# Adventures in R: Creating a Pseudo-CDF Plot for Binary Data

(Alternate title: “Ha, I’m Dumb”)
(Alternate alternate title: “Skip This if Statistics Bore You”)

You may recall a few days ago during one of my Blog Stats blogs I mentioned the problem of creating a cumulative distribution function-type plot for binary data, which would show the cumulative number of times one of the two binary variables occurred over some duration of another variable.

Um, let’s go to the actual example, ‘cause that description sucked.

Let’s say I have two variables called Blogs and Images for a set of data for which N = 2193. The variable Blogs gives the blog number for each post, so it runs from 1 to 2193. The variable Images is a binary variable and is coded 0 if the blog in question contains no image(s) and 1 if the blog contains 1 or more images.

Simple enough, right?

So what I was trying to do was create an easy-to-interpret visual that would show the increase in the cumulative number of blogs containing images over time, where time was measured by the Blogs variable.

Not being ultra well-versed in the world of visually representing binary data, this was the best I could come up with in the heat of the analysis: If you take a look at the y-axis, it becomes clear that due to the coding, the Images variable could only either equal 0 or 1. When it equaled 1, this plot drew a vertical black line at the spot on the x-axis that matched the corresponding Blogs variable. It’s not the worst graph (and if you scan it at the grocery store, you’ll probably end up with a bag of Fritos or something), but it’s not the easiest-to-interpret graph on the planet either, now is it?

What I was really looking for was some sort of cumulative distribution function (CDF) plot, but for binary data. I like how Wiki puts it: “Intuitively, [the CDF] is the “area so far” function of the probability distribution.” As you move right on the x-axis, the CDF curve lines up with the probability (given on the y-axis) that the variable, at that point on the x-axis, is less than or equal to the value indicated by the curve. Assuming your y-axis is set for probability (mine isn’t, but it’s still easy to interpret). This is all well and good for well-behaving ratio data, but what happens if I want to do such a plot for a dichotomously-coded variable?

1) Be a spazz and write some R code to get it done, or
2) Be an anti-spazz and look up if anybody’s written some R code to get it done.

I originally wanted to do A, which I did, but B was actually a lot harder than it should have been.

Let’s look at A first. I wanted to plot the number of surveys containing images against time, measured by the Blogs variable. Since I coded blogs containing images as 1 and blogs not containing images as 0, all I needed to get R to do was spit out a list of the cumulative sum of the Images variable at each instance of the Blogs variable (so a total of 2193 sums). Then plot it.

R and I have a…history when it comes to me attempting to write “for” loops. But it finally worked this time. I’ll just give you that little segment, ‘cause the rest of the code’s for the plotting parameters and too long/bothersome to throw on here.

```for (m in (1:length(ximage))){
newimage=ximage[1:m]
xnew=sum(newimage)
t=cbind(m,xnew)
points(t,type="h",pch="1")
}```

ximage is the name of the vector containing the coded Images variable. So what this little “for” loop does is create a new variable (newimage) for every vector length between 1 and 2193 instances of the Images variable. Another new variable (xnew) calculated the sum of 1s in each newimage. t combines the Blogs number (1 through 2193) with the matching xnew. Finally, the points of t are plotted (on a pre-created blank plot).

So. Wanna see? Woo!

So I actually figured this out on Wednesday, but I didn’t blog about it because I wanted to see if I could find a function that already does what I wanted. Why did it take an extra three days to find it? Because I couldn’t for the life of me figure out what that type of plot was called. It’s not a true CDF because it’s not a continuous variable we’re dealing with. But after obsessively searching (this is the reason for the alternate title—I should have known what this type of plot was called), I finally found a (very, very simple) function that makes what this is: a cumulative frequency graph (I know, I know, duh, right?).

So here’s the miniscule little bit of code needed to do what I did:

```cumfreq=cumsum(ximage)
plot(cumfreq, type="h")```

The built-in function (it was even in the damn base package. SHAME, Claudia, SHAME!!) cumsum gives a vector of the sum at each instance of ximage; plotting that makes the exact same graph as my code (except I manually fancied up my axes in my code). Cool, eh?

Maybe I’ll post my full code once I make it uncustomized to this particular problem.

# Pretty R

I love R. This is an established fact in the universe. The only thing I love more than R is revising code I’ve written for it.

For my thesis, I had to make a metric ton of plots. For each scenario I ran, I ran it for seven different fit indices. I included plots for four of these indices for every scenario. With a total of 26 scenarios, that’s a grand total of 104 plots (and one of the reasons why my thesis was 217 pages long).

Normally, once I write code for something and know it works, I like to take the time to clean up the code so that it’s short, as self-explanatory as possible, and given notations in places where it’s not self-explanatory. In the case of my thesis, however, my goal was not “make pretty code” but rather “crap out as many of these plots as fast as possible.” Thus, rather than taking the time to write code that would basically automate the plot-making process and only force me to change one or two lines for each different plot and scenario, I basically made new code for each and every single plot.

In hindsight, I realize that probably cost  me way more time than just sitting down and making a “template plot” code would have. In fact, I now know that it would have taken less time, as I have made it my project over the past few days to actually go back and create such code for a template plot that I could easily extend to all plots and all scenarios.

Side note: I’m going to be sharing code here, so if you have absolutely no interest in this at all, I suggest you stop reading now and skip down to today’s meme to conclude today’s blog.

This code is old code for a plot of the comparative fit index’s (CFI’s) behavior for a  1-factor model with eight indicators for an increasingly large omitted error correlation (for six different loading sizes; those are the colored lines). As you can see in the file, there are quite a few (okay, a lot) of lines “commented out,” as indicated by the pound signs in front of the lines of code. This is because for each chunk of code, I had to write a specific line for each of the different plots. Each of these customizing lines took quite awhile to get correct, as many of them refer to plotting the “λ = some number” labels at the correct coordinates as well as making sure the axis labels are accurate.

This other code, on the other hand, is one in which I need to change only the data file and the name of the y-axis. It’s a lot cleaner in the sense that there’s not a lot of messy commented out lines, lines are annotated regarding what they do, and—best of all—this took me maybe five hours to create but would make creating 104 plots so easy. Some of the aspects of “automating” plot-making were somewhat difficult to figure out, like making it so that the y-axis would be appropriately segmented labeled in all cases, and thus the code is still kind of messy in some places, but it’s a lot better than it was. Plus, now that I know that this shortened code works, I can go back in and make it even more simplified and streamlined.

Side-by-side comparison, old vs. new, respectively: Yeah, I know it’s not perfect, but it’s pretty freaking good considering I have to change like two lines of the code to get it to do a plot for another fit index. Huzzah!

30-Day Meme – Day 17: An art piece (painting, drawing, sculpture, etc.) that is your favorite.
As much as I love Dali’s Persistence of Memory, I have to say that one of my favorite paintings is Piet Mondrian’s Composition with Red, Blue, and Yellow. It’s ridiculously simple, but that’s what I like about it. There’s quite a lot of art I don’t “get” and I think Mondrian’s work may fall into that category. However, there’s something implicitly appealing about this to me. I love stuff that just uses primary colors and I really like squares/straight lines/structure. So I guess this is just a pretty culmination of all that.