When analyzing a questionnaire, one often wants to view the correlation between two or more Likert questionnaire item’s (for example: two ordered categorical vectors ranging from 1 to 5).
When dealing with several such Likert variable’s, a clear presentation of all the pairwise relation’s between our variable can be achieved by inspecting the (Spearman) correlation matrix (easily achieved in R by using the “cor.test” command on a matrix of variables). Yet, a challenge appears once we wish to plot this correlation matrix. The challenge stems from the fact that the classic presentation for a correlation matrix is a scatter plot matrix – but scatter plots don’t (usually) work well for ordered categorical vectors since the dots on the scatter plot often overlap each other.
There are four solution for the point-overlap problem that I know of:
Jitter the data a bit to give a sense of the “density” of the points
Use a color spectrum to represent when a point actually represent “many points”
Use different points sizes to represent when there are “many points” in the location of that point
Add a LOWESS (or LOESS) line to the scatter plot – to show the trend of the data
In this post I will offer the code for the a solution that uses solution 3-4 (and possibly 2, please read this post comments). Here is the output (click to see a larger image):
The integration of R into online web services is (for me) one of the more exciting prospects in R’s future. That is way I was very excited coming across Jamie Love’s recent creation: R-Node.
What is R-Node
R-Node is a (open source) web front-end to R (the statistical analysis package).
Using this front-end, you can from any web browser connect to an R instance running on a remote (or local) server, and interact with it, sending commands and receiving the responses. In particular, graphing commands such as plot() and hist() will execute in the browser, drawing the graph as an SVG image.
You can see a live demonstration of this interface by visiting: http://69.164.204.238:2904/ And using the following user/password login info: User: pvdemouser Password: svL35NmPwMnt (This link was originally posted here)
Here are some screenshots:
In the second screenshot you see the results of the R command ‘plot(x, y)’ (with the reimplementation of plot doing the actual plotting), and in the fourth screenshot you see a similar plot command along with a subsequent best fit line (data points calculated with ‘lowess()’) drawn in.
Once in, you can try out R by typing something like:
x <- rnorm(100)
plot(x, main="Random numbers")
l <- lowess(x)
lines (l$y)
The plot and lines commands will bring up a graph - you can escape out of it, download the graph as a SVG file, and change the graph type (e.g. do: plot (x, type="o") ). Many R commands will work, though only the hist(), plot() and lines() work for graphing. Please don't type the R command q() - it will quit the server, stopping it working for everyone! Also, as everyone shares the same session for now, using more unique variable name than 'x' and 'l' will help you.
Currently there is only limited error checking but the code continues to be improved and developed. You can download it from: http://gitorious.org/r-node
How do you may imagine yourself using something like this? Feel invited to share with me and everyone else in the comments.
In this post I will provide R code that implement’s the combination of repeated running quantile with the LOESS smoother to create a type of “quantile LOESS” (e.g: “Local Quantile Regression”).
This method is useful when the need arise to fit robust and resistant (Need to be verified) a smoothed line for a quantile (an example for such a case is provided at the end of this post).
If you wish to use the function in your own code, simply run inside your R console the following line:
In recent years, a growing need has arisen in different fields, for the development of computational systems for automated analysis of large amounts of data (high-throughput). Dealing with non-standard noise structure and outliers, that could have been detected and corrected in manual analysis, must now be built into the system with the aid of robust methods. […] we use a non-standard mix of robust and resistant methods: LOWESS and repeated running median.
The motivation for this technique came from “Path data” (of mice) which is
prone to suffer from noise and outliers. During progression a tracking system might lose track of the animal, inserting (occasionally very large) outliers into the data. During lingering, and even more so during arrests, outliers are rare, but the recording noise is large relative to the actual size of the movement. The statistical implications are that the two types of behavior require different degrees of smoothing and resistance. An additional complication is that the two interchange many times throughout a session. As a result, the statistical solution adopted needs not only to smooth the data, but also to recognize, adaptively, when there are arrests. To the best of our knowledge, no single existing smoothing technique has yet been able to fulfill this dual task. We elaborate on the sources of noise, and propose a mix of LOWESS (Cleveland, 1977) and the repeated running median (RRM; Tukey, 1977) to cope with these challenges
If all we wanted to do was to perform moving average (running average) on the data, using R, we could simply use the rollmean function from the zoo package. But since we wanted also to allow quantile smoothing, we turned to use the rollapply function.
R function for performing Quantile LOESS
Here is the R function that implements the LOESS smoothed repeated running quantile (with implementation for using this with a simple implementation for using average instead of quantile):
Someone on the R mailing list (link) asked: how can you easily (daily) collect data from many people into a spreadsheet and then analyse it using R.
The answer people gave to it where on various ways of using excel. But excel files (at least for now), are not “on the cloud”. A better answer might be to create a google form that will update a google spreadsheet that will then be read by R.
If my last sentence wasn’t clear to you, then this post is for you.
JRR Tolkien wrote a story (sans hobbits) called ‘Leaf by Niggle’ that has always resonated with me. I offer you an imperfect, incomplete tree (but my roof is intact).
Suggestions for improvements are encouraged.
And here is the link tree for the document (for your easy reviewing of the offered content) :
In this post I showcase a nice bar-plot and a balloon-plot listing recommended Nutritional supplements , according to how much evidence exists for thier benefits, scroll down to see it(and click here for the data behind it) * * * * The gorgeous blog “Information Is Beautiful” recently publish an eye candy post showing a “balloon race” image (see a static version of the image here) illustrating how much evidence exists for the benefits of various Nutritional supplements (such as: green tea, vitamins, herbs, pills and so on) . The higher the bubble in the Y axis score (e.g: the bubble size) for the supplement the greater the evidence there is for its effectiveness (But only for the conditions listed along side the supplement).
There are two reasons this should be of interest to us:
This shows a fun plot, that R currently doesn’t know how to do (at least I wasn’t able to find an implementation for it). So if anyone thinks of an easy way for making one – please let me know.
The data for the graph is openly (and freely) provided to all of us on this Google Doc.
The advantage of having the data on a google doc means that we can see when the data will be updated. But more then that, it means we can easily extract the data into R and have our way with it (Thanks to David Smith’s post on the subject)
For example, I was wondering what are ALL of the top recommended Nutritional supplements, an answer that is not trivial to get from the plot that was in the original post.
In this post I will supply two plots that present the data: A barplot (that in retrospect didn’t prove to be good enough) and a balloon-plot for a table (that seems to me to be much better).
Barplot (You can click the image to enlarge it)
The R code to produce the barplot of Nutritional supplements efficacy score (by evidence for its effectiveness on the listed condition).
# loading the data
supplements.data.0 <- read.csv("http://spreadsheets.google.com/pub?key=0Aqe2P9sYhZ2ndFRKaU1FaWVvOEJiV2NwZ0JHck12X1E&output=csv")
supplements.data <- supplements.data.0[supplements.data.0[,2] >2,] # let's only look at "good" supplements
supplements.data <- supplements.data[!is.na(supplements.data[,2]),] # and we don't want any missing data
supplement.score <- supplements.data[, 2]
ss <- order(supplement.score, decreasing = F) # sort our data
supplement.score <- supplement.score[ss]
supplement.name <- supplements.data[ss, 1]
supplement.benefits <- supplements.data[ss, 4]
supplement.score.col <- factor(as.character(supplement.score))
levels(supplement.score.col) <- c("red", "orange", "blue", "dark green")
supplement.score.col <- as.character(supplement.score.col)
# mar: c(bottom, left, top, right) The default is c(5, 4, 4, 2) + 0.1.
par(mar = c(5,9,4,13)) # taking care of the plot margins
bar.y <- barplot(supplement.score, names.arg= supplement.name, las = 1, horiz = T, col = supplement.score.col, xlim = c(0,6.2),
main = c("Nutritional supplements efficacy score","(by evidence for its effectiveness on the listed condition)", "(2010)"))
axis(4, labels = supplement.benefits, at = bar.y, las = 1) # Add right axis
abline(h = bar.y, col = supplement.score.col , lty = 2) # add some lines so to easily follow each bar
Also, the nice things is that if the guys at Information Is Beautiful will update there data, we could easily run the code and see the updated list of recommended supplements.
Balloon plot So after some web surfing I came around an implementation of a balloon plot in R (Thanks to R graph gallery) There where two problems with using the command out of the box. The first one was that the colors where non informative (easily fixed), the second one was that the X labels where overlapping one another. Since there is no "las" parameter in the function, I just opened the function up, found where this was plotted and changed it manually (a bit messy, but that's what you have to do sometimes...)
Here are the result (you can click the image for a larger image):
And here is The R code to produce the Balloon plot of Nutritional supplements efficacy score (by evidence for its effectiveness on the listed condition). (it's just the copy of the function with a tiny bit of editing in line 146, and then using it)
Daniel Malter just shared on the R mailing list (link to the thread) his code for performing the Siegel-Tukey (Nonparametric) test for equality in variability. Excited about the find, I contacted Daniel asking if I could republish his code here, and he kindly replied “yes”. From here on I copy his note at full.
My goal in this post is to give an overview of Friedman’s Test and then offer R code to perform post hoc analysis on Friedman’s Test results. (The R function can be downloaded from here)
Preface: What is Friedman’s Test
Friedman test is a non-parametric randomized block analysis of variance. Which is to say it is a non-parametric version of a one way ANOVA with repeated measures. That means that while a simple ANOVA test requires the assumptions of a normal distribution and equal variances (of the residuals), the Friedman test is free from those restriction. The price of this parametric freedom is the loss of power (of Friedman’s test compared to the parametric ANOVa versions).
The hypotheses for the comparison across repeated measures are:
H0: The distributions (whatever they are) are the same across repeated measures
H1: The distributions across repeated measures are different
The test statistic for the Friedman’s test is a Chi-square with [(number of repeated measures)-1] degrees of freedom. A detailed explanation of the method for computing the Friedman test is available on Wikipedia.
Performing Friedman’s Test in R is very simple, and is by using the “friedman.test” command.
Post hoc analysis for the Friedman’s Test
Assuming you performed Friedman’s Test and found a significant P value, that means that some of the groups in your data have different distribution from one another, but you don’t (yet) know which. Therefor, our next step will be to try and find out which pairs of our groups are significantly different then each other. But when we have N groups, checking all of their pairs will be to perform [n over 2] comparisons, thus the need to correct for multiple comparisons arise. The tasks: Our first task will be to perform a post hoc analysis of our results (using R) – in the hope of finding out which of our groups are responsible that we found that the null hypothesis was rejected. While in the simple case of ANOVA, an R command is readily available (“TukeyHSD”), in the case of friedman’s test (until now) the code to perform the post hoc test was not as easily accessible. Our second task will be to visualize our results. While in the case of simple ANOVA, a boxplot of each group is sufficient, in the case of a repeated measures – a boxplot approach will be misleading to the viewer. Instead, we will offer two plots: one of parallel coordinates, and the other will be boxplots of the differences between all pairs of groups (in this respect, the post hoc analysis can be thought of as performing paired wilcox.test with correction for multiplicity).
R code for Post hoc analysis for the Friedman’s Test
The analysis will be performed using the function (I wrote) called “friedman.test.with.post.hoc”, based on the packages “coin” and “multcomp”. Just a few words about it’s arguments:
formu – is a formula object of the shape: Y ~ X | block (where Y is the ordered (numeric) responce, X is a group indicator (factor), and block is the block (or subject) indicator (factor)
data – is a data frame with columns of Y, X and block (the names could be different, of course, as long as the formula given in “formu” represent that)
All the other parameters are to allow or suppress plotting of the results.
friedman.test.with.post.hoc <- function(formu, data, to.print.friedman = T, to.post.hoc.if.signif = T, to.plot.parallel = T, to.plot.boxplot = T, signif.P = .05, color.blocks.in.cor.plot = T, jitter.Y.in.cor.plot =F)
{
# formu is a formula of the shape: Y ~ X | block
# data is a long data.frame with three columns: [[ Y (numeric), X (factor), block (factor) ]]
# Note: This function doesn't handle NA's! In case of NA in Y in one of the blocks, then that entire block should be removed.
# Loading needed packages
if(!require(coin))
{
print("You are missing the package 'coin', we will now try to install it...")
install.packages("coin")
library(coin)
}
if(!require(multcomp))
{
print("You are missing the package 'multcomp', we will now try to install it...")
install.packages("multcomp")
library(multcomp)
}
if(!require(colorspace))
{
print("You are missing the package 'colorspace', we will now try to install it...")
install.packages("colorspace")
library(colorspace)
}
# get the names out of the formula
formu.names <- all.vars(formu)
Y.name <- formu.names[1]
X.name <- formu.names[2]
block.name <- formu.names[3]
if(dim(data)[2] >3) data <- data[,c(Y.name,X.name,block.name)] # In case we have a "data" data frame with more then the three columns we need. This code will clean it from them...
# Note: the function doesn't handle NA's. In case of NA in one of the block T outcomes, that entire block should be removed.
# stopping in case there is NA in the Y vector
if(sum(is.na(data[,Y.name])) > 0) stop("Function stopped: This function doesn't handle NA's. In case of NA in Y in one of the blocks, then that entire block should be removed.")
# make sure that the number of factors goes with the actual values present in the data:
data[,X.name ] <- factor(data[,X.name ])
data[,block.name ] <- factor(data[,block.name ])
number.of.X.levels <- length(levels(data[,X.name ]))
if(number.of.X.levels == 2) { warning(paste("'",X.name,"'", "has only two levels. Consider using paired wilcox.test instead of friedman test"))}
# making the object that will hold the friedman test and the other.
the.sym.test <- symmetry_test(formu, data = data, ### all pairwise comparisons
teststat = "max",
xtrafo = function(Y.data) { trafo( Y.data, factor_trafo = function(x) { model.matrix(~ x - 1) %*% t(contrMat(table(x), "Tukey")) } ) },
ytrafo = function(Y.data){ trafo(Y.data, numeric_trafo = rank, block = data[,block.name] ) }
)
# if(to.print.friedman) { print(the.sym.test) }
if(to.post.hoc.if.signif)
{
if(pvalue(the.sym.test) < signif.P)
{
# the post hoc test
The.post.hoc.P.values <- pvalue(the.sym.test, method = "single-step") # this is the post hoc of the friedman test
# plotting
if(to.plot.parallel & to.plot.boxplot) par(mfrow = c(1,2)) # if we are plotting two plots, let's make sure we'll be able to see both
if(to.plot.parallel)
{
X.names <- levels(data[, X.name])
X.for.plot <- seq_along(X.names)
plot.xlim <- c(.7 , length(X.for.plot)+.3) # adding some spacing from both sides of the plot
if(color.blocks.in.cor.plot)
{
blocks.col <- rainbow_hcl(length(levels(data[,block.name])))
} else {
blocks.col <- 1 # black
}
data2 <- data
if(jitter.Y.in.cor.plot) {
data2[,Y.name] <- jitter(data2[,Y.name])
par.cor.plot.text <- "Parallel coordinates plot (with Jitter)"
} else {
par.cor.plot.text <- "Parallel coordinates plot"
}
# adding a Parallel coordinates plot
matplot(as.matrix(reshape(data2, idvar=X.name, timevar=block.name,
direction="wide")[,-1]) ,
type = "l", lty = 1, axes = FALSE, ylab = Y.name,
xlim = plot.xlim,
col = blocks.col,
main = par.cor.plot.text)
axis(1, at = X.for.plot , labels = X.names) # plot X axis
axis(2) # plot Y axis
points(tapply(data[,Y.name], data[,X.name], median) ~ X.for.plot, col = "red",pch = 4, cex = 2, lwd = 5)
}
if(to.plot.boxplot)
{
# first we create a function to create a new Y, by substracting different combinations of X levels from each other.
subtract.a.from.b <- function(a.b , the.data)
{
the.data[,a.b[2]] - the.data[,a.b[1]]
}
temp.wide <- reshape(data, idvar=X.name, timevar=block.name,
direction="wide") #[,-1]
wide.data <- as.matrix(t(temp.wide[,-1]))
colnames(wide.data) <- temp.wide[,1]
Y.b.minus.a.combos <- apply(with(data,combn(levels(data[,X.name]), 2)), 2, subtract.a.from.b, the.data =wide.data)
names.b.minus.a.combos <- apply(with(data,combn(levels(data[,X.name]), 2)), 2, function(a.b) {paste(a.b[2],a.b[1],sep=" - ")})
the.ylim <- range(Y.b.minus.a.combos)
the.ylim[2] <- the.ylim[2] + max(sd(Y.b.minus.a.combos)) # adding some space for the labels
is.signif.color <- ifelse(The.post.hoc.P.values < .05 , "green", "grey")
boxplot(Y.b.minus.a.combos,
names = names.b.minus.a.combos ,
col = is.signif.color,
main = "Boxplots (of the differences)",
ylim = the.ylim
)
legend("topright", legend = paste(names.b.minus.a.combos, rep(" ; PostHoc P.value:", number.of.X.levels),round(The.post.hoc.P.values,5)) , fill = is.signif.color )
abline(h = 0, col = "blue")
}
list.to.return <- list(Friedman.Test = the.sym.test, PostHoc.Test = The.post.hoc.P.values)
if(to.print.friedman) {print(list.to.return)}
return(list.to.return)
} else {
print("The results where not significant, There is no need for a post hoc test")
return(the.sym.test)
}
}
# Original credit (for linking online, to the package that performs the post hoc test) goes to "David Winsemius", see:
# http://tolstoy.newcastle.edu.au/R/e8/help/09/10/1416.html
}
Example
(The code for the example is given at the end of the post)
Let's make up a little story: let's say we have three types of wine (A, B and C), and we would like to know which one is the best one (in a scale of 1 to 7). We asked 22 friends to taste each of the three wines (in a blind fold fashion), and then to give a grade of 1 till 7 (for example sake, let's say we asked them to rate the wines 5 times each, and then averaged their results to give a number for a persons preference for each wine. This number which is now an average of several numbers, will not necessarily be an integer).
After getting the results, we started by performing a simple boxplot of the ratings each wine got. Here it is:
The plot shows us two things: 1) that the assumption of equal variances here might not hold. 2) That if we are to ignore the "within subjects" data that we have, we have no chance of finding any difference between the wines.
So we move to using the function "friedman.test.with.post.hoc" on our data, and we get the following output:
$Friedman.Test
Asymptotic General Independence Test
data: Taste by
Wine (Wine A, Wine B, Wine C)
stratified by Taster
maxT = 3.2404, p-value = 0.003421
$PostHoc.Test
Wine B - Wine A 0.623935139
Wine C - Wine A 0.003325929
Wine C - Wine B 0.053772757
The conclusion is that once we take into account the within subject variable, we discover that there is a significant difference between our three wines (significant P value of about 0.0034). And the posthoc analysis shows us that the difference is due to the difference in tastes between Wine C and Wine A (P value 0.003). and maybe also with the difference between Wine C and Wine B (the P value is 0.053, which is just borderline significant).
Plotting our analysis will also show us the direction of the results, and the connected answers of each of our friends answers:
Here is the code for the example:
source("https://www.r-statistics.com/wp-content/uploads/2010/02/Friedman-Test-with-Post-Hoc.r.txt") # loading the friedman.test.with.post.hoc function from the internet
### Comparison of three Wine ("Wine A", "Wine B", and
### "Wine C") for rounding first base.
WineTasting <- data.frame(
Taste = c(5.40, 5.50, 5.55,
5.85, 5.70, 5.75,
5.20, 5.60, 5.50,
5.55, 5.50, 5.40,
5.90, 5.85, 5.70,
5.45, 5.55, 5.60,
5.40, 5.40, 5.35,
5.45, 5.50, 5.35,
5.25, 5.15, 5.00,
5.85, 5.80, 5.70,
5.25, 5.20, 5.10,
5.65, 5.55, 5.45,
5.60, 5.35, 5.45,
5.05, 5.00, 4.95,
5.50, 5.50, 5.40,
5.45, 5.55, 5.50,
5.55, 5.55, 5.35,
5.45, 5.50, 5.55,
5.50, 5.45, 5.25,
5.65, 5.60, 5.40,
5.70, 5.65, 5.55,
6.30, 6.30, 6.25),
Wine = factor(rep(c("Wine A", "Wine B", "Wine C"), 22)),
Taster = factor(rep(1:22, rep(3, 22))))
with(WineTasting , boxplot( Taste ~ Wine )) # boxploting
friedman.test.with.post.hoc(Taste ~ Wine | Taster ,WineTasting) # the same with our function. With post hoc, and cool plots
If you find this code useful, please let me know (in the comments) so I will know there is a point in publishing more such code snippets...
I just noticed a google buzz from Jeroen ooms, with a Youtube video titled “RApache Hello World + POST arguments + catching errors.”
In this ~7 min video tutorial, Jeroen shares with us:
How to write “Hello World” in a website using RApache.
How to extract arguments from a form submited by the website visitor (and then inserting it into an “rnorm” function so to control the output). And finally,
How to catch an error in case of an invalid argument on an R Web Application.
Thank you Jeroen for a very simple, step by step, tutorial:
