Example 9.16: Small multiples

Small multiples are one of the great ideas of graphics visionary Edward Tufte (e.g., in Envisioning Information). Briefly, the idea is that if many variations on a theme are presented, differences quickly become apparent. Today we offer general guidance on creating figures with small multiples.

As an example, we'll show graphics for the popularity, salary, and unemployment rates for college majors. This data was discussed here where a scatterplot graphic was presented. We draw on data and code presented there as well. The scatterplot does not show the unemployment rate, and the width of the field names and arbitrarily sized text makes it difficult to determine the popularity ranking. In contrast, the small multiples plot, demonstrated above, makes each of these features easy to see. (Click on the picture for a clearer image.)

R

The graphics options in R, particularly par("mfrow") or par("mfcol"), are well-suited to small multiples. The main tip here is to minimize the space reserved for margins and titles. In the example below, we do this with the mar, mgp, and oma settings. We'll begin by setting up the data in a process that relies heavily on the code here. (Note that the zip file referred to includes data already in the R format-- since our point today is not data management, we don't replicate the process used to make this out of the raw data.)

clean = function(x) as.numeric(gsub("\\$|, ", "", x))
clean2 = function(x) as.numeric(gsub("%", "", x))
load("table.rda")
X[,2] = clean2(X[,2])
for (i in 3:5) X[,i] = clean(X[,i])


X$cols = NA
X$cols[grep("BUSI|ACC|FINAN",X[,1])] = 1
X$cols[grep("ENGINEERING",X[,1])] = 2
X$cols[grep("STAT|COMPU",X[,1])] = 3
X$cols[grep("BIOL|CHEMI|PHYSICS|MATHEM",X[,1])] =  4
X$cols[grep("ENGLISH|HISTORY|LANG|FINE|MUSIC|PHILOS|DRAMA|LIBERAL|ARCH|THEO",X[,1])] = 5
X$cols[grep("SOCIO|PSYCH|POLI|ECONO|JOURNAL",X[,1])] = 6
X$cols[grep("COMMUN|MARKET|COMMER|MULTI|MASS|ADVERT",X[,1])] = 7
X$cols[grep("NURS|CRIM|EDU|PHYSICAL|FAMI|SOCIAL|TREAT|HOSP|HUMAN",X[,1])] = 8

This removes some funny characters and groups the fields together in a coherent manner. Then we write a function to set the par() values we need to change, and plot a pie for each row of the data set. Here a for loop is used-- we're not aware of a vectorized version of the pie() function. Colors for each pie are assigned via the colors.

sortx = X[order(X$Popularity),]

smajors = function(mt) {
  old.par = par(no.readonly=TRUE) 
  on.exit(par(old.par))
  nrows = sqrt(nrow(mt)) + (ceiling(sqrt(nrow(mt))) !=  sqrt(nrow(mt)))
  par(mfrow=c(nrows,nrows), mar=c(1,0,0,0), oma=c(0,0,0,0), mgp=c(0,0,0))
  colors = c("blue", "purple", "purple", "gray", "orange", "gray", "red", "black")
  for (i in 1:nrow(mt)) {
    pie(c(mt[i,2], 100 - mt[i,2]), labels=NA, radius=mt[i,4]/max(mt[,4]), 
        col = c("white",colors[mt[i,7]]))
    mtext(substr(mt[i,1],1,19), side=1, cex=.8)
  }
}

smajors(sortx[1:49,])

The resulting plot is shown above. There may be too many colors, though statistics and computing were assigned the same color as engineering. We can easily read from the plot that computing, statistics, and engineering (purple) are the largest circles, and thus the best paying. Similarly, the humanities (orange) are the worst paying. They are also not terribly popular-- the first orange pie appears in the second row. The "professions" (nursing, teaching, policing, therapy) don't pay well but are fairly popular. Most pies have roughly equal unemployment, though nursing and the professions generally are notable for near full employment. All in all, the rank, salary, unemployment percentage, and field are all clearer than in the scatterplot.

SAS

In SAS, one can use the greplay procedure to reproduce images in miniature. One has to define the size and shape allotted for each replayed plot, in a stored "template." This allows enormous control, but at the cost of some complexity. For example, one can create a scatterplot matrix using proc gplot instead of proc sgplot, as in this implementation by Michael Friendly. If you can generate your multiple images with a by statement, the coding for this is not too painful. However, in this case, it was not obvious how to change the color and radius for each pie using a by statement in proc gchart which includes pie charts, and would thus have been the obvious choice. In such cases, it may be easier to plot the figures directly using an annotate data set.

However, having demonstrated the use of annotate previously (e.g., Example 8.13), we show here an application using greplay, though the coding is a little bit involved. In outline, we use a macro to call for a pie to be made from each observation of the original data set. Then we use a template-making macro found here to generate the 7X7 grid template. Finally, we replay the pies into the grid.

/* read the data-- note that text file edited to remove spaces in 
    variable names */
proc import datafile = 
   'c:\sas-r dictionary\p\book\web\blog\majors\majors\table.txt'
   out = majors;
   getnames = yes;
   run;

/* set up the field categories and colors */
data m2;
set majors;
cols="      ";     /* make a missing character variable to hold them */
mf = majorfield;   /* just a copy to save keystrokes */
   /* the find() function is discussed in section 1.4.6 */
if sum(find(mf,"BUSI"), find(mf,"ACC"), find(mf,"FINAN")) ne 0 then cols = "blue";
if find(mf,"ENGINEERING") ne 0 the cols = "purple";
if sum(find(mf,"STAT"), find(mf,"COMPU"), find(mf,"SYSTEMS")) ne 0 then cols = "purple";
if sum(find(mf,"BIOL"), find(mf,"CHEMI"), find(mf,"PHYSICS"), find(mf,"MATH")) ne 0 then cols = "gray";
if sum(find(mf,"ENGL"), find(mf,"HIST"), find(mf,"FRENCH"), find(mf,"FINE"),
     find(mf,"MUSIC"), find(mf,"PHIL"), find(mf,"DRAMA"), find(mf,"LIBERAL"),
     find(mf,"ARCH"), find(mf,"THEO")) ne 0 then cols = "orange";
if sum(find(mf,"SOCI"), find(mf,"PSYCH"), find(mf,"POLI"), find(mf,"ECON"),
     find(mf,"JOURN"), find(mf,"LIBERAL")) ne 0 then cols = "gray";
if sum(find(mf,"COMMU"), find(mf,"MARKET"), find(mf,"COMMER"), find(mf,"MULTI"),
     find(mf,"MASS"), find(mf,"ADVERT")) ne 0 then cols = "red";
if sum(find(mf,"NURS"), find(mf,"CRIM"), find(mf,"EDU"), find(mf,"PHYSICAL"),
     find(mf,"FAMI"), find(mf,"SOCIAL"), find(mf,"TREAT"),
     find(mf,"HOSP"), find(mf,"HUMAN")) ne 0 then cols = "black";
drop MF;   /* get rid of that keystroke-saver */
run; 

/* order by popularity */
proc sort data = m2; by popularity; run;

The next macro takes a line number as input. A data step then reads that line from the real data set and uses call symput (section A.8.2) to extract as macro variables the median earnings used for the radius, the color, and the major name. It then produces two rows of data-- one with the unemployed percent and the other with the employed percent. We need this for the proc gchart input, as shown in the second half of the macro.

%macro smpie(obs);
data t1;
set m2 (firstobs = &obs obs = &obs);
call symput('rm', medianearnings);
call symput('color', cols);
call symput('name', strip(substr(majorfield,1,19)));
employed = "No"; percent = unemploymentpercent; output;
employed = "Yes"; percent = 100 - unemploymentpercent; output;
run;

pattern1 color= white v=solid;
pattern2 color= &color v=solid;  /* only pattern2 should be needed, I think, but */
pattern3 color= &color v=solid;  /* sometimes SAS required pattern3, in my trials */
title h=7pct "&name";
proc gchart data = t1 gout = kkpies;
pie percent / group = majorfield sumvar = percent value = none 
    noheading nogroupheading radius = %sysevalf((&rm * 45)/ 105000)
    name = "PIE&obs" ; 
run;quit;
%mend smpie;

Of particular note in the forgoing are the gout and name options. The former specifies a location where output plots should be stored. The latter assigns a name to this particular plot. In addition, the %sysevalf macro function is needed to perform mathematical functions on the radius variable.

Next, we write and call another macro to call the first repeatedly. Making the image small to begin with (using the goptions statement [section 5.3]) reduces quality loss when replaying as small multiples.

%macro pies;
goptions hsize=1in vsize=1in;
%do i = 1 %to 49;
  %smpie(&i);
%end;
%mend;  

%pies;

Finally, we can make the template to replay the images, and replay them, both using proc greplay.

/* key elements of the %makegridtemplate macro: 
     how many rows and columns (down and across). 
     name for the template.
   Note that the macro is called *inside* the proc greplay statement, 
   which allows the user access to  pro greplay statment options */
proc greplay nofs  tc=work.templates;
  %makeGridTemplate (across=7, down=7, ordering=LRTB, 
      hgap=0, vgap=0, gapT=0, gapL=0, gapr=0, name=sevensq,bordercolor=white)
quit;

/* this macro just types out text for us the sequence 1:pie1 2:pie2 ... 49:pie49 */
/* we need that to replay the figures in proc greplay */
%macro pielist;
%do i = 1 %to 49; &i:pie&i %end;;
%mend;

filename pies "c:\temp\pies2.png";
goptions hsize=7in vsize=7in gsfname=pies device=png;

/* now ready to replay the plots
   The proc greplay options say what template to use and where to find it, 
     and where to find the input and place the output */
/* The treplay statement plays the old plots to the locations specified 
     in the template
proc greplay template=sevensq tc=work.templates nofs gout=kkpies igout=kkpies;
treplay %pielist;
run;
quit;

The net outcome of this is shown below. The image is pretty disappointing-- the circles are not round,and the text is pretty blurry. However, the message is as clear as in the prettier R version.

Example 9.3: augmented display of contingency table

SAS and R often provide different levels of details from output. This is particularly true for the descriptive analysis of contingency tables, where SAS makes it easy to display tables with additional quantities (such as the observed cell count).

The mosaic package has added functionality to calculate these quantities in R. We demonstrate using an example from the HELP dataset.

R

ds = read.csv("http://www.math.smith.edu/r/data/help.csv")
library(mosaic)
ds$gender = ifelse(ds$female==1, "female", "male")
ds$homeless = ifelse(ds$homeless==1, "homeless", "housed")
tab = xtabs(~ gender + homeless, data=ds)
> tab
        homeless
gender   homeless housed
  female       40     67
  male        169    177
> xchisq.test(tab)

 Pearson's Chi-squared test with Yates' continuity correction

data:  tab 
X-squared = 3.8708, df = 1, p-value = 0.04913

  40.00    67.00 
( 49.37) ( 57.63)
 [1.78]   [1.52] 
<-1.33>  < 1.23> 
   
 169.00   177.00 
(159.63) (186.37)
 [0.55]   [0.47] 
< 0.74>  <-0.69> 
   
key:
 observed
 (expected)
 [contribution to X-squared]
 

We see that there is a borderline statistically significant association between gender and homeless status in the HELP study. We interpret that we see fewer than expected females who are homeless, and more males who are homeless.

Another idea is to use graphical depictions of the association in this table. One approach is a mosaic plot (note: no relation to Project MOSAIC and the mosaic package). A mosaic plot starts as a square with area equal to one. It is divided into columns based on the prevalence in each of the values for the column variable (in this case, gender). Then each bar is divided vertically based on the conditional probability of the other variable within that category.

Another graphical display of a table is the association plot. In an association plot, there is also a box for each cell of the table. The area of the box is proportional to the difference between the observed and expected (assuming no association) frequencies. In a typical presentation, excess observed counts are black and above the line, while deficient counts are red and below the line.

Above, we show the mosaic plot (on the left) and association plot (on the right). Both of these displays demonstrate that there is an association. The mosaic plot indicates that only about a quarter of the sample is female (indicated by the width of the columns), and that homelessness is present in about half the subjects (area shaded in light grey). The slight association demonstrated is that there are fewer homeless women than expected (since the horizontal line moves down between the first and second column). Similarly, for the association plot we note that the expected cell count is less than the observed (indicated in red with values below the line) for the female homeless group.

par(mfrow=c(1,2))
mosaicplot(tab, color=TRUE, main="mosaic plot")
assocplot(tab)
title("association plot")

SAS
As in Example 8.32, we find SAS macros for mosaic plots among the contributions of Michael Friendly. In this complex case, they are somewhat more difficult to access than others. The code for the plots themselves can be downloaded here, while it's useful to also run a wrapper macro. After downloading the files, the following code can be used to make the figure below.

title 'Install mosaic modules';
* location of the zipped files;
filename mosaic  'c:\ken\sasmacros\mosaics';
* storage location of compiled macros;
libname  mosaic   'c:\ken\sasmacros\mosaics';

* Code to read in, compile and store the macros;
proc iml ;
   reset storage=mosaic.mosaic;
   %include mosaic(mosaics) ;
   store module=_all_;
   show storage;
quit;

* Prep: create the table, save the cell counts;
proc freq data = "c:\book\help.sas7bdat";
tables homeless * female / out=outhelp;
run;

* Read in the wrapper macro;
%include "c:\ken\sasmacros\mosaics\mosaic.sas";

* Make the plot;
%mosaic(data=outhelp,var = female homeless, 
        sort=homeless descending female, space = 1 1);

The sort and space options make the results more similar to those shown for mosaicplot(). In this version, the colors reflect the signs of the residuals.

Example 8.32: The HistData package, sunflower plots, and getting data from R into SAS

This entry is mainly a promotion of the fascinating HistData R package. The package, compiled by the psychologist, statistician, and graphics innovator Michael Friendly, contains a number of small data sets of historical interest. These include data from John Snow's map of cholera in London, Minard's map of Napoleon's Russian campaign of 1812, Galton's data on heights of parents and children, and many others.

If you have any interest in Minard's map, Friendly also hosts a site about the map, Minard, and a gallery with some re-imaginings of the map data, at http://datavis.ca/gallery/re-minard.php. The gallery includes R and SAS versions, as well as one which uses Google Maps.

R
Once you install the package and library() it (section B.6.1), you can gain access to the data with the data() function. For example, we show Galton's data, which lead to the description of regression to the mean.

install.packages("HistData")
library(HistData)
> data(Galton)
> head(Galton)
  parent child
1   70.5  61.7
2   68.5  61.7
3   65.5  61.7
4   64.5  61.7
5   64.0  61.7
6   67.5  62.2

The package also includes example() methods for many of the data sets: example(Galton) results in the sunflower plot shown above. The sunflower plot (section 5.1.14) is an alternative to jittering when many observations share values. If the data start as more continuous, you might see the sunflower plot as a form of two-dimensional histogram. You can get a list of data sets available with ?'HistData-package'

We're not aware of a companion set of SAS data sets. An easy way to access the data sets in SAS is to load the package into R and export the data into SAS using the foreign package (section 1.2.2).

> library(foreign)
> write.foreign(Galton,"galton.dat","galton.sas",package="SAS")

SAS
Running the galton.sas file written by the write.foreign function makes a SAS data set called rdata with varibles parent and child. We can make a sunflower plot in SAS using a macro written, coincidentally, by Michael Friendly, which he hosts here. Making a plot requires running the "sunfont.sas" file and the "sunplot.sas" file. I had to modify the "sunfont.sas" file slightly, and I give the edited file here:

libname gfont0 'c:\temp';
                        
data sunsymb;                                                                   
  alpha = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ';                                         
  do n=1 to 26;                                                                 
     char=substr(alpha,n,1);                                                    
     segment=n;                                                                 
     x = .2; y = .2; output;         /* Draw small box at center */             
     x =-.2; y = .2; output;         /* of each symbol           */             
     x =-.2; y =-.2; output;                                                    
     x = .2; y =-.2; output;                                                    
     x = .2; y = .2; output;                                                    
     if n>1 then                                                                
       do i=1 to n;                  /* draw n radial lines      */             
         x=0; y=0; output;                                                      
         x=cos(2*atan(1) + i/n*(8*atan(1)));                                    
         y=sin(2*atan(1) + i/n*(8*atan(1)));                                    
         output;                                                                
       end;                                                                     
  end;          
                                                                
proc gfont data=sunsymb             /* name=GB0426 */                
           name=sun showroman h=3 romht=2 resol=2; 

In this step, Friendly is constructing a font whose "letters" are the sunflower symbols with various numbers of petals. Note that if you already define a gfont0 library, the first line above is not needed.

Then the sunplot macro can be read in and run.

%include "c:\ken\sasmacros\sunplot.sas";
%sunplot(data=rdata, x=parent, y = child); run;

The resulting plot is shown below. The SAS version is rather more primitive, (and I did not bother to add the ellipses or regression line) but both the SAS and R versions show that children tend to be less unusual than their parents, and the more unusual the parent is, the more the child shrinks toward the mean.