study or user +testing. + diff --git a/content/posts/riddler-2/index.Rmd b/content/posts/riddler-2/index.Rmd @@ -0,0 +1,101 @@ +--- +title: "Riddler #2" +author: "Eamon Caddigan" +date: "2015-12-19" +output: html_document +layout: post +summary: Solving and simulating a probability puzzle. +categories: R stats +--- + +FiveThirtyEight has a new puzzle feature called The Riddler. This week they posted [their second puzzle](http://fivethirtyeight.com/features/which-geyser-gushes-first/), which involves probability: + +> You arrive at the beautiful Three Geysers National Park. You read a placard +> explaining that the three eponymous geysers — creatively named A, B and C — +> erupt at intervals of precisely two hours, four hours and six hours, +> respectively. However, you just got there, so you have no idea how the three +> eruptions are staggered. Assuming they each started erupting at some +> independently random point in history, what are the probabilities that A, B +> and C, respectively, will be the first to erupt after your arrival? + +### Analytic solution + +Responses were due last night at midnight, so I hope I'm not spoiling anything by sharing mine. + +When you arrive at the park, the first eruption of geyser A is likely to occur at any time within the next two hours with a uniform probability. Denoting the number of hours until the first eruption of the geyser as “A”, A ~ Uniform(0, 2). Similarly, B ~ Uniform(0, 4) and C ~ Uniform(0, 6). + +To compute the probability of geyser A erupting first, separately consider the cases where geysers B and C do and do not erupt within the first two hours of waiting. + +Using Bayes Theorem: + +$$Pr(A first \cap B<2, C<2) = Pr(A first | B < 2, C < 2) Pr(B < 2, C < 2)$$ + +Assuming independence of the geysers: + +$$= Pr(A first | B < 2, C < 2) Pr(B < 2) Pr(C < 2)$$ + +Considering the case here, in which all three geysers erupt in the first two hours, the probability of any geyser erupting first is 1/3. The probability of geysers B and C erupting in the first two hours is easy to calculate. + +$$= (1/3) \times (1/2) \times (1/3) = 1/18$$ + +Using similar logic: + +$$Pr(A first \cap B > 2, C < 2) = (1/2) \times (1/2) \times (1/3) = 1/12\\ +Pr(A first \cap B < 2, C > 2) = (1/2) \times (1/2) \times (2/3) = 1/6\\ +Pr(A first \cap B > 2, C > 2) = 1 \times (1/2) \times (2/3) = 1/3$$ + +These disjoint events partition the sample space, so the law of total probability dictates: + +$$Pr(A first) = 1/18 + 1/12 + 1/6 + 1/3 = 23/36 \approx 0.6389$$ + +Do the same thing to calculate the probability of geyser B erupting before the others: + +$$Pr(B first \cap B < 2, C < 2) = (1/3) \times (1/2) \times (1/3) = 1/18\\ +Pr(B first \cap B < 2, C > 2) = (1/2) \times (1/2) \times (2/3) = 1/6$$ + +Note that when geyser B does not erupt within the first two hours, another geyser is guaranteed to erupt before it: + +$$Pr(B first \cap B > 2, C < 2) = 0\\ +Pr(B first \cap B > 2, C > 2) = 0$$ + +Therefore: + +$$Pr(B first) = 1/18 + 1/6 = 4/18 \approx 0.2222$$ + +And geyser C is similar: + +$$Pr(C first \cap B < 2, C < 2) = (1/3) \times (1/2) \times (1/3) = 1/18\\ +Pr(C first \cap B > 2, C < 2) = (1/2) \times (1/2) \times (1/3) = 1/12\\ +Pr(C first) = 1/18 + 1/12 = 5/36 \approx 0.1389$$ + +### Quick simulation + +It never hurts to check results with a simulation. After all, math is hard and programming is easy. + +```{r, warning=FALSE, message=FALSE} +library(dplyr) +library(ggplot2) + +numSamples <- 1e6 + +# Generate random wait times for each geyser's next eruption +geysers <- data_frame(A = runif(numSamples, 0, 2), + B = runif(numSamples, 0, 4), + C = runif(numSamples, 0, 6)) +geyserNames <- colnames(geysers) + +# Identify the geyser with the smallest time-to eruption +geysers <- geysers %>% + mutate(first_geyser = geyserNames[max.col(-geysers[, geyserNames])]) + +# Plot the results +geysers %>% + ggplot(aes(x = first_geyser)) + geom_bar() + +# Count observations and estimate probabilities +geysers %>% + count(first_geyser) %>% + mutate(prob_first = n / numSamples) +``` + +Close enough! diff --git a/content/posts/riddler-2/index.md b/content/posts/riddler-2/index.md @@ -0,0 +1,130 @@ +--- +title: "Riddler #2" +date: "2015-12-19" +description: Solving and simulating a probability puzzle. +categories: +- Data Science +tags: +- Statistics +katex: true +--- + +FiveThirtyEight has a new puzzle feature called The Riddler. This week they +posted [their second +puzzle](http://fivethirtyeight.com/features/which-geyser-gushes-first/), which +involves probability: + +> You arrive at the beautiful Three Geysers National Park. You read a placard +> explaining that the three eponymous geysers — creatively named A, B and C — +> erupt at intervals of precisely two hours, four hours and six hours, +> respectively. However, you just got there, so you have no idea how the three +> eruptions are staggered. Assuming they each started erupting at some +> independently random point in history, what are the probabilities that A, B +> and C, respectively, will be the first to erupt after your arrival? + +### Analytic solution + +Responses were due last night at midnight, so I hope I'm not spoiling anything +by sharing mine. + +When you arrive at the park, the first eruption of geyser A is likely to occur +at any time within the next two hours with a uniform probability. Denoting the +number of hours until the first eruption of the geyser as “A”, A ~ Uniform(0, +2). Similarly, B ~ Uniform(0, 4) and C ~ Uniform(0, 6). + +To compute the probability of geyser A erupting first, separately consider the +cases where geysers B and C do and do not erupt within the first two hours of +waiting. + +Using Bayes Theorem: + +$$Pr(A first \cap B<2, C<2) = Pr(A first | B < 2, C < 2) Pr(B < 2, C < 2)$$ + +Assuming independence of the geysers: + +$$= Pr(A first | B < 2, C < 2) Pr(B < 2) Pr(C < 2)$$ + +Considering the case here, in which all three geysers erupt in the first two +hours, the probability of any geyser erupting first is 1/3. The probability of +geysers B and C erupting in the first two hours is easy to calculate. + +$$= (1/3) \times (1/2) \times (1/3) = 1/18$$ + +Using similar logic: + +$$Pr(A first \cap B > 2, C < 2) = (1/2) \times (1/2) \times (1/3) = 1/12$$ +$$Pr(A first \cap B < 2, C > 2) = (1/2) \times (1/2) \times (2/3) = 1/6$$ +$$Pr(A first \cap B > 2, C > 2) = 1 \times (1/2) \times (2/3) = 1/3$$ + +These disjoint events partition the sample space, so the law of total +probability dictates: + +$$Pr(A first) = 1/18 + 1/12 + 1/6 + 1/3 = 23/36 \approx 0.6389$$ + +Do the same thing to calculate the probability of geyser B erupting before the +others: + +$$Pr(B first \cap B < 2, C < 2) = (1/3) \times (1/2) \times (1/3) = 1/18$$ +$$Pr(B first \cap B < 2, C > 2) = (1/2) \times (1/2) \times (2/3) = 1/6$$ + +Note that when geyser B does not erupt within the first two hours, another +geyser is guaranteed to erupt before it: + +$$Pr(B first \cap B > 2, C < 2) = 0$$ +$$Pr(B first \cap B > 2, C > 2) = 0$$ + +Therefore: + +$$Pr(B first) = 1/18 + 1/6 = 4/18 \approx 0.2222$$ + +And geyser C is similar: + +$$Pr(C first \cap B < 2, C < 2) = (1/3) \times (1/2) \times (1/3) = 1/18$$ +$$Pr(C first \cap B > 2, C < 2) = (1/2) \times (1/2) \times (1/3) = 1/12$$ +$$Pr(C first) = 1/18 + 1/12 = 5/36 \approx 0.1389$$ + +### Quick simulation + +It never hurts to check results with a simulation. After all, math is hard and +programming is easy. + +```r +library(dplyr) +library(ggplot2) + +numSamples <- 1e6 + +# Generate random wait times for each geyser's next eruption +geysers <- data_frame(A = runif(numSamples, 0, 2), + B = runif(numSamples, 0, 4), + C = runif(numSamples, 0, 6)) +geyserNames <- colnames(geysers) + +# Identify the geyser with the smallest time-to eruption +geysers <- geysers %>% + mutate(first_geyser = geyserNames[max.col(-geysers[, geyserNames])]) + +# Plot the results +geysers %>% + ggplot(aes(x = first_geyser)) + geom_bar() +``` + + + +```r +# Count observations and estimate probabilities +geysers %>% + count(first_geyser) %>% + mutate(prob_first = n / numSamples) +``` +``` +## Source: local data frame [3 x 3] +## +## first_geyser n prob_first +## 1 A 640093 0.640093 +## 2 B 221439 0.221439 +## 3 C 138468 0.138468 +``` + +Close enough! + diff --git a/content/posts/riddler-2/unnamed-chunk-1-1.png b/content/posts/riddler-2/unnamed-chunk-1-1.png Binary files differ. diff --git a/content/posts/rmarkdown-hugo/index.md b/content/posts/rmarkdown-hugo/index.md @@ -0,0 +1,150 @@ +--- +title: Using RStudio and RMarkdown with Hugo +description: One approach to blogging with RMarkdown and Hugo. +date: 2022-07-10T17:03:47-04:00 +draft: False +categories: +- Meta +- Programming +- Data Science +tags: +- R +--- + +I converted my site to [Hugo](https://gohugo.io/) recently, and I finally +figured out a workflow to create blog posts using RMarkdown from inside +RStudio. None of the instructions that I found online worked the way I +wanted (for instance, [hugodown](https://hugodown.r-lib.org/) requires a +specific out-of-date version of Hugo), so I'm sharing my workflow in case +it's useful for anybody else. + +## Things to do once + +There are a few basic setup steps that should only need to be performed +once. + +### Setup Hugo + +Hugo setup is beyond the scope of this post. I mostly followed [this +quickstart guide](https://gohugo.io/getting-started/quick-start/). + +### Set a `HUGO_ROOT` environment variable + +Create a new environment variable `HUGO_ROOT` and set it to the directory in +which you created your site. In my case, I'm using: + +```bash +HUGO_ROOT="~/web/www.eamoncaddigan.net/" +``` + +There are (too) many ways to set an environment variable. I edited +`~/.profile`, but `~/.bashrc` will work for many folks. Using `~/.Renviron` +would also be appropriate if you're not planning to use this variable for +anything outside of R and RStudio. + +### Create a location for RMarkdown files outside of Hugo + +You could keep your `.rmd` files in your Hugo site, and it might even be +possible to have Hugo knit them for you. But since I'm currently on my third +static site generator, I wanted to use a separate git repository for blog +posts, outside of the rest of my site configuration. + +## Things to do for every post + +Here are the steps to take every time you create a new blog post. + +### Launch the Hugo server + +Running Hugo's built-in server lets you preview your post as you work on it. +Run the following command in the shell: + +```bash +hugo server -DF +``` + +When you initially run this in a terminal, it will print a URI at which you +can point your web browser, e.g., `http://localhost:1313/`. Go ahead and +open that in your browser. + +### Create a new RMarkdown file in RStudio + +When you create a new RMarkdown file in RStudio, you can fill in a title for +your post in the GUI, or you can do it later. It doesn't matter which output +format you select since we're going to change that in the next step. + +### Edit the RMarkdown YAML + +Here's the YAML block for my last post: + +```md +--- +title: "Labeling bar charts (and other graphics) in ggplot2" +description: "How to combine stats and geoms to simplify complex plots." +date: 2022-07-08T19:32:57-04:00 +draft: False +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +--- +``` + +Change the title, description, and date as appropriate for your post, and +set `draft` to `True` for now. + +The function used with `knit` is invoked when you press the "Knit" button in +RStudio. It specifies that the rendered content (a markdown file) is put in +`$HUGO_ROOT/content/posts`. + +The options passed to `output` tell `knitr` to generate Markdown output by +default. Preserving YAML is important because Hugo uses that to organize +posts, and the `markdown` variant has good code highlighting, etc. + +You might want to set `tags`, I ought to start doing that soon. + +### Set chunk and knit options + +Set `knitr` chunk and knit options in the first code chunk of the file: + +```r +knitr::opts_chunk$set( + echo = TRUE, + fig.path = file.path("figs", + sub("\\.Rmd$", "", + basename(rstudioapi::getActiveDocumentContext()$path)), + "") +) +knitr::opts_knit$set( + base.dir = file.path(Sys.getenv("HUGO_ROOT"), "static"), + base.url = "/" +) +``` + +These options ensure that figures are put in the correct local directory, +and that the links will work online. This specific configuration places +figures in `http://example.com/figs/rmarkdown-filename/chunk-name-N.png`, +and you can tweak this as you see fit. You can pass additional named +arguments to `knitr::opts_chunk$set()` that you like, such as `fig.width`. + +### Write a good post + +If it's *really* good, please let me know about it! + +Clicking the Knit button in RStudio will create a new markdown file inside +your local Hugo site. The Hugo server will see the changes and generate a +new site, and your browser should refresh the site to display the changes +(Hugo injects special JavaScript to do this when you're previewing with its +server). + +### Finish up + +When you finish your post, set `draft` to `False` in the YAML, kill the Hugo +server, and run `hugo` (with no additional options) to generate your static +site. Upload that site to your host and feel good about freely sharing your +knowledge with the broader community. diff --git a/content/posts/sister-probability-puzzle/index.Rmd b/content/posts/sister-probability-puzzle/index.Rmd @@ -0,0 +1,180 @@ +--- +title: "Sister probability puzzle" +description: "My solution to a question about the probability of having a sister." +date: 2023-01-18T21:47:38-08:00 +draft: False +katex: True +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set( + echo = TRUE, + fig.path = file.path("figs", + sub("\\.Rmd$", "", + basename(rstudioapi::getActiveDocumentContext()$path)), + "") +) +knitr::opts_knit$set( + base.dir = file.path(Sys.getenv("HUGO_ROOT"), "static"), + base.url = "/" +) +``` + +A smart and talented friend, who's a fellow data scientist by profession, came +across a probability puzzle that's supposedly given in some job interviews for +data science roles. The problem asks the following: + +> Assume the distribution of children per family is such that the probability of +> having 0 children is 0.30, 1 child is 0.25, 2 children is 0.20, 3 children is +> 0.15, 4 children is 0.10, and 5 or more children is 0. Consider a random girl +> in the population of children. What is the probability that she has a sister? + +Checking her work, my friend disagreed with the answers she found online, and +wanted to know how I'd solve the problem. Since my solution seems to be +different than others I've found so far, I thought I'd share it with the whole +Internet, which will certainly tell me whether I'm wrong. + +## Simulating the problem + +I'll start with a simulation—I'm a bit more confident in my programming than my +probability theory (I've been doing it longer), and it makes some of the tricky +parts of the problem explicit. + +First, we'll simulate a random sample of _families_, since the problem gives us +probabilities in terms of _children per family_. After generating a pool of +random family sizes, we can use the binomial distribution to generate a random +number of girls for each family (naively assuming that the probability of a +child being a girl is 0.5). + +```{r simulate_families} +set.seed(232636039) +num_families <- 100000 + +family_size <- seq(0, 5) +p_family_size <- c(0.3, 0.25, 0.20, 0.15, 0.1, 0.0) + +girls_per_family <- sample(family_size, num_families, replace = TRUE, + prob = p_family_size) |> + (\(n) rbinom(num_families, size = n, prob = 0.5))() +``` + +If a family has more than two girls, these girls have sisters. The probability +that a randomly selected girl has a sister is approximated by the number of +girls with sisters divided by the total number of girls in our simulation. + +```{r estimate_p} +# If there is more than one girl in a family, these girls have sisters +girls_with_sisters <- sum(girls_per_family[girls_per_family > 1]) +girls_total <- sum(girls_per_family) + +(p_est <- girls_with_sisters / girls_total) +``` + +The code above estimates that the probability that a girl (sampled at random +from the _population of children_) has a sister is approximately `r round(p_est, +2)`. + +## Plotting the simulation + +Just for fun, let's plot the estimate as it develops over the number of +simulated families. This also helps us get a sense of how trustworthy the +estimate is—has it converged to a stable value, or is it still swinging around? +For this, I'll finally use parts of the [Tidyverse](https://www.tidyverse.org/). + +```{r load_tidyverse} +suppressPackageStartupMessages(library(dplyr)) +suppressPackageStartupMessages(library(ggplot2)) +``` + +```{r construct_df, cache=TRUE, dependson="simulate_families"} +sister_dat <- tibble(girls_per_family) |> + mutate(families = seq(n()), + has_sister = girls_per_family > 1, + total_girls = cumsum(girls_per_family), + girls_with_sisters = cumsum(girls_per_family * has_sister), + p_est = girls_with_sisters / total_girls) +``` + +```{r plot_estimate, cache=TRUE, dependson="construc_df"} +sister_dat |> + # We'll skip any beginning rows that were generated before we sampled girls, + # since 0/0 is undefined. + filter(total_girls > 0) |> + ggplot(aes(families, p_est)) + + geom_step() + + geom_hline(yintercept = 71/120, linetype = "dashed") + + scale_x_log10() + + theme_minimal() + + labs(x = "Number of random families", y = "Observed proportion of girls with sisters") +``` + +## Analytic solution + +If you're wondering how I chose a value for the dashed line, here's an analytic +solution to the puzzle. + +We'll let _S_ represent the event that a girl has a sister, _Fₙ_ represent the +event that a family has _n_ children, and _Cₙ_ represent the event that a girl +comes from a family of _n_ children (i.e., the girl has _n - 1_ siblings). By +the law of total probability: + +$$ \mathbb{P}(S) = \sum_{n} \mathbb{P}(S|C_n) \mathbb{P}(C_n) $$ + +The conditional probability that a girl from a family with _n_ children has a +sister is the compliment of the probability that all of her siblings are +brothers. Therefore: + +$$ \mathbb{P}(S|C_n) = 1 - \frac{1}{2^{n-1}} $$ + +For the next component, it's important to call out the fact that the problem +text gives us P(_Fₙ_) (the probability that a family has _n_ children), which is +**not the same** as P(_Cₙ_) (the probability that a child comes from a family +with _n_ children). I suspect that this trips some people up, and explains some +of the answers that are different than mine. + +To illustrate the difference, let's imagine that the probabilities were +constructed from a population of 100 families. Twenty five of these families +have one child, while only ten have four children. However, this arrangement +results in 25 children with no siblings, while 40 children would have 3 each. In +other words, a randomly selected _family_ is more likely to have one child than +four children, but a randomly selected _child_ is more likely to come from a +family with four children than a family with one child. Formalizing this +reasoning a bit, we find: + +$$ \mathbb{P}(C_n) = \frac{n \mathbb{P}(F_n)}{\sum_{m} m \mathbb{P}(F_m)} $$ + +With our terms defined, we'll use R once more to calculate _P(S)_: + +```{r calculate_p} +n <- family_size +fn <- p_family_size +s_given_cn <- 1 - 1/(2^(n-1)) +cn <- n * fn / sum(n * fn) +(s <- sum(s_given_cn * cn)) +``` + +This value is equal to `71/120`, and is quite close to what we found through +simulation—but only reliably so after generating around 10,000 families. + +## Concluding note + +I'm ambivalent about the practice of asking job applicants to solve probability +puzzles during interviews, but it's true that sometimes our intuitions can lead +us astray (e.g, confusing P(_Fₙ_) and P(_Cₙ_)), and this does come up in +real-life data analyses. When I find myself dealing with such situations, I'm +flexible in the approach I take: sometimes I try to find an exact solution using +probability theory first, but often I program a quick simulation instead. Most +of the time, I wind up doing both, because these approaches complement one +another: simulations are great because they force you to be explicit about the +assumptions that you're making about the problem, while analytic solutions give +exact answers and are insensitive to randomness. diff --git a/content/posts/sister-probability-puzzle/index.md b/content/posts/sister-probability-puzzle/index.md @@ -0,0 +1,186 @@ +--- +title: "Sister probability puzzle" +description: "My solution to a question about the probability of having a sister." +date: 2023-01-18T21:47:38-08:00 +draft: False +katex: True +knit: (function(input, ...) { + rmarkdown::render( + input, + output_dir = file.path(Sys.getenv("HUGO_ROOT"), "content/posts") + ) + }) +output: + md_document: + variant: markdown + preserve_yaml: true +categories: +- Data Science +tags: +- R +- Statistics +--- + +A smart and talented friend, who's a fellow data scientist by +profession, came across a probability puzzle that's supposedly given in +some job interviews for data science roles. The problem asks the +following: + +> Assume the distribution of children per family is such that the +> probability of having 0 children is 0.30, 1 child is 0.25, 2 children +> is 0.20, 3 children is 0.15, 4 children is 0.10, and 5 or more +> children is 0. Consider a random girl in the population of children. +> What is the probability that she has a sister? + +Checking her work, my friend disagreed with the answers she found +online, and wanted to know how I'd solve the problem. Since my solution +seems to be different than others I've found so far, I thought I'd share +it with the whole Internet, which will certainly tell me whether I'm +wrong. + +## Simulating the problem + +I'll start with a simulation---I'm a bit more confident in my +programming than my probability theory (I've been doing it longer), and +it makes some of the tricky parts of the problem explicit. + +First, we'll simulate a random sample of *families*, since the problem +gives us probabilities in terms of *children per family*. After +generating a pool of random family sizes, we can use the binomial +distribution to generate a random number of girls for each family +(naively assuming that the probability of a child being a girl is 0.5). + +``` r +set.seed(232636039) +num_families <- 100000 + +family_size <- seq(0, 5) +p_family_size <- c(0.3, 0.25, 0.20, 0.15, 0.1, 0.0) + +girls_per_family <- sample(family_size, num_families, replace = TRUE, + prob = p_family_size) |> + (\(n) rbinom(num_families, size = n, prob = 0.5))() +``` + +If a family has more than two girls, these girls have sisters. The +probability that a randomly selected girl has a sister is approximated +by the number of girls with sisters divided by the total number of girls +in our simulation. + +``` r +# If there is more than one girl in a family, these girls have sisters +girls_with_sisters <- sum(girls_per_family[girls_per_family > 1]) +girls_total <- sum(girls_per_family) + +(p_est <- girls_with_sisters / girls_total) +``` + + ## [1] 0.5878486 + +The code above estimates that the probability that a girl (sampled at +random from the *population of children*) has a sister is approximately +0.59. + +## Plotting the simulation + +Just for fun, let's plot the estimate as it develops over the number of +simulated families. This also helps us get a sense of how trustworthy +the estimate is---has it converged to a stable value, or is it still +swinging around? For this, I'll finally use parts of the +[Tidyverse](https://www.tidyverse.org/). + +``` r +suppressPackageStartupMessages(library(dplyr)) +suppressPackageStartupMessages(library(ggplot2)) +``` + +``` r +sister_dat <- tibble(girls_per_family) |> + mutate(families = seq(n()), + has_sister = girls_per_family > 1, + total_girls = cumsum(girls_per_family), + girls_with_sisters = cumsum(girls_per_family * has_sister), + p_est = girls_with_sisters / total_girls) +``` + +``` r +sister_dat |> + # We'll skip any beginning rows that were generated before we sampled girls, + # since 0/0 is undefined. + filter(total_girls > 0) |> + ggplot(aes(families, p_est)) + + geom_step() + + geom_hline(yintercept = 71/120, linetype = "dashed") + + scale_x_log10() + + theme_minimal() + + labs(x = "Number of random families", y = "Observed proportion of girls with sisters") +``` + + + +## Analytic solution + +If you're wondering how I chose a value for the dashed line, here's an +analytic solution to the puzzle. + +We'll let *S* represent the event that a girl has a sister, *Fₙ* +represent the event that a family has *n* children, and *Cₙ* represent +the event that a girl comes from a family of *n* children (i.e., the +girl has *n - 1* siblings). By the law of total probability: + +$$ \mathbb{P}(S) = \sum_{n} \mathbb{P}(S|C_n) \mathbb{P}(C_n) $$ + +The conditional probability that a girl from a family with *n* children +has a sister is the compliment of the probability that all of her +siblings are brothers. Therefore: + +$$ \mathbb{P}(S|C_n) = 1 - \frac{1}{2^{n-1}} $$ + +For the next component, it's important to call out the fact that the +problem text gives us P(*Fₙ*) (the probability that a family has *n* +children), which is **not the same** as P(*Cₙ*) (the probability that a +child comes from a family with *n* children). I suspect that this trips +some people up, and explains some of the answers that are different than +mine. + +To illustrate the difference, let's imagine that the probabilities were +constructed from a population of 100 families. Twenty five of these +families have one child, while only ten have four children. However, +this arrangement results in 25 children with no siblings, while 40 +children would have 3 each. In other words, a randomly selected *family* +is more likely to have one child than four children, but a randomly +selected *child* is more likely to come from a family with four children +than a family with one child. Formalizing this reasoning a bit, we find: + +$$ \mathbb{P}(C_n) = \frac{n \mathbb{P}(F_n)}{\sum_{m} m \mathbb{P}(F_m)} $$ + +With our terms defined, we'll use R once more to calculate *P(S)*: + +``` r +n <- family_size +fn <- p_family_size +s_given_cn <- 1 - 1/(2^(n-1)) +cn <- n * fn / sum(n * fn) +(s <- sum(s_given_cn * cn)) +``` + + ## [1] 0.5916667 + +This value is equal to `71/120`, and is quite close to what we found +through simulation---but only reliably so after generating around 10,000 +families. + +## Concluding note + +I'm ambivalent about the practice of asking job applicants to solve +probability puzzles during interviews, but it's true that sometimes our +intuitions can lead us astray (e.g, confusing P(*Fₙ*) and P(*Cₙ*)), and this +does come up in real-life data analyses. When I find myself dealing with +such situations, I'm flexible in the approach I take: [sometimes I try to +find an exact solution using probability theory first]({{< ref +"posts/riddler-2/index.md" >}}), but often I program a quick simulation +instead. Most of the time, I wind up doing both, because these approaches +complement one another: simulations are great because they force you to be +explicit about the assumptions that you're making about the problem, while +analytic solutions give exact answers and are insensitive to randomness. diff --git a/content/posts/sister-probability-puzzle/plot_estimate-1.png b/content/posts/sister-probability-puzzle/plot_estimate-1.png Binary files differ. diff --git a/content/posts/tufte-plot/graph_1-1.png b/content/posts/tufte-plot/graph_1-1.png Binary files differ. diff --git a/content/posts/tufte-plot/graph_2-1.png b/content/posts/tufte-plot/graph_2-1.png Binary files differ. diff --git a/content/posts/tufte-plot/graph_3-1.png b/content/posts/tufte-plot/graph_3-1.png Binary files differ. diff --git a/content/posts/tufte-plot/index.Rmd b/content/posts/tufte-plot/index.Rmd @@ -0,0 +1,185 @@ +--- +title: "Recreating a Tufte Slopegraph" +author: "Eamon Caddigan" +date: "2018-07-05" +output: md_document +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE) +``` +```{r load_libraries, include=FALSE, warning=FALSE, message=FALSE} +#extrafont::loadfonts(device="win") +suppressPackageStartupMessages(library(tibble)) +suppressPackageStartupMessages(library(dplyr)) +suppressPackageStartupMessages(library(ggplot2)) +suppressPackageStartupMessages(library(ggrepel)) +``` + +Recently on Twitter, data visualization guru Edward R. Tufte wrote that graphics produced by R are not “publication ready”. His proposed workflow is to use statistical software to create an initial version of a plot, and then make final improvements in Adobe Illustrator. + +I disagree with this advice. First I’ll show the steps a data analyst might take to create a high-quality graphic entirely in R. Then, I’ll explain why I think this is a better approach. + +## Publication quality graphics in R + +Page 158 of Tufte’s classic book, [The Visual Display of Quantitative Information (2nd ed.)](https://www.edwardtufte.com/tufte/books_vdqi), features a “slope graph” that shows the change in government receipts for several countries between 1970 and 1979. Below are the first few rows of these data in a [tidy data frame](https://www.jstatsoft.org/article/view/v059i10), `receiptData`, along with a quick and dirty slopegraph. + +```{r receipt_data, echo=FALSE} +receiptData <- tribble( + ~country, ~year, ~receipts, + "Belgium", 1970L, 35.2, + "Belgium", 1979L, 43.2, + "Britain", 1970L, 40.7, + "Britain", 1979L, 39.0, + "Canada", 1970L, 35.2, + "Canada", 1979L, 35.8, + "Finland", 1970L, 34.9, + "Finland", 1979L, 38.2, + "France", 1970L, 39.0, + "France", 1979L, 43.4, + "Germany", 1970L, 37.5, + "Germany", 1979L, 42.9, + "Greece", 1970L, 26.8, + "Greece", 1979L, 30.6, + "Italy", 1970L, 30.4, + "Italy", 1979L, 35.7, + "Japan", 1970L, 20.7, + "Japan", 1979L, 26.6, + "Netherlands", 1970L, 44.0, + "Netherlands", 1979L, 55.8, + "Norway", 1970L, 43.5, + "Norway", 1979L, 52.2, + "Spain", 1970L, 22.5, + "Spain", 1979L, 27.1, + "Sweden", 1970L, 46.9, + "Sweden", 1979L, 57.4, + "Switzerland", 1970L, 26.5, + "Switzerland", 1979L, 33.2, + "United States", 1970L, 30.3, + "United States", 1979L, 32.5 + ) + +receiptData %>% + head(6) %>% + knitr::kable() +``` +```{r graph_1} +ggplot(receiptData, aes(year, receipts, group = country)) + + geom_line() + + geom_text_repel(aes(label = country)) + + labs(x = "Year", y = "Government receipts as percentage of GDP") +``` + +This plot is not attractive, but it is useful for getting a handle on the data. Whether [iterating through an exploratory data analysis]({{< ref "/posts/2015-09-09-data-science.md" >}}) or preparing a graphic for publication, analysts will create many ugly graphics on the path to settling on a design and refining it. + +For our first round of improvements, we can change the aspect ratio of the graphic and arrange the country labels so they don’t overlap with the data. We should also remove the “chart junk” in the background, such as the background grid, and label only the years of interest on the x-axis. + +```{r graph_2, fig.height=8, fig.width=5} +ggplot(receiptData, aes(year, receipts, group = country)) + + geom_line() + + geom_text_repel(aes(label = country), + data = filter(receiptData, year == 1970), + nudge_x = -0.5, hjust = 1, + direction = "y", size = 5) + + geom_text_repel(aes(label = country), + data = filter(receiptData, year == 1979), + nudge_x = 0.5, hjust = 0, + direction = "y", size = 5) + + scale_x_continuous(breaks = c(1970, 1979), limits = c(1966, 1983)) + + theme(panel.background = element_blank(), + axis.title = element_text(size = 16), + axis.text = element_text(size = 12)) + + labs(x = "Year", y = "Government receipts as percentage of GDP") +``` + +The [ggrepel](https://github.com/slowkow/ggrepel) package has done a great job preventing the labels from overlapping; I usually use `geom_text_repel()` instead of `geom_text()` during exploratory data analysis. Here, however, the segments connecting the labels to data points create confusing clutter. While these can be removed within the function, our final figure will be easier to understand if we nudge labels manually so that they’re as close to their data as possible. + +We can also drop the axes; the year labels will go right above the data, and we’ll show each country’s value next to its label. Since we’re losing the axis titles, we’ll also embed a caption in this version of the graphic. + +Finally, we’ll change the typeface. Since we’re trying to make something that would please Tufte, we’ll use a serif font. If you haven’t done so before, you may need to run `loadfonts()` from the [extrafont package](https://github.com/wch/extrafont) to tell R how to find system fonts. We’ll also further boost our “data-ink ratio” by making the lines thinner. + +```{r graph_3, fig.height=8, fig.width=8} +labelAdjustments <- tribble( + ~country, ~year, ~nudge_y, + "Netherlands", 1970L, 0.3, + "Norway", 1970L, -0.2, + "Belgium", 1970L, 0.9, + "Canada", 1970L, -0.1, + "Finland", 1970L, -0.8, + "Italy", 1970L, 0.4, + "United States", 1970L, -0.5, + "Greece", 1970L, 0.4, + "Switzerland", 1970L, -0.3, + "France", 1979L, 0.8, + "Germany", 1979L, -0.7, + "Britain", 1979L, 0.1, + "Finland", 1979L, -0.1, + "Canada", 1979L, 0.4, + "Italy", 1979L, -0.5, + "Switzerland", 1979L, 0.2, + "United States", 1979L, -0.1, + "Spain", 1979L, 0.3, + "Japan", 1979L, -0.2 + ) + +receiptData <- left_join(receiptData, labelAdjustments, + by = c("country", "year")) %>% + mutate(receipts_nudged = ifelse(is.na(nudge_y), 0, nudge_y) + receipts) + +update_geom_defaults("text", list(family = "Georgia", size = 4.0)) +ggplot(receiptData, aes(year, receipts, group = country)) + + # Slope lines + geom_line(size = 0.1) + + # Country names (manually nudged) + geom_text(aes(year, receipts_nudged, label = country), + data = filter(receiptData, year == 1970), + hjust = 1, nudge_x = -3) + + geom_text(aes(year, receipts_nudged, label = country), + data = filter(receiptData, year == 1979), + hjust = 0, nudge_x = 3) + + # Data values + geom_text(aes(year, receipts_nudged, label = sprintf("%0.1f", receipts)), + data = filter(receiptData, year == 1970), + hjust = 1, nudge_x = -0.5) + + geom_text(aes(year, receipts_nudged, label = sprintf("%0.1f", receipts)), + data = filter(receiptData, year == 1979), + hjust = 0, nudge_x = 0.5) + + # Column labels + annotate("text", x = c(1970, 1979) + c(-0.5, 0.5), + y = max(receiptData$receipts) + 3, + label = c("1970", "1979"), + hjust = c(1, 0)) + + # Plot annotation + annotate("text", x = 1945, y = 58, hjust = 0, vjust = 1, + label = paste("Current Receipts of Government as a", + "Percentage of Gross Domestic\nProduct, 1970 and 1979", + sep = "\n"), + family = "Georgia", size = 4.0) + + coord_cartesian(xlim = c(1945, 1990)) + + theme(panel.background = element_blank(), + axis.title = element_blank(), + axis.text = element_blank(), + axis.ticks = element_blank()) +``` + +## Why it’s worth it + +It took several iterations to get the aesthetics of this plot just right, while an adept user of a graphics editor would be able to recreate it in minutes. However, this initial time savings obscures several advantages to completing this process in code as opposed to switching to a tool like Illustrator. + +### R is free software + +All of the programs I used to create this graphic (and share it with you) are [free software](https://www.fsf.org/about/what-is-free-software), unlike Adobe’s terrific but expensive Illustrator. [Inkscape](https://inkscape.org/en/) is an excellent open source alternative, but it is not as powerful as its commercial competitor. On the other hand, [R](https://www.r-project.org/) is arguably the most advanced and well-supported statistical analysis tool. Even if the politics of the open source movement aren’t important, free is a better price-point. + +### Code can be reproduced + +Anybody who wants to recreate the final figure using a different set of countries, a new pair of years, or a favored economic indicator can run the code above on their own data. With minimal tweaking, they will have a graphic with aesthetics identical to those above. Reproducing this graphic using a multi-tool workflow is more complicated; a novice would first need to learn how to create a “rough draft” of it in software, and then learn how to use a graphics editor to improve its appearance. + +### Scripted graphics are easier to update + +Imagine that an analyst discovered a mistake in their analysis that needed to be corrected. Or imagine the less stressful situation where a colleague suggested replacing some of the countries in the figure. In such cases, the work of creating the graphic will need to be redone: the analyst will need to add data or correct errors, generate a new plot in software, and re-edit the plot in their graphics editor. Using a scripted, code-based workflow, the analyst would only need to do the first step, and possibly update some manual tweaks. The initial time savings afforded by a graphics editor disappears after the first time this happens. + +### Automation prevents errors + +Not only does scripted workflow make it easier to deal with errors, it guards against them. When analysts adjust graphic elements in a GUI, there’s a risk of mistakenly moving, deleting, or mislabeling data points. Such mistakes are difficult to detect, but code-based workflows avoid these risks; if the data source and analysis are error-free, then the graphic will also be. + +These considerations are among the reasons why scripted analyses are [considered best practice](https://peerj.com/preprints/3210/) in statistical analysis. Most of Tufte’s advice on creating graphics is excellent, but I recommend ignoring his suggestion to make the final edits in a program like Illustrator. Learning how to make polished graphics in software will ultimately save analysts time and help them avoid mistakes. +\ No newline at end of file diff --git a/content/posts/tufte-plot/index.md b/content/posts/tufte-plot/index.md @@ -0,0 +1,228 @@ +--- +title: "Recreating a Tufte Slope Graph" +description: Publication-ready graphics should be created in code, not a graphics editor. +date: 2018-07-22 +categories: +- Programming +- Data Science +tags: +- R +- Dataviz +--- + +Recently on Twitter, data visualization guru Edward R. Tufte wrote that +graphics produced by R are not “publication ready”. His proposed +workflow is to use statistical software to create an initial version of +a plot, and then make final improvements in Adobe Illustrator. + +I disagree with this advice. First I’ll show the steps a data analyst +might take to create a high-quality graphic entirely in R. Then, I’ll +explain why I think this is a better approach. + +## Publication quality graphics in R + +Page 158 of Tufte’s classic book, [The Visual Display of Quantitative +Information (2nd ed.)](https://www.edwardtufte.com/tufte/books_vdqi), +features a “slope graph” that shows the change in government receipts +for several countries between 1970 and 1979. Below are the first few +rows of these data in a [tidy data +frame](https://www.jstatsoft.org/article/view/v059i10), `receiptData`, +along with a quick and dirty slopegraph. + +|country | year| receipts| +|:-------|----:|--------:| +|Belgium | 1970| 35.2| +|Belgium | 1979| 43.2| +|Britain | 1970| 40.7| +|Britain | 1979| 39.0| +|Canada | 1970| 35.2| +|Canada | 1979| 35.8| + +```r +ggplot(receiptData, aes(year, receipts, group = country)) + + geom_line() + + geom_text_repel(aes(label = country)) + + labs(x = "Year", y = "Government receipts as percentage of GDP") +``` + + + +This plot is not attractive, but it is useful for getting a handle on the +data. Whether [iterating through an exploratory data analysis]({{< ref +"/posts/art-of-data-science/index.md" >}}) or preparing a graphic for +publication, analysts will create many ugly graphics on the path to settling +on a design and refining it. + +For our first round of improvements, we can change the aspect ratio of +the graphic and arrange the country labels so they don’t overlap with +the data. We should also remove the “chart junk” in the background, such +as the background grid, and label only the years of interest on the +x-axis. + +```r +ggplot(receiptData, aes(year, receipts, group = country)) + + geom_line() + + geom_text_repel(aes(label = country), + data = filter(receiptData, year == 1970), + nudge_x = -0.5, hjust = 1, + direction = "y", size = 5) + + geom_text_repel(aes(label = country), + data = filter(receiptData, year == 1979), + nudge_x = 0.5, hjust = 0, + direction = "y", size = 5) + + scale_x_continuous(breaks = c(1970, 1979), limits = c(1966, 1983)) + + theme(panel.background = element_blank(), + axis.title = element_text(size = 16), + axis.text = element_text(size = 12)) + + labs(x = "Year", y = "Government receipts as percentage of GDP") +``` + + + +The [ggrepel](https://github.com/slowkow/ggrepel) package has done a +great job preventing the labels from overlapping; I usually use +`geom_text_repel()` instead of `geom_text()` during exploratory data +analysis. Here, however, the segments connecting the labels to data +points create confusing clutter. While these can be removed within the +function, our final figure will be easier to understand if we nudge +labels manually so that they’re as close to their data as possible. + +We can also drop the axes; the year labels will go right above the data, +and we’ll show each country’s value next to its label. Since we’re +losing the axis titles, we’ll also embed a caption in this version of +the graphic. + +Finally, we’ll change the typeface. Since we’re trying to make something +that would please Tufte, we’ll use a serif font. If you haven’t done so +before, you may need to run `loadfonts()` from the [extrafont +package](https://github.com/wch/extrafont) to tell R how to find system +fonts. We’ll also further boost our “data-ink ratio” by making the lines +thinner. + +```r +labelAdjustments <- tribble( + ~country, ~year, ~nudge_y, + "Netherlands", 1970L, 0.3, + "Norway", 1970L, -0.2, + "Belgium", 1970L, 0.9, + "Canada", 1970L, -0.1, + "Finland", 1970L, -0.8, + "Italy", 1970L, 0.4, + "United States", 1970L, -0.5, + "Greece", 1970L, 0.4, + "Switzerland", 1970L, -0.3, + "France", 1979L, 0.8, + "Germany", 1979L, -0.7, + "Britain", 1979L, 0.1, + "Finland", 1979L, -0.1, + "Canada", 1979L, 0.4, + "Italy", 1979L, -0.5, + "Switzerland", 1979L, 0.2, + "United States", 1979L, -0.1, + "Spain", 1979L, 0.3, + "Japan", 1979L, -0.2 + ) + +receiptData <- left_join(receiptData, labelAdjustments, + by = c("country", "year")) %>% + mutate(receipts_nudged = ifelse(is.na(nudge_y), 0, nudge_y) + receipts) + +update_geom_defaults("text", list(family = "Georgia", size = 4.0)) +ggplot(receiptData, aes(year, receipts, group = country)) + + # Slope lines + geom_line(size = 0.1) + + # Country names (manually nudged) + geom_text(aes(year, receipts_nudged, label = country), + data = filter(receiptData, year == 1970), + hjust = 1, nudge_x = -3) + + geom_text(aes(year, receipts_nudged, label = country), + data = filter(receiptData, year == 1979), + hjust = 0, nudge_x = 3) + + # Data values + geom_text(aes(year, receipts_nudged, label = sprintf("%0.1f", receipts)), + data = filter(receiptData, year == 1970), + hjust = 1, nudge_x = -0.5) + + geom_text(aes(year, receipts_nudged, label = sprintf("%0.1f", receipts)), + data = filter(receiptData, year == 1979), + hjust = 0, nudge_x = 0.5) + + # Column labels + annotate("text", x = c(1970, 1979) + c(-0.5, 0.5), + y = max(receiptData$receipts) + 3, + label = c("1970", "1979"), + hjust = c(1, 0)) + + # Plot annotation + annotate("text", x = 1945, y = 58, hjust = 0, vjust = 1, + label = paste("Current Receipts of Government as a", + "Percentage of Gross Domestic\nProduct, 1970 and 1979", + sep = "\n"), + family = "Georgia", size = 4.0) + + coord_cartesian(xlim = c(1945, 1990)) + + theme(panel.background = element_blank(), + axis.title = element_blank(), + axis.text = element_blank(), + axis.ticks = element_blank()) +``` + + + +## Why it’s worth it + +It took several iterations to get the aesthetics of this plot just +right, while an adept user of a graphics editor would be able to +recreate it in minutes. However, this initial time savings obscures +several advantages to completing this process in code as opposed to +switching to a tool like Illustrator. + +### R is free software + +All of the programs I used to create this graphic (and share it with +you) are [free +software](https://www.fsf.org/about/what-is-free-software), unlike +Adobe’s terrific but expensive Illustrator. +[Inkscape](https://inkscape.org/en/) is an excellent open source +alternative, but it is not as powerful as its commercial competitor. On +the other hand, [R](https://www.r-project.org/) is arguably the most +advanced and well-supported statistical analysis tool. Even if the +politics of the open source movement aren’t important, free is a better +price-point. + +### Code can be reproduced + +Anybody who wants to recreate the final figure using a different set of +countries, a new pair of years, or a favored economic indicator can run +the code above on their own data. With minimal tweaking, they will have +a graphic with aesthetics identical to those above. Reproducing this +graphic using a multi-tool workflow is more complicated; a novice would +first need to learn how to create a “rough draft” of it in software, and +then learn how to use a graphics editor to improve its appearance. + +### Scripted graphics are easier to update + +Imagine that an analyst discovered a mistake in their analysis that +needed to be corrected. Or imagine the less stressful situation where a +colleague suggested replacing some of the countries in the figure. In +such cases, the work of creating the graphic will need to be redone: the +analyst will need to add data or correct errors, generate a new plot in +software, and re-edit the plot in their graphics editor. Using a +scripted, code-based workflow, the analyst would only need to do the +first step, and possibly update some manual tweaks. The initial time +savings afforded by a graphics editor disappears after the first time +this happens. + +### Automation prevents errors + +Not only does scripted workflow make it easier to deal with errors, it +guards against them. When analysts adjust graphic elements in a GUI, +there’s a risk of mistakenly moving, deleting, or mislabeling data +points. Such mistakes are difficult to detect, but code-based workflows +avoid these risks; if the data source and analysis are error-free, then +the graphic will also be. + +These considerations are among the reasons why scripted analyses are +[considered best practice](https://peerj.com/preprints/3210/) in +statistical analysis. Most of Tufte’s advice on creating graphics is +excellent, but I recommend ignoring his suggestion to make the final +edits in a program like Illustrator. Learning how to make polished +graphics in software will ultimately save analysts time and help them +avoid mistakes. + diff --git a/content/posts/use-the-gpl/index.md b/content/posts/use-the-gpl/index.md @@ -0,0 +1,70 @@ +--- +title: "Just use the GPL" +description: "The GNU General Public License is the best license to attach to your small open-source projects." +date: 2022-10-18T20:46:57-07:00 +draft: False +categories: +- Programming +- Data Science +--- + +**Tl;dr:** if you choose to publish some code that you've written by +yourself, and you want attach an "open source" license to that code, you'll +probably be happiest if you choose the +[GPLv3](https://www.gnu.org/licenses/gpl-3.0.en.html). + +There are many of reasons to publish your code (or data analysis) with an +open source license (maybe it's something you've made [just for +fun](https://justforfunnoreally.dev/)), and there are nearly as many +licenses to choose from. Twenty years ago, when the free and open source +software (FOSS) phenomenon was starting to penetrate the public conscious, +the GNU GPL was practically synonymous with "open source". But in +contemporary practice, more permissive FOSS licenses are more popular (due +in part, I suspect, to the [encouragement of organizations such as +Microsoft-owned +GitHub](https://tom.preston-werner.com/2011/11/22/open-source-everything.html)). + +The GPL is a "copyleft" license, designed to use copyright law to spread +open source across the computing ecosystem; people who mix code with a GPL +license with code of their own must release the ensuing product under the +same license. The [MIT license](https://mit-license.org/), which was [the +most popular license for GitHub projects as of +2015](https://github.blog/2015-03-09-open-source-license-usage-on-github-com/), +is an example of a "permissive" license; it mainly protects the original +code author from claims of liability, and allows people to use it however +they wish. You can incorporate MIT-licensed code into a closed-source +project without asking for permission, or even informing the original author +of the code. + +I'm not here to evangelize FOSS, or argue that any license (or class of +license) is better than any other _in general_. The most successful and +important FOSS projects are community efforts, and the choice of license +should be made by the community. But while it might be true that most FOSS +_code_ is written as part of such projects, I would guess that most FOSS +_projects_ are small one-off efforts undertaken by individuals who happen to +have chosen to publish their code in a manner that allows its reuse. If +you're thinking of doing this, I recommend that you license your code under +the GPL. + +The solo-programmer (or data scientist) releasing a small project of their +own is best served by the GPL because it offers a compromise between +maintaining full control of their code (as does traditional copyright) and +supporting other FOSS projects. You might argue, "I'm not an open-source +zealot, I don't mind some projects being closed source!" That's not a +problem; if you release your own code under the GPL, you can still offer it +under different licenses on a case-by-case basis. If somebody contacts you +asking to use your code in their closed-source project—and you should +encourage people to do so—you get to decide whether their product, company, +and business model are things that you want to support. The only people who +are allowed to use your code without checking in with you are other +open-source developers releasing FOSS of their own. As a programmer +considering open-sourcing your project, this is presumably something that +you support. + +I'm actually not a fan of "intellectual property" restrictions; I believe +that copyright and patents do more harm than good for science, the arts, and +even commerce. However, as long as we live in a world with copyright laws, I +believe that we should use them to ensure that our values can flourish. I +haven't bothered changing the license on all of my (small and simple) public +projects—I'm not even sure it's worth the effort. However, moving forward, +almost everything I post will be available under the GPL. diff --git a/content/posts/violin-plots/index.Rmd b/content/posts/violin-plots/index.Rmd @@ -0,0 +1,124 @@ +--- +title: "Violin plots are great" +author: "Eamon Caddigan" +date: '2015-09-26' +output: html_document +layout: post +summary: Fiddling with a visualization technique that's not common in psychology (yet). +categories: dataviz R psych +--- + +```{r global_options, include=FALSE} +knitr::opts_chunk$set(cache=TRUE, echo=TRUE, warning=FALSE, message=FALSE, + fig.width=8, fig.height=5, fig.align="center") + +source("geom_flat_violin.R") +``` + +Anybody who's used the ggplot2 package in R is probably familiar with `geom_violin`, which creates [violin plots](https://en.wikipedia.org/wiki/Violin_plot). I'm not going to reproduce the Wikipedia article here; just think of violin plots as sideways density plots (which themselves are basically smooth histograms). They look like this: + +```{r} +library(ggplot2) +ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) + + geom_violin() +``` + +I wasn't familiar with this type of plot until I started using ggplot2. Judging by a recent conversation with friends (because my friends and I are nerds), that's not uncommon among people coming from psychology (but check out Figure 1 in the [recent report on reproducability in psychology](https://osf.io/ezcuj/wiki/home/) by the Open Science Collaboration). + +That's a shame, because this is a useful technique; a quick glance shows viewers the shape of the distribution and lets them easily estimate its mode and range. If you also need the median and interquartile range, it's simple to display them by overlaying a box plot (violin plots are usually made this way). + +```{r} +ggplot(mtcars, aes(x = factor(cyl), y = mpg)) + + geom_violin(aes(fill = factor(cyl))) + + geom_boxplot(width = 0.2) +``` + +### Violin plots vs. bar graphs + +Violin plots aren't popular in the psychology literature--at least among vision/cognition researchers. Instead, it's more common to see bar graphs, which throw away all of the information present in a violin plot. + +```{r} +library(dplyr) +mtcarsSummary <- mtcars %>% + group_by(cyl) %>% + summarize(mpg_mean = mean(mpg), + mpg_se = sqrt(var(mpg)/length(mpg))) + +ggplot(mtcarsSummary, aes(x = factor(cyl), y = mpg_mean, fill = factor(cyl))) + + geom_bar(stat = "identity") +``` + +Bar graphs highlight a single statistic of the analyst's choosing. In psychology (and many other fields), researchers use bar graphs to visualize the mean of the data, and usually include error bars to show the standard error (or another confidence interval). + +However, when audiences see bar graphs of means, they erroneously judge values that fall *inside* a bar (i.e., below the mean) as more probable than values equidistant from the mean but outside a bar ([Newman & Scholl, 2012](http://perception.research.yale.edu/papers/12-Newman-Scholl-PBR.pdf)). This bias doesn't affect violin plots because the region inside the violin contains *all* of the observed data. I'd guess that observers will correctly intuit that values in the wider parts of the violin are more probable than those in narrower parts. + +The mean and standard error are only useful statistics when you assume that your data are normally distributed; bar graphs don't help you check that assumption. For small sample size studies, it's more effective to just plot every single observation ([Weissgerber et al., 2015](http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002128)). Till Bergmann [explored this approach](http://tillbergmann.com/blog/articles/barplots-are-pies.html) in a post that includes R code. + +If it's important to display the mean and standard error, these values can be overlaid on any visualization. + +```{r, fig.width=11, fig.height=5} +library(gridExtra) + +plotBars <- ggplot(mtcarsSummary, aes(x = factor(cyl), y = mpg_mean, fill = factor(cyl))) + + geom_bar(aes(fill = factor(cyl)), stat = "identity") + + geom_errorbar(aes(y = mpg_mean, ymin = mpg_mean-mpg_se, ymax = mpg_mean+mpg_se), + color = "black", width = 0.4) + + ylim(0, 35) + + theme(legend.position = "none") + + ggtitle("Bar graph") + +plotPoints <- ggplot(mtcars, aes(x = factor(cyl), y = mpg, color = factor(cyl))) + + geom_point(aes(y = mpg, color = factor(cyl)), + position = position_jitter(width = 0.25, height = 0.0), + alpha = 0.6) + + geom_point(aes(y = mpg_mean), color = "black", size = 2, data = mtcarsSummary) + + geom_errorbar(aes(y = mpg_mean, ymin = mpg_mean-mpg_se, ymax = mpg_mean+mpg_se), + color = "black", width = 0.2, data = mtcarsSummary) + + ylim(0, 35) + + theme(legend.position = "none") + + ggtitle("Every observation") + +plotViolins <- ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) + + geom_violin(aes(y = mpg, fill = factor(cyl))) + + geom_point(aes(y = mpg_mean), color = "black", size = 2, data = mtcarsSummary) + + geom_errorbar(aes(y = mpg_mean, ymin = mpg_mean-mpg_se, ymax = mpg_mean+mpg_se), + color = "black", width = 0.2, data = mtcarsSummary) + + ylim(0, 35) + + theme(legend.position = "none") + + ggtitle("Violin plot") + +grid.arrange(plotBars, plotPoints, plotViolins, ncol = 3) +``` + +### Violin plots vs. density plots + +A violin plot shows the distribution's density using the width of the plot, which is symmetric about its axis, while traditional density plots use height from a common baseline. It may be easier to estimate relative differences in density plots, though I don't know of any research on the topic. More importantly, density plots (or histograms) readily display the density estimates, whereas violin plots typically don't present these. + +```{r} +ggplot(mtcars, aes(x = mpg, fill = factor(cyl))) + + geom_density(alpha = 0.6) +``` + +Figures like the one above quickly become crowded as the number of factors increases. It's easy to flip the coordinates and use faceting to construct figures similar to violin plots. + +```{r} +# trim = TRUE trims the tails to the range of the data, +# which is the default for geom_violin +ggplot(mtcars, aes(x = mpg, fill = factor(cyl))) + + geom_density(trim = TRUE) + + coord_flip() + + facet_grid(. ~ cyl) +``` + +I asked twitter about making plots like this without faceting. [David Robinson](http://varianceexplained.org/) came through with a [new geom that does it](https://gist.github.com/dgrtwo/eb7750e74997891d7c20). Like traditional violin plots, these toss out the density estimates--and currently only work with the development version of ggplot2--but they do the trick. + +```{r} +ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) + + geom_flat_violin() +``` + +### Use violin plots + +If you're into R's base graphics (why?), it looks like the [vioplot package](http://www.inside-r.org/packages/cran/vioplot/docs/vioplot) can make violin plots without using ggplot2. Seaborn appears to bring [very powerful violin plots](http://stanford.edu/~mwaskom/software/seaborn/generated/seaborn.violinplot.html) to python, but I haven't had much opportunity to explore the awesome pandas world that's emerged since I last used python for most of my analyses. + +Psychologists should use violin plots more often. They're ideal for displaying non-normal data, which we frequently encounter when looking at a single participant's performance (e.g., response times). More importantly, previous research--*in psychology*--has shown that viewers have difficulty interpreting bar graphs, and violin plots present a viable alternative. diff --git a/content/posts/violin-plots/index.md b/content/posts/violin-plots/index.md @@ -0,0 +1,188 @@ +--- +title: "Violin plots are great" +date: '2015-09-26' +description: Fiddling with a visualization technique that's not common in psychology (yet). +categories: +- Data Science +tags: +- R +- Dataviz +- Statistics +--- + +Anybody who's used the ggplot2 package in R is probably familiar with +`geom_violin`, which creates [violin +plots](https://en.wikipedia.org/wiki/Violin_plot). I'm not going to reproduce +the Wikipedia article here; just think of violin plots as sideways density +plots (which themselves are basically smooth histograms). They look like this: + +```r +library(ggplot2) +ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) + + geom_violin() +``` + + + +I wasn't familiar with this type of plot until I started using ggplot2. Judging +by a recent conversation with friends (because my friends and I are nerds), +that's not uncommon among people coming from psychology (but check out Figure 1 +in the [recent report on reproducability in +psychology](https://osf.io/ezcuj/wiki/home/) by the Open Science +Collaboration). + +That's a shame, because this is a useful technique; a quick glance shows +viewers the shape of the distribution and lets them easily estimate its mode +and range. If you also need the median and interquartile range, it's simple to +display them by overlaying a box plot (violin plots are usually made this way). + +```r +ggplot(mtcars, aes(x = factor(cyl), y = mpg)) + + geom_violin(aes(fill = factor(cyl))) + + geom_boxplot(width = 0.2) +``` + + + +### Violin plots vs. bar graphs + +Violin plots aren't popular in the psychology literature--at least among +vision/cognition researchers. Instead, it's more common to see bar graphs, +which throw away all of the information present in a violin plot. + +```r +library(dplyr) +mtcarsSummary <- mtcars %>% + group_by(cyl) %>% + summarize(mpg_mean = mean(mpg), + mpg_se = sqrt(var(mpg)/length(mpg))) + +ggplot(mtcarsSummary, aes(x = factor(cyl), y = mpg_mean, fill = factor(cyl))) + + geom_bar(stat = "identity") +``` + + + +Bar graphs highlight a single statistic of the analyst's choosing. In +psychology (and many other fields), researchers use bar graphs to visualize the +mean of the data, and usually include error bars to show the standard error (or +another confidence interval). + +However, when audiences see bar graphs of means, they erroneously judge values +that fall *inside* a bar (i.e., below the mean) as more probable than values +equidistant from the mean but outside a bar ([Newman & Scholl, +2012](http://perception.research.yale.edu/papers/12-Newman-Scholl-PBR.pdf)). +This bias doesn't affect violin plots because the region inside the violin +contains *all* of the observed data. I'd guess that observers will correctly +intuit that values in the wider parts of the violin are more probable than +those in narrower parts. + +The mean and standard error are only useful statistics when you assume that +your data are normally distributed; bar graphs don't help you check that +assumption. For small sample size studies, it's more effective to just plot +every single observation ([Weissgerber et al., +2015](http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002128)). +Till Bergmann [explored this +approach](http://tillbergmann.com/blog/articles/barplots-are-pies.html) in a +post that includes R code. + +If it's important to display the mean and standard error, these values can be +overlaid on any visualization. + +```r +library(gridExtra) + +plotBars <- ggplot(mtcarsSummary, aes(x = factor(cyl), y = mpg_mean, fill = factor(cyl))) + + geom_bar(aes(fill = factor(cyl)), stat = "identity") + + geom_errorbar(aes(y = mpg_mean, ymin = mpg_mean-mpg_se, ymax = mpg_mean+mpg_se), + color = "black", width = 0.4) + + ylim(0, 35) + + theme(legend.position = "none") + + ggtitle("Bar graph") + +plotPoints <- ggplot(mtcars, aes(x = factor(cyl), y = mpg, color = factor(cyl))) + + geom_point(aes(y = mpg, color = factor(cyl)), + position = position_jitter(width = 0.25, height = 0.0), + alpha = 0.6) + + geom_point(aes(y = mpg_mean), color = "black", size = 2, data = mtcarsSummary) + + geom_errorbar(aes(y = mpg_mean, ymin = mpg_mean-mpg_se, ymax = mpg_mean+mpg_se), + color = "black", width = 0.2, data = mtcarsSummary) + + ylim(0, 35) + + theme(legend.position = "none") + + ggtitle("Every observation") + +plotViolins <- ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) + + geom_violin(aes(y = mpg, fill = factor(cyl))) + + geom_point(aes(y = mpg_mean), color = "black", size = 2, data = mtcarsSummary) + + geom_errorbar(aes(y = mpg_mean, ymin = mpg_mean-mpg_se, ymax = mpg_mean+mpg_se), + color = "black", width = 0.2, data = mtcarsSummary) + + ylim(0, 35) + + theme(legend.position = "none") + + ggtitle("Violin plot") + +grid.arrange(plotBars, plotPoints, plotViolins, ncol = 3) +``` + + + +### Violin plots vs. density plots + +A violin plot shows the distribution's density using the width of the plot, +which is symmetric about its axis, while traditional density plots use height +from a common baseline. It may be easier to estimate relative differences in +density plots, though I don't know of any research on the topic. More +importantly, density plots (or histograms) readily display the density +estimates, whereas violin plots typically don't present these. + +```r +ggplot(mtcars, aes(x = mpg, fill = factor(cyl))) + + geom_density(alpha = 0.6) +``` + + + +Figures like the one above quickly become crowded as the number of factors +increases. It's easy to flip the coordinates and use faceting to construct +figures similar to violin plots. + +```r +# trim = TRUE trims the tails to the range of the data, +# which is the default for geom_violin +ggplot(mtcars, aes(x = mpg, fill = factor(cyl))) + + geom_density(trim = TRUE) + + coord_flip() + + facet_grid(. ~ cyl) +``` + + + +I asked twitter about making plots like this without faceting. [David +Robinson](http://varianceexplained.org/) came through with a [new geom that +does it](https://gist.github.com/dgrtwo/eb7750e74997891d7c20). Like traditional +violin plots, these toss out the density estimates--and currently only work +with the development version of ggplot2--but they do the trick. + +```r +ggplot(mtcars, aes(x = factor(cyl), y = mpg, fill = factor(cyl))) + + geom_flat_violin() +``` + + + +### Use violin plots + +If you're into R's base graphics (why?), it looks like the [vioplot +package](http://www.inside-r.org/packages/cran/vioplot/docs/vioplot) can make +violin plots without using ggplot2. Seaborn appears to bring [very powerful +violin +plots](http://stanford.edu/~mwaskom/software/seaborn/generated/seaborn.violinplot.html) +to python, but I haven't had much opportunity to explore the awesome pandas +world that's emerged since I last used python for most of my analyses. + +Psychologists should use violin plots more often. They're ideal for displaying +non-normal data, which we frequently encounter when looking at a single +participant's performance (e.g., response times). More importantly, previous +research--*in psychology*--has shown that viewers have difficulty interpreting +bar graphs, and violin plots present a viable alternative. + diff --git a/content/posts/violin-plots/unnamed-chunk-1-1.png b/content/posts/violin-plots/unnamed-chunk-1-1.png Binary files differ. diff --git a/content/posts/violin-plots/unnamed-chunk-2-1.png b/content/posts/violin-plots/unnamed-chunk-2-1.png Binary files differ. diff --git a/content/posts/violin-plots/unnamed-chunk-3-1.png b/content/posts/violin-plots/unnamed-chunk-3-1.png Binary files differ. diff --git a/content/posts/violin-plots/unnamed-chunk-4-1.png b/content/posts/violin-plots/unnamed-chunk-4-1.png Binary files differ. diff --git a/content/posts/violin-plots/unnamed-chunk-5-1.png b/content/posts/violin-plots/unnamed-chunk-5-1.png Binary files differ. diff --git a/content/posts/violin-plots/unnamed-chunk-6-1.png b/content/posts/violin-plots/unnamed-chunk-6-1.png Binary files differ. diff --git 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