# Graphically exploring data using ggplot2

Your second step after importing should always be to look at the data. That means plotting lots of things, and getting a sense of how everything fits together. Never run a statistical test until you’ve looked at your data in as many ways as you can. Doing so can give you good intuitions about whether the comparisons you planned make sense to do, and whether any unexpected relationships are apparent in the data. The best tool for reproducible data exploration that I have used is Hadley Wickham’s ggplot2 package.

## A brief introduction to the mindset of ggplot

The first thing to note about ggplot2 is that it is better thought of as a data exploration tool than a plotting package (like base graphics in Matlab, R, or Python). In those systems, you typically create an x variable and a y variable, then plot them as something like a line, then maybe add a new line in a different colour. ggplot tries to separate your data from how you display it by making links between the data and the visual representations explicit, including any transformations. There’s a little introduction to this philosophy here.

For me, what this means in practice is that you need to start thinking in terms of long format data frames rather than separate x- and y vectors. A long format data frame is one where each value that we want on the y-axis in our plot is in a separate row (see wiki article here). The Cookbook for R has some good recipes for going between wide and long format data frames here. For example, imagine we have measured something (say, reaction time) in a within-subjects design where the same people performed the task under two conditions. For ggplot we want a data frame with columns like:

subject condition rt
s1 A 373
s1 B 416
s2 A 360
s2 B 387

not like:

subject rt condition A rt condition B
s1 373 416
s2 360 387

and not like (familiar to anyone plotting with Matlab or Matplotlib):

x = [s1, s2]
y_1 = [373, 360]
y_2 = [416, 387]

For the first few weeks of using ggplot2 I found this way of thinking about data took some getting used to, particularly when trying to do things as I’d done in Matlab. However, once you make the mental flip, the ggplot universe will open up to you.

## Contrast detection data example

Now we will look at the data from my data import post. This consists of data from a psychophysical experiment where five subjects detected sine wave gratings at different contrasts and spatial frequencies. You can download the data from my github repository here. For each trial, we have a binary response (grating left or right) which is either correct or incorrect. Each row in the data frame is a trial, which means that this is already in long format:

##   subject contrast     sf target_side response
## 1      S1 0.069483  0.500       right    right
## 2      S1 0.013124 40.000       right     left
## 3      S1 0.069483  4.472        left     left
## 4      S1 0.069483 40.000        left    right
## 5      S1 0.367879 13.375        left     left
## 6      S1 0.002479  0.500        left    right
##                              unique_id correct
## 1 544ee9ff-2569-4f38-b04e-7e4d0a0be4d2       1
## 2 b27fe910-e3ba-48fb-b168-5afb1f115d8f       0
## 3 72c9d6ce-0a90-4d4b-a199-03435c15291b       1
## 4 48b5bbb2-e6ee-4848-b77e-839ed5320c01       0
## 5 32a5cce4-3f8a-4e63-80c1-3fee3230d1bd       1
## 6 47ebce53-9d5a-48de-936b-25d5105a0784       0

### Baby steps

Building a plot in ggplot2 starts with the ggplot() function:

library(ggplot2)
fig <- ggplot(data = dat, aes(x = contrast, y = correct))

This command creates fig, which is a ggplot object, in our workspace. We’ve specified the data frame to use (dat), and two “aesthetics” using the aes() function. Aesthetics are how ggplot assigns variables in our data frame to things we want to plot. In this example we have specified that we want to plot contrast on the x-axis and correct on the y-axis.

We can try plotting this just by typing fig into the command window:

fig
## Error: No layers in plot

but this returns an error because we haven’t specified how we want to display the data. We must add a geom to the fig object (note the iterative notation, where we overwrite the fig object with itself plus the new element):

fig <- fig + geom_point()
fig

Now we get a plot of the data, with each correct trial as a point at 1 and each incorrect trial as a point at 0. But that’s not very informative, because there’s a lot of overplotting — we’re really interested in how often the subjects get the trials correct at each contrast level. That is, we want to know the proportion of correct responses.

To do that we could create a new data frame where we compute the mean of all correct values for each cell of our experiment (i.e. for each subject, at each level of contrast and spatial frequency). However, it’s also possible for ggplot2 to do that for us as we plot, using the stat_summary command:

fig <- fig + stat_summary(fun.data = "mean_cl_boot", colour = "red")
fig

The mean_cl_boot command computes the means and bootstrapped 95% confidence intervals on the mean, for all the y-values falling into each unique x-value. These are shown as the red points in the above plot. Type ?stat_summary and look at the examples (or run example(stat_summary) to get an idea of what you can do out-of-the-box with this command. It also allows you to define your own functions to summarise the y values for each value of x, so it’s incredibly flexible.

Since the contrast values in our experiment were sampled logarithmically, the values for all the small contrasts are all squished up to the left of the plot. Therefore, the last thing we might want to do with this basic plot is to log scale the x-axis:

fig <- fig + scale_x_log10()
fig

Now we can see that the mean proportion correct starts from 0.5 for low contrasts (i.e. 50% correct, or chance performance on the task) and gradually rises up to near 100% correct in an S-shaped fashion.

### Facets and smooths

The goal of this experiment was to see whether and how human visual sensitivity to contrast changes depending on the spatial scale of the information (loosely, whether the pattern is coarse or fine). While the basic data representation makes sense (i.e. looking at proportion correct), the plot above is not very useful because it averages over all the different subjects and over the experimental variable we’re most interested in (spatial frequency). Thus it doesn’t tell us anything about the goal of the experiment.

Here’s where ggplot2 gets really cool. We can apply the same basic plot to each subset of the data we’re interested in, in one line of code, by using faceting. First, here’s the basic plot again, but in a more succinct form (note how I string together subfunctions using the + sign across multiple lines):

fig <- ggplot(data = dat, aes(x = contrast, y = correct)) +
stat_summary(fun.data = "mean_cl_boot") +
scale_x_log10() +
scale_y_continuous(limits = c(0, 1))
fig

Now we want to do the same thing, but look at the data for each subject and spatial frequency separately. The facet_grid command allows us to lay out the data subsets on a grid. Since we want to compare how the performance shifts as a function of contrast within each subject, it makes sense to arrange the facets with subjects in each column and spatial frequencies in the rows. This is done by adding one element to the fig object above:

fig <- fig + facet_grid(sf ~ subject)  # specifies rows ~ columns of the facet_grid.
fig

<a href="http://tomwallisblog.files.wordpress.com/2014/04/unnamed-chunk-8.png"><img src="http://tomwallisblog.files.wordpress.com/2014/04/unnamed-chunk-8.png&quot; alt="unnamed-chunk-8" width="504" height="504" class="aligncenter size-full wp-image-289" /></a>

Now we get a replication of the basic x-y plot but for each subject and spatial frequency. The axes have been scaled identically by default so it's easy to see variation across the facets. If you follow down each column, you can see that performance as a function of contrast first improves and then gets worse again, relative to the first spatial frequency (0.5 cycles of the grating per degree of visual angle). To see this more clearly it will help to add trend lines, which again we can do in one line in ggplot2:

fig <- fig + stat_smooth(method = "glm", family = binomial())
fig

In this case I've used a Generalised Linear Model specifying that we have binomial data (this defaults to a logistic link function). The blue lines show the maximum likelihood model prediction and the grey shaded regions show the 95% confidence limits on these predictions. However, this model isn't taking account of the fact that we know performance will asymptote at 0.5 (because this is chance performance on the task), so the slopes look all wrong. A psychophysicist would now fit this model with a custom link function that asymptotes at 0.5. Such link functions are implemented in Ken Knoblauch's psyphy package for R.

We could implement that within ggplot2 as well, but instead here I will use a Generalised Additive Model (GAM) to show more flexible fitting of splines. This could come in handy if you didn't have a good approximation for the functional form for your dataset (i.e. you have only vague expectations for what the relationship between x and y should be).

library(mgcv)
## This is mgcv 1.7-28. For overview type 'help("mgcv-package")'.
fig <- fig + stat_smooth(method = "gam", family = binomial(),
formula = y ~ s(x, bs = "cs", k = 3),
colour = "red")
fig

<a href="http://tomwallisblog.files.wordpress.com/2014/04/unnamed-chunk-10.png"><img src="http://tomwallisblog.files.wordpress.com/2014/04/unnamed-chunk-10.png&quot; alt="unnamed-chunk-10" width="504" height="504" class="aligncenter size-full wp-image-291" /></a>

The above code fits a cubic spline ("cs") with three knots ("k=3"). Essentially this is a really flexible way to consider nonlinear univariate relationships (a bit like polynomial terms in normal GLMs). You can see that these data are probably overfit (i.e. the model is capturing noise in the data and is unlikely to generalise well to new data), and some of the confidence regions are pretty crazy (because the model is so flexible and the data are not well sampled for the observer's sensitivity) but that it gives a reasonable impression for the purposes of exploration. If you scan down the columns for each subject, you can see that the point on the x-axis where the red curves have the steepest slope is furthest to the left for spatial frequencies of 1.5 and 4.5 cycles per degree. These observers reach a higher level of performance with less contrast than in the other conditions: their thresholds are lower. Humans are most sensitive to contrast in the 1–4 cycles per degree range (Campbell and Robson, 1968).

### Appearance matters

Finally, we can adjust the appearance of our plot. First, let's get rid of the ugly decimal-point labels in the spatial frequency dimension by creating a new variable, a factor of sf:

dat\$sf_factor <- factor(dat\$sf)
levels(dat\$sf_factor) <- round(sort(unique(dat\$sf)), digits = 1)  # rename levels

Second, some people don't like the grey background theme of the ggplot default. It took me a little while to get used to, but now I quite like it: by attending to things that are darker than the background you can concentrate on the data, but the gridlines are there if you need them. However, if you prefer a more traditional plot, just add the classic theme (fig + theme_classic()). Personally my favourite is now theme_minimal(). So having done all this, our entire plot call becomes:

fig <- ggplot(data = dat, aes(x = contrast, y = correct)) +
facet_grid(sf_factor ~ subject) +
stat_summary(fun.data = "mean_cl_boot") +
stat_smooth(method = "gam", family = binomial(),
formula = y ~ s(x, bs = "cs", k = 3)) +
scale_x_log10(name = "Contrast") +
scale_y_continuous(name ="Proportion Correct",
limits=c(0, 1), breaks=c(0, 0.5, 1)) +
theme_minimal()
fig

## Going further with ggplot2

What would happen if we wanted to see whether performance changed depending on the side of the retina (left or right of fixation) the grating was presented? Perhaps sensitivity is different, or the person has a bias in responding to a side. We can look at this by simply adding a new argument in the aes() function when we call ggplot: colour = target_side. Try it at home! There's an example of doing this in the plots.R script on my github page. Here you can also see how the plots are saved to the /figs subdirectory, where a document file (like a .tex doc) can be set up to automatically pull in the figures. You can also see a nice vector graphic version of the final figure above.

This post was just a little taste of what you can do in ggplot2, with a focus on vision science data. There are many more thorough introductions for ggplot2 available on the web, like here and here. I find that The Cookbook for R has heaps of useful little tips and code snippets, as well as showing you lots of basic ggplot things in the plotting section. If you want an example of some published figures made with ggplot2 as well as the code that generated them, you can see our recent paper here.

# Data import: follow-up

This is a quick update post following up my data import post. I have put a script file into the /funs/ directory of my blog project that repeats the import and saving stuff I stepped through in that last post. You can find it on Github here. Feel free to fork that repository, but if you don’t want to deal with all the git and version control stuff you can just click the Download Zip button on the right to get all the files as a zip archive. The data_import.R script can be sourced via RStudio or an R command prompt, and will reproduce the contrast_data.RData file in the /out/ directory. For this to work, your working directory needs to be set to the project’s root directory; the easiest way to do this is by setting up a Project in RStudio located in the root directory. When you open your R project in RStudio, the working directory will automatically be set to the root.

I also wanted to point you to this article on using the “good parts” of R. It’s certainly true that some of R’s base syntax and functions are kind of horrible; using those add-on packages is really helpful. I learned some new things there too – like the use of data.table.

# Data import in R

In this post, I will demonstrate one way to import and collate a data set (using the R environment). This is a follow up to a post in which I argued that a good principle for reproducible research is to avoid humans touching data. That is, once the data from the experiment are saved we want them to be “read only” and never altered by a human in some undocumented way (such as editing in a spreadsheet).

Using R is not the only way to do the following, and I would encourage you to replicate these steps in the environment of your choice. If your scientific computing environment makes following what I do here really hard, maybe you should consider switching…

## Data set

First, we need a data set. To make this more interesting let’s build on a classic paper from vision science.

Imagine we’ve conducted an experiment similar to the classic Campbell & Robson (1968)^1 study but with a few modifications. As a participant in our experiment, you’re seated in front of a monitor showing a grey screen. You’re going to be shown a sequence of trials, and for each trial you make a response with a button press.
On each trial you are asked to keep your eyes on a small dot on the centre of the screen. On each trial, a pattern of dark-and-light stripes (a grating) is shown on one side of the screen (left or right of your eye position). The computer randomly decides whether to present the grating on the left or on the right (the other side just stays as the grey background). You have to respond either “grating on the left” or “grating on the right” — you can’t say “I don’t know”. The computer waits for your response before showing the next trial.
We are going to vary both the contrast of the grating pattern (how different from grey the dark and light stripes are) and also the spatial frequency of the pattern (how wide the bars are) over trials.

If the contrast is so low that you can’t see the grating, your responses across many trials will be near chance performance (here 50% correct). If the grating is really easy to see, your performance will be near 100%. We determine how your performance on the task changes as a function of contrast, for each spatial frequency tested.

We’ve tested 5 subjects in this experiment, showing them 7 contrasts at 5 spatial frequencies, with the targets equally on the left and right. They did 20 trials for each condition (so each subject did 7 * 5 * 20 * 2 = 1400 trials). Let’s say that our experiment program saves the data as a .csv file in our project’s /data/ directory. We have one .csv file per subject, and one of them might look something like this when opened in a text editor:

A few things to notice here: each comma , in the file denotes a new column, and each new line denotes a row. Secondly, note that there’s a header row: the first line of the file contains column names for our variables.

Finally, notice how our target_side and response columns contain text strings (left and right). The reason I’ve done this is that it makes the data easily human-readable. It’s obvious what the entries mean (imagine if instead target_side could be either 0 or 1). This can be used to great effect to avoid needing a data key later.

## Installing R

This couldn’t be simpler. Go here and get the right binary for your system, install it, then immediately go here and get RStudio, which is awesome. To follow along with my stuff here, you can install any packages I use (the library() calls in future posts) via RStudio’s “Packages” tab.

While I’m going to demonstrate this stuff using R, I would encourage you to follow along in your package of choice. I’d be interested to know how easy / hard it is to duplicate this stuff in other environments (for example, last I used Matlab handling .csv files with mixed numeric and text was a massive pain).

## Reading each file into R and putting them together

Now we want to read each subject’s data file into R, then stick the files together to create one big data file.

### The paste0 command

To do this, I’m going to make use of the paste command, which allows you to concatenate (stick together) strings. Actually, I’m going to use the paste0 command, which is a shortcut for paste. By default paste adds a space between each pasted item, which we usually don’t want. paste0 just puts together the items you give it. For example:

paste0("A text string", 42, ", another text string")
## [1] "A text string42, another text string"

What we get is that R automatically converts the number “42″ to text, and sticks it together with the preceeding and subsequent stuff. Usefully, we can also include ranges of numbers, which produces a number of strings:

paste0("A text string", 41:43, ", another text string")
## [1] "A text string41, another text string"
## [2] "A text string42, another text string"
## [3] "A text string43, another text string"

The file for subject one is labelled like this:

“data_S1.csv”

and subject 2′s results are in the file “data_S2.csv”, and so on. The following script uses a for loop to read in the data, then appends it to a data frame called dat.

dat <- data.frame()  # create an empty data frame.
for (i in 1:5) {
file <- paste0(getwd(), "/data/data_S", i, ".csv")
this_dat <- read.csv(file = file)  # read the subject's file, put in a data frame called this_dat
dat <- rbind(dat, this_dat)  # append to larger data frame
}

What this for loop gives us is a data frame object called dat. Let’s examine it using the str (“structure”) command:

str(dat)
## 'data.frame':  7000 obs. of  6 variables:
##  \$ subject    : Factor w/ 5 levels "S1","S2","S3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  \$ contrast   : num  0.0695 0.0131 0.0695 0.0695 0.3679 ...
##  \$ sf         : num  0.5 40 4.47 40 13.37 ...
##  \$ target_side: Factor w/ 2 levels "left","right": 2 2 1 1 1 1 2 2 1 2 ...
##  \$ response   : Factor w/ 2 levels "left","right": 2 1 1 2 1 2 2 1 2 2 ...
##  \$ unique_id  : Factor w/ 7000 levels "00004355-345d-403e-b244-79c8adb8f1f8",..: 451 983 595 395 277 387 132 809 711 582 ...

## Data frames

Data frames are the most important (or at least useful) data type in R, and what you’re going to be using a lot. Many methods use data frames. The most awesome thing about a data frame is that it can store both numerical data and text. This allows us to read in that csv file no problem, where other basic data types would really struggle (I’m looking at you, Matlab).

Furthermore, data frames can explicitly treat text as a “factor”, which means that when you fit a model, it won’t try to use this numerically but will rather dummy code it. Note how in the str call above, several variables (in fact, all those that were strings in the .csv file) have been imported as factors. Let’s look at some behaviour of factors now by looking at the summary of our data:

summary(dat)
##  subject      contrast            sf        target_side   response
##  S1:1400   Min.   :0.0025   Min.   : 0.50   left :3500   left :3488
##  S2:1400   1st Qu.:0.0057   1st Qu.: 1.50   right:3500   right:3512
##  S3:1400   Median :0.0302   Median : 4.47
##  S4:1400   Mean   :0.0927   Mean   :11.97
##  S5:1400   3rd Qu.:0.1599   3rd Qu.:13.37
##            Max.   :0.3679   Max.   :40.00
##
##                                 unique_id
##  00448030-70e5-4010-b954-4a35c107841e:   1
##  0086b264-17ed-4fbb-8e32-8c7814ae6b6a:   1
##  00a070b7-f849-4727-a710-0453d6f27c50:   1
##  00b414aa-3f65-4b4d-8d12-f0d41ec7ae42:   1
##  (Other)                             :6994

See how we get some distribution summaries for the covariates (e.g. contrast), but only told how many instances of each factor level there are? Neat huh?

## Data munging

In our data file there is a “response” variable, that is a string of the side the subject responded to. What we really want however is to know whether they got the trial correct. That is, is the string in “target_side” the same as the string in “response”? Let’s create this new variable now:

dat\$correct <- 0  # initialises the variable 'correct' with all zeros.
dat\$correct[dat\$target_side == dat\$response] <- 1  # logical indexing; if target == response, returns TRUE
summary(dat\$correct)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
##    0.00    1.00    1.00    0.77    1.00    1.00
hist(dat\$correct)

Now we have a variable in the data frame dat that gives a 1 where the subject was correct and a 0 elsewhere. In the next post, I will show some basic graphical exploration of this data set using the ggplot2 package.

## PS

This blog was written in R Markdown (in R Studio as a .Rmd file -> “knit HTML”, then paste the .md code directly into wordpress… too easy!)

You can check out the repository for this and some upcoming posts at my Github page.

[1] Campbell, F. W., & Robson, J. G. (1968). Application of Fourier analysis to the visibility of gratings. The Journal of Physiology, 197(3), 551–566.

# Python setup

Ben Vincent over at inferencelab.com has a nice post on two simple ways to get set up with a Python scientific computing environment. I hadn’t heard of Wakari before – thanks Ben! Basically this lets you run python scripts on cloud computers, and share these scripts with others without requiring them to set up an identical software installation to yours. You could send collaborators, reviewers or readers a link to a web based interface that would allow them to re-run your analysis. Pretty cool! Yay free software!

# Version control Part 2: Remote repository

The second stage in my version control workflow is to push my local changes to a remote repository. A remote repository is basically an identical repository to the one stored locally on your computer, but is on a remote server somewhere in the internet ether. Much like using dropbox, this provides an additional layer of backup for your project (with the advantage of a full version history). So if you ever lose your local copy of your project for some reason, you can just re-clone it from the remote repository to get everything back (not including files that were never committed, of course). ** NOTE that I don’t recommend using this, or any one tool, as your only backup: your scientific projects should be backed up with multiple means, in multiple locations, all the time **.

However, the main advantage of pushing things up to a remote repository is that this facilitates sharing. With various methods that I’ll outline below, you can keep the remote repository private and invite your collaborators to use it, or you can make it public so that anyone can see it, clone it, etc (though of course in this case, you control whether to use anyone else’s changes or not).

I use two services to host remote repositories: Github and Bitbucket. These companies offer similar services with a few key differences, which means that in my current workflow I switch between both.

#### Github

Github is the “one that started it all”. They have a really slick web interface, awesome graphs for looking at repository activity, great tools for interacting with other members, wikis and issue trackers that can be associated with a repo, and a big user base. Plus they offer the free GUI that I talked about in my last post. However, their pricing structure is that they charge you to have private repositories. That is, they host unlimited public repositories – i.e. anyone can see the respository’s contents, contributors and history. If you want to keep your repository to a few invited collaborators however, you need a paid account. Seven dollars a month gets you 5 private repositories. The idea here would be that you have some projects on the go, then when one is ready for sharing (say, the article is accepted), you switch the repo from “private” to “public”. Now everyone can see your code and data, and you have another private repo slot to use.

However, since I know that I would need more than 5 private repos (projects languishing, maybe one day, etc), I’ve so far avoided a paid Github account (the idea of just working with everything open is for another post). Thankfully we’re helped by Bitbucket.

UPDATE: Thanks to Ariel Rokem for pointing out in the comments that Github actually offer a Micro plan (5 private repositories) for educational users. Send them an email with your educational email address at this site.

#### Bitbucket

Bitbucket is basically Github with a different pricing structure. Their web interface and user community is a fair bit behind Github. For scientists however, the advantage is that they offer unlimited free private code repositories. The catch is that you’re only allowed 5 collaborators (i.e. people who have joined any of your repositories, like co-authors). However, an academic email address will get you unlimited collaborators too, so this is essentially a free service.

#### Using Remote Repositories on Bitbucket with the Github GUI

Generously, Github have not restricted their GUI to use Github repositories. So what I do is basically use the Github GUI to manage my version control day-to-day, but push the local repository to a remote repository on Bitbucket. I can share this with collaborators and keep it private.

Here’s how:

1. Set up a local repository as explained here.
3. Follow the steps to set up a new repository. Select “git” as the version control flavour.
4. This should then give you an option to “push up an existing repository”.
5. On the command line that starts `git remote add origin`, copy the following link to your repository (something like `git@bitbucket.org:tomwallis/test.git`. This might look different, depending whether you’re using SSH or a password to authenticate (if you’re using a password, your link will start with https; either works). The Bitbucket / Github help pages will explain how to set up an SSH key if you’d like to do that.
6. In the Github GUI, open your local repository and go to the “Settings” pane. On the line that says “Primary Remote Repository”, paste in the link to your repo. Hit “Update Remote”.
7. Switch back to the “Changes” pane of the Github GUI. See the button in the top left? It should have changed from “Push to Github” to “Sync Branch” (if not, close and re-open the Github GUI).
8. Press this button. You might be asked for your password (depending whether you’ve set up an SSH key).
9. Github should synch, and the list of “unsynched commits” should disappear.