Bob Williams recently posted a question to EVALTALK about open source software for plotting survey responses in three dimensions:

I’m wondering how to display Likert scale data in three dimensions (ie the Likert scores for each subject on 3 scale dimensions). My graphic software is not that sophisticated and I haven’t been able to find an open source equivalent…. that can plot something along three dimensions (X,Y,Z) like this:

X, Y, Z Subject A 2, 5, 8 Subject B 3, 5, 9 Subject C 3, 7, 3

Another evaluator, Bill Harris, recommended and ggplot2 in particular.

Bob’s question and the mention of inspired me to write up a brief demonstration of plotting multi-dimensional data. As I have mentioned in the past (see here, here, and here), plotting or mapping three or more dimensions can be difficult and potentially misleading because plots and maps are inherently two-dimensional. I would say that plotting three survey response dimensions actually requires plotting four dimensions: X, Y, Z, and the frequency of each X, Y, and Z combination. That’s because evaluators commonly have large data sets with repeated response patterns. I simulated a larger data set from Bob’s example in order to illustrate plotting four dimensions.

#Open a recording window (if using Windows). windows(record=T) #Manually read in the data. data.3D <- data.frame(Subject = c("A", "B", "C"), X = c(2, 3, 3), Y = c(5, 5, 7), Z = c(8, 9, 3)) data.3D #Larger data sets will contain frequently repeated combinations of responses. #Simulate a larger data set with repeated responses combinations. data.4D <- data.3D for(i in 1:200) { temp <- data.frame(Subject=factor(paste(as.character(data.3D[, 1]), i, sep=".")), X=round(jitter(data.3D[, 2], 7), 0), Y=round(jitter(data.3D[, 2], 7), 0), Z=round(jitter(data.3D[, 4], 7), 0)) data.4D <- rbind(data.4D, temp) } library(plyr) data.4D <- ddply(data.4D, c("X", "Y", "Z"), "nrow") names(data.4D)[which(names(data.4D)=="nrow")] <- "Frequency" data.4D <- data.4D[order(data.4D$Frequency, decreasing=T), ] #Scatterplot matrices pairs(data.3D[2:4], xlim=c(0, 10), ylim=c(0, 10), main="Responses to three Likert scale items") library(psych) pairs.panels(sapply(data.4D[1:3], jitter), xlim=c(0, 10), ylim=c(0, 10), ellipses=F, hist.col="blue", pch=1, scale=T, main="Responses to three Likert scale items")

#Load ggplot2 library; set theme without gray background. library(ggplot2) theme_set(theme_bw()) #Create a scatterplot with size and color varying by the third dimension. plot1 <- ggplot(data=data.3D, aes(x=X, y=Y, color=Z, size=Z)) + geom_point() + xlim(0, 10) + ylim(0, 10) + scale_colour_gradient(breaks=0:10, limits=c(0, 10), low="lightblue", high="darkblue") + scale_size_continuous(breaks=0:10, limits=c(0, 10)) + opts(title="Responses to three Likert scale items") plot1 #Create a jittered scatterplot with color varying by the third dimension #and size by response combination frequency. plot2 <- ggplot(data=data.4D, aes(x=X, y=Y, color=Z, size=Frequency)) + geom_jitter() + xlim(0, 10) + ylim(0, 10) + scale_colour_gradient(breaks=0:10, limits=c(0, 10), low="lightblue", high="darkblue") + scale_size_continuous() + opts(title="Responses to three Likert scale items") plot2

#Reshape data from wide to longer. data.3D.longer <- melt(data.3D, id.vars=c("Subject", "Y"), variable_name="Item") names(data.3D.longer)[which(names(data.3D.longer)=="value")] <- "Response" data.3D.longer #Create a scatterplot with faceted second and third dimensions. plot3 <- ggplot(data=data.3D.longer, aes(x=Response, y=Y)) + geom_point(color="blue") + xlim(0, 10) + ylim(0, 10) + facet_grid(. ~ Item) + opts(title="Responses to three Likert scale items") plot3 #Reshape simulated data from wide to longer. data.4D.longer <- melt(data.4D, id.vars=c("Y", "Frequency"), variable_name="Item") names(data.4D.longer)[which(names(data.4D.longer)=="value")] <- "Response" head(data.4D.longer) #Create a scatterplot with faceted second and third dimensions #and size varying by response combination frequency. plot4 <- ggplot(data=data.4D.longer, aes(x=Response, y=Y, size=Frequency)) + geom_jitter(color="blue") + xlim(0, 10) + ylim(0, 10) + facet_grid(. ~ Item) + opts(title="Responses to three Likert scale items") plot4