Visualization of regression coefficients (in R)

Update (07.07.10): The function in this post has a more mature version in the “arm” package. See at the end of this post for more details.
* * * *

Imagine you want to give a presentation or report of your latest findings running some sort of regression analysis. How would you do it?

This was exactly the question Wincent Rong-gui HUANG has recently asked on the R mailing list.

One person, Bernd Weiss, responded by linking to the chapter “Plotting Regression Coefficients” on an interesting online book (I have never heard of before) called “Using Graphs Instead of Tables” (I should add this link to the free statistics e-books list…)

Letter in the conversation, Achim Zeileis, has surprised us (well, me) saying the following

I’ve thought about adding a plot() method for the coeftest() function in the “lmtest” package. Essentially, it relies on a coef() and a vcov() method being available – and that a central limit theorem holds. For releasing it as a general function in the package the code is still too raw, but maybe it’s useful for someone on the list. Hence, I’ve included it below.

(I allowed myself to add some bolds in the text)

So for the convenience of all of us, I uploaded Achim’s code in a file for easy access. Here is an example of how to use it:

data("Mroz", package = "car")
fm <- glm(lfp ~ ., data = Mroz, family = binomial)
coefplot(fm, parm = -1)

Here is the resulting graph:

I hope Achim will get around to improve the function so he might think it worthy of joining his“lmtest” package. I am glad he shared his code for the rest of us to have something to work with in the meantime šŸ™‚

* * *

Update (07.07.10):
Thanks to a comment by David Atkins, I found out there is a more mature version of this function (called coefplot) inside the {arm} package. This version offers many features, one of which is the ability to easily stack several confidence intervals one on top of the other.

It works for baysglm, glm, lm, polr objects and a default method is available which takes pre-computed coefficients and associated standard errors from any suitable model.

(Notice that the Poisson model in comparison with the binomial models does not make much sense, but is enough to illustrate the use of the function)

data("Mroz", package = "car")
M1<-      glm(lfp ~ ., data = Mroz, family = binomial)
M2<- bayesglm(lfp ~ ., data = Mroz, family = binomial)
M3<-      glm(lfp ~ ., data = Mroz, family = binomial(probit))
coefplot(M2, xlim=c(-2, 6),            intercept=TRUE)
coefplot(M1, add=TRUE, col.pts="red",  intercept=TRUE)
coefplot(M3, add=TRUE, col.pts="blue", intercept=TRUE, offset=0.2)

(hat tip goes to Allan Engelhardt for help improving the code, and for Achim Zeileis in extending and improving the narration for the example)

Resulting plot

* * *
Lastly, another method worth mentioning is the Nomogram, implemented by Frank Harrell’a rms package.

Clustergram: visualization and diagnostics for cluster analysis (R code)

About Clustergrams

In 2002, Matthias Schonlau published in “The Stata Journal” an article named “The Clustergram: A graph for visualizing hierarchical and . As explained in the abstract:

In hierarchical cluster analysis dendrogram graphs are used to visualize how clusters are formed. I propose an alternative graph named ā€œclustergramā€ to examine how cluster members are assigned to clusters as the number of clusters increases.
This graph is useful in exploratory analysis for non-hierarchical clustering algorithms like k-means and for hierarchical cluster algorithms when the number of observations is large enough to make dendrograms impractical.

A similar article was later written and was (maybe) published in “computational statistics”.

Both articles gives some nice background to known methods like k-means and methods for hierarchical clustering, and then goes on to present examples of using these methods (with the Clustergarm) to analyse some datasets.

Personally, I understand the clustergram to be a type of parallel coordinates plot where each observation is given a vector. The vector contains the observation’s location according to how many clusters the dataset was split into. The scale of the vector is the scale of the first principal component of the data.

Clustergram in R (a basic function)

After finding out about this method of visualization, I was hunted by the curiosity to play with it a bit. Therefore, and since I didn’t find any implementation of the graph in R, I went about writing the code to implement it.

The code only works for kmeans, but it shows how such a plot can be produced, and could be later modified so to offer methods that will connect with different clustering algorithms.

How does the function work: The function I present here gets a data.frame/matrix with a row for each observation, and the variable dimensions present in the columns.
The function assumes the data is scaled.
The function then goes about calculating the cluster centers for our data, for varying number of clusters.
For each cluster iteration, the cluster centers are multiplied by the first loading of the principal components of the original data. Thus offering a weighted mean of the each cluster center dimensions that might give a decent representation of that cluster (this method has the known limitations of using the first component of a PCA for dimensionality reduction, but I won’t go into that in this post).
Finally all of our data points are ordered according to their respective cluster first component, and plotted against the number of clusters (thus creating the clustergram).

My thank goes to Hadley Wickham for offering some good tips on how to prepare the graph.

Here is the code (example follows)

The R function can be downloaded from here
Corrections and remarks can be added in the comments bellow, or on the github code page.

Example on the iris dataset

The iris data set is a favorite example of many R bloggers when writing about R accessors , Data Exporting, Data importing, and for different visualization techniques.
So it seemed only natural to experiment on it here.

source("") # Making sure we can source code from github
par(cex.lab = 1.5, cex.main = 1.2)
Data <- scale(iris[,-5]) # notice I am scaling the vectors)
clustergram(Data, k.range = 2:8, line.width = 0.004) # notice how I am using line.width.  Play with it on your problem, according to the scale of Y.

Here is the output:

Looking at the image we can notice a few interesting things. We notice that one of the clusters formed (the lower one) stays as is no matter how many clusters we are allowing (except for one observation that goes way and then beck).
We can also see that the second split is a solid one (in the sense that it splits the first cluster into two clusters which are not “close” to each other, and that about half the observations goes to each of the new clusters).
And then notice how moving to 5 clusters makes almost no difference.
Lastly, notice how when going for 8 clusters, we are practically left with 4 clusters (remember – this is according the mean of cluster centers by the loading of the first component of the PCA on the data)

If I where to take something from this graph, I would say I have a strong tendency to use 3-4 clusters on this data.

But wait, did our clustering algorithm do a stable job?
Let’s try running the algorithm 6 more times (each run will have a different starting point for the clusters)

source("") # Making sure we can source code from github
Data <- scale(iris[,-5]) # notice I am scaling the vectors)
par(cex.lab = 1.2, cex.main = .7)
par(mfrow = c(3,2))
for(i in 1:6) clustergram(Data, k.range = 2:8 , line.width = .004, = T)

Resulting with: (press the image to enlarge it)

Repeating the analysis offers even more insights.
First, it would appear that until 3 clusters, the algorithm gives rather stable results.
From 4 onwards we get various outcomes at each iteration.
At some of the cases, we got 3 clusters when we asked for 4 or even 5 clusters.

Reviewing the new plots, I would prefer to go with the 3 clusters option. Noting how the two “upper” clusters might have similar properties while the lower cluster is quite distinct from the other two.

By the way, the Iris data set is composed of three types of flowers. I imagine the kmeans had done a decent job in distinguishing the three.

Limitation of the method (and a possible way to overcome it?!)

It is worth noting that the current way the algorithm is built has a fundamental limitation: The plot is good for detecting a situation where there are several clusters but each of them is clearly “bigger” then the one before it (on the first principal component of the data).

For example, let’s create a dataset with 3 clusters, each one is taken from a normal distribution with a higher mean:

source("") # Making sure we can source code from github
Data <- rbind(
				cbind(rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3)),
				cbind(rnorm(100,1, sd = 0.3),rnorm(100,1, sd = 0.3),rnorm(100,1, sd = 0.3)),
				cbind(rnorm(100,2, sd = 0.3),rnorm(100,2, sd = 0.3),rnorm(100,2, sd = 0.3))
clustergram(Data, k.range = 2:5 , line.width = .004, = T)

The resulting plot for this is the following:

The image shows a clear distinction between three ranks of clusters. There is no doubt (for me) from looking at this image, that three clusters would be the correct number of clusters.

But what if the clusters where different but didn’t have an ordering to them?
For example, look at the following 4 dimensional data:

source("") # Making sure we can source code from github
Data <- rbind(
				cbind(rnorm(100,1, sd = 0.3),rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3)),
				cbind(rnorm(100,0, sd = 0.3),rnorm(100,1, sd = 0.3),rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3)),
				cbind(rnorm(100,0, sd = 0.3),rnorm(100,1, sd = 0.3),rnorm(100,1, sd = 0.3),rnorm(100,0, sd = 0.3)),
				cbind(rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3),rnorm(100,0, sd = 0.3),rnorm(100,1, sd = 0.3))
clustergram(Data, k.range = 2:8 , line.width = .004, = T)

In this situation, it is not clear from the location of the clusters on the Y axis that we are dealing with 4 clusters.
But what is interesting, is that through the growing number of clusters, we can notice that there are 4 “strands” of data points moving more or less together (until we reached 4 clusters, at which point the clusters started breaking up).
Another hope for handling this might be using the color of the lines in some way, but I haven’t yet figured out how.

Clustergram with ggplot2

Hadley Wickham has kindly played with recreating the clustergram using the ggplot2 engine. You can see the result here:
And this is what he wrote about it in the comments:

Iā€™ve broken it down into three components:
* run the clustering algorithm and get predictions (many_kmeans and all_hclust)
* produce the data for the clustergram (clustergram)
* plot it (plot.clustergram)
I donā€™t think I have the logic behind the y-position adjustment quite right though.

Conclusions (some rules of thumb and questions for the future)

In a first look, it would appear that the clustergram can be of use. I can imagine using this graph to quickly run various clustering algorithms and then compare them to each other and review their stability (In the way I just demonstrated in the example above).

The three rules of thumb I have noticed by now are:

  1. Look at the location of the cluster points on the Y axis. See when they remain stable, when they start flying around, and what happens to them in higher number of clusters (do they re-group together)
  2. Observe the strands of the datapoints. Even if the clusters centers are not ordered, the lines for each item might (needs more research and thinking) tend to move together – hinting at the real number of clusters
  3. Run the plot multiple times to observe the stability of the cluster formation (and location)

Yet there is more work to be done and questions to seek answers to:

  • The code needs to be extended to offer methods to various clustering algorithms.
  • How can the colors of the lines be used better?
  • How can this be done using other graphical engines (ggplot2/lattice?) – (Update: look at Hadley’s reply in the comments)
  • What to do in case the first principal component doesn’t capture enough of the data? (maybe plot this graph to all the relevant components. but then – how do you make conclusions of it?)
  • What other uses/conclusions can be made based on this graph?

I am looking forward to reading your input/ideas in the comments (or in reply posts).

The new GUI for ggplot2 (using Deducer) – the designer wants your opinion

After discovering that R is expected (this summer) to have a GUI for ggplot2 (through deducer), I later found Ian’s gsoc proposal for this GUI. Ā Since the system is in it’s early stages of development, Ian has invited people to give comments, input and critique on his plans for the project.

For your convenience (and with Ian’s permission), I am reposting his proposal here. You are welcome to send him feedback by e-mailing him (at: [email protected]), or by leaving a comment here (and I will direct him to your comment).

Continue reading “The new GUI for ggplot2 (using Deducer) – the designer wants your opinion”

Jeroen Ooms's ggplot2 web interface – a new version released (V0.2)

Good news.

Jeroen Ooms released a new version of his (amazing) online ggplot2 web interface: is a web interface for Hadley Wickham’s R package ggplot2. It is used as a tool for rapid prototyping, exploratory graphical analysis and education of statistics and R. The interface is written completely in javascript, therefore there is no need to install anything on the client side: a standard browser will do.

The new version has a lot of cool new features, like advanced data import, integration with Google docs, converting variables from numeric to factor to dates and vice versa, and a lot of new geom’s. Some of which you can watch in his new video demo of the application:

The application is on:

p.s: other posts about this (including videos explaining how some of this was done) can be views on the category page: R and the web

Correlation scatter-plot matrix for ordered-categorical data

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:

  1. Jitter the data a bit to give a sense of the “density” of the points
  2. Use a color spectrum toĀ representĀ when a point actually represent “many points”
  3. Use different points sizes to representĀ when there are “many points” in the location of that point
  4. 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 Ā 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):

And here is the code to produce this plot:

Continue reading “Correlation scatter-plot matrix for ordered-categorical data”

R-Node: a web front-end to R with Protovis

Update (April 6 – 2010) : R-Node now has it’s own a website, with a dedicated google group (you can join it here)

* * * *

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:
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:

How do you may imagine yourself using something like this? Feel invited to share with me and everyone else in the comments.

Here are some of the more technical details of R-Node:
Continue reading “R-Node: a web front-end to R with Protovis”

Quantile LOESS – Combining a moving quantile window with LOESS (R function)

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:



I came a cross this idea in an article titled “High throughput data analysis in behavioral genetics” by Anat Sakov, Ilan Golani, Dina Lipkind and my advisor Yoav Benjamini. From the abstract:

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):

Continue reading “Quantile LOESS – Combining a moving quantile window with LOESS (R function)”

Nutritional supplements efficacy score – Graphing plots of current studies results (using R)

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 ā€œballoon raceā€ 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:

  1. 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.
  2. 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 topĀ recommendedĀ 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).

(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 < - read.csv("") <-[[,2] >2,] # let's only look at "good" supplements < -[![,2]),] # and we don't want any missing data
supplement.score <-[, 2]
ss <- order(supplement.score, decreasing  = F)	# sort our data
supplement.score <- supplement.score[ss] <-[ss, 1]
supplement.benefits <-[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=, 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)

Continue reading “Nutritional supplements efficacy score – Graphing plots of current studies results (using R)”

Fun interpretive dances for common statistical plots

My wife is a big lover of dance (especially Dance In Israel), and while reading through the NYtimes article: “To Impress, Tufts Prospects Turn to YouTube“, she found me a pearl: A woman performing interpretive dances for math/statistical plots. That includes small dance for: scatter plots, boxplots, barplots and a few others. Enjoy:

Web Development with R – an HD video tutorial of Jeroen Ooms talk

Here is a HD version of a video tutorial on web development with R, a lecture that was given by Jeroen Ooms (the guy who madeĀ A web application for Rā€™s ggplot2). This talk was given at the Bay Area UseR Group meeting on R-Powered Web Apps.

You can also view theĀ slides for his talk and view (great) examples for:Ā stockplot,Ā lme4, andĀ gpplot2.

Thanks again to Jeroen for sharing his knowledge and experience!