corPlot: Create an image plot for a correlation or factor matrix

Description

Correlation matrices may be shown graphically by using the image function to emphasize structure. This is a particularly useful tool for showing the structure of correlation matrices with a clear structure. Partially meant for the pedagogical value of the graphic for teaching or discussing factor analysis and other multivariate techniques. The sort option uses iclust to sort the matrix before plotting.

Usage

corPlot(r,numbers=TRUE,colors=TRUE,n=51,main=NULL,zlim=c(-1,1),
  show.legend=TRUE, labels=NULL,n.legend=10,keep.par=TRUE,select=NULL, pval=NULL, 
  digits=2, trailing=TRUE, cuts=c(.001,.01),scale=TRUE,cex,MAR,upper=TRUE,diag=TRUE, 
  symmetric=TRUE,stars=FALSE, adjust="holm",xaxis=1, xlas=0, ylas=2,ysrt=0,xsrt=0, 
   gr=NULL, alpha=.75,  min.length=NULL,sort=FALSE,n.obs=NULL, ...)
corPlotUpperLowerCi(R,numbers=TRUE,cuts=c(.001,.01,.05),select=NULL,
      main="Upper and lower confidence intervals of correlations",adjust=FALSE,...)
 
 cor.plot(r,numbers=TRUE,colors=TRUE,n=51,main=NULL,zlim=c(-1,1),
 show.legend=TRUE, labels=NULL,n.legend=10,keep.par=TRUE,select=NULL, pval=NULL, 
  digits=2, trailing=TRUE, cuts=c(.001,.01),scale=TRUE,cex,MAR,upper=TRUE,diag=TRUE, 
  symmetric=TRUE,stars=FALSE, adjust="holm",xaxis=1, xlas=0, ylas=2,ysrt=0,xsrt=0,
     gr=NULL, alpha=.75, min.length=NULL, sort=FALSE, n.obs=NULL,...)     #deprecated
           
cor.plot.upperLowerCi(R,numbers=TRUE,cuts=c(.001,.01,.05),select=NULL,
      main="Upper and lower confidence intervals of correlations",adjust=FALSE,...)
      #deprecated

Arguments

Details

When summarizing the correlations of large data bases or when teaching about factor analysis or cluster analysis, it is useful to graphically display the structure of correlation matrices. This is a simple graphical display using the image function.

The difference between mat.plot with a regular image plot is that the primary diagonal goes from the top left to the lower right. zlim defines how to treat the range of possible values. -1 to 1 and the color choice is more reasonable. Setting it as c(0,1) will lead to negative correlations treated as zero. This is advantageous when showing general factor structures, because it makes the 0 white.

There is an interesting case when plotting correlations corrected for attenuation. Some of these might exceed 1. In this case, either set zlim = NULL (to use the observed maximum and minimum values) or all values above 1 will be given a slightly darker shade than 1, but do not differ.

The default shows a legend for the color coding on the right hand side of the figure.

Inspired, in part, by a paper by S. Dray (2008) on the number of components problem.

Modified following suggestions by David Condon and Josh Wilt to use a more meaningful color choice ranging from dark red (-1) through white (0) to dark blue (1). Further modified to allow for color choices using the gr option (suggested by Lorien Elleman). Further modified to include the numerical value of the correlation. (Inspired by the corrplot package). These values may be scaled according the the probability values found in cor.ci or corTest.

Unless specified, the font size is dynamically scaled to have a cex = 10/max(nrow(r),ncol(r). This can produce fairly small fonts for large problems. The font size of the labels may be adjusted using cex.axis which defaults to one.

By default cor.ci calls corPlotUpperLowerCi and scales the correlations based upon "significance" values. The correlations plotted are the upper and lower confidence boundaries. To show the correlations themselves, call corPlot directly.

If using the output of corTest, the upper off diagonal will be scaled by the corrected probability, the lower off diagonal the scaling is the uncorrected probabilities.

If given raw data or correlation matrix, corPlotUpperLowerCi will automatically call corTest or cor.ci.

If using the output of corTest or cor.ci as input to corPlotUpperLowerCi, the upper off diagonal will be the upper bounds and the lower off diagonal the lower bounds of the confidence intervals. If adjust=TRUE, these will use the Holm or Bonferroni adjusted values (depending upon corTest).

To compare the elements of two correlation matrices, corPlot the results from lowerUpper.

To do multiple corPlot on the same plot, specify that show.legend=FALSE and keep.par=FALSE. See the last examples.

Care should be taken when selecting rows and columns from a non-symmetric matrix (e.g., the corrected correlations from scoreItems or scoreOverlap).

To show a factor loading matrix (or any non-symmetric matrix), set symmetric=FALSE. Otherwise the input will be treated as raw data and correlations will be found.

The sort option will sort the matrix using the output from iclust. To sort the matrix use another order, use mat.sort first. To find correlations other than Pearson, plot the output from e.g., mixed.cor.

References

Dray, Stephane (2008) On the number of principal components: A test of dimensionality based on measurements of similarity between matrices. Computational Statistics & Data Analysis. 52, 4, 2228-2237.

Examples

Run this code

corPlot(Thurstone,main="9 cognitive variables from Thurstone") 
#just blue implies positive manifold
#select just some variables to plot
corPlot(Thurstone, zlim=c(0,1),main="9 cognitive variables from Thurstone",select=c(1:3,7:9))
#now show a non-symmetric plot
corPlot(Thurstone[4:9,1:3], zlim=c(0,1),main="9 cognitive variables
 from Thurstone",numbers=TRUE,symmetric=FALSE)

#Two ways of including stars to show significance
#From the raw data
corPlot(sat.act,numbers=TRUE,stars=TRUE)
#from a correlation matrix with pvals
cp <- corTest(sat.act)  #find the correlations and pvals
r<- cp$r
p <- cp$p
corPlot(r,numbers=TRUE,diag=FALSE,stars=TRUE, pval = p,main="Correlation plot
 with Holm corrected 'significance'")

#now red means less than .5
corPlot(mat.sort(Thurstone),TRUE,zlim=c(0,1), 
       main="9 cognitive variables from Thurstone (sorted by factor loading) ")
simp <- sim.circ(24)
corPlot(cor(simp),main="24 variables in a circumplex")

#scale by raw and adjusted probabilities
rs <- corTest(sat.act[1:200,] ) #find the probabilities of the correlations
corPlot(r=rs$r,numbers=TRUE,pval=rs$p,main="Correlations scaled by probability values") 
 #Show the upper and lower confidence intervals
corPlotUpperLowerCi(R=rs,numbers=TRUE) 

#now do this again, but with lighter colors
gr <- colorRampPalette(c("#B52127", "white", "#2171B5"))
corPlot(r=rs$r,numbers=TRUE,pval=rs$p,main="Correlations scaled by probability values",gr=gr) 

corPlotUpperLowerCi(R=rs,numbers=TRUE,gr=gr) 



if(require(psychTools)) {
#do multiple plots 
#Also show the xaxis option
op <- par(mfrow=c(2,2))
corPlot(psychTools::ability,show.legend=FALSE,keep.par=FALSE,upper=FALSE)
f4 <- fa(psychTools::ability,4)
corPlot(f4,show.legend=FALSE,keep.par=FALSE,numbers=TRUE,xlas=3)
om <- omega(psychTools::ability,4)
corPlot(om,show.legend=FALSE,keep.par=FALSE,numbers=TRUE,xaxis=3)
par(op)


corPlotUpperLowerCi(rs,adjust=TRUE,main="Holm adjusted confidence intervals",gr=gr)
}