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.

```
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,
cuts=c(.001,.01),scale=TRUE,cex,MAR,upper=TRUE,diag=TRUE, symmetric=TRUE,stars=FALSE,
adjust="holm",xaxis=1, xlas=0,ylas=2,gr=NULL,alpha=.75,min.length=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,
cuts=c(.001,.01),scale=TRUE,cex,MAR,upper=TRUE,diag=TRUE,
symmetric=TRUE,stars=FALSE,adjust="holm",xaxis=1,xlas=0,ylas=2,gr=NULL,alpha=.75,
min.length=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

R

The object returned from `cor.ci`

numbers

Display the numeric value of the correlations. (As of September, 2019) Defaults to TRUE.

colors

Defaults to TRUE and colors use colors from the colorRampPalette from red through white to blue, but colors=FALSE will use a grey scale

n

The number of levels of shading to use. Defaults to 51

main

A title. Defaults to "correlation plot"

zlim

The range of values to color -- defaults to -1 to 1. If specified as NULL, then defaults to min and max observed correlation.

show.legend

A legend (key) to the colors is shown on the right hand side

labels

if NULL, use column and row names, otherwise use labels

n.legend

How many categories should be labelled in the legend?

keep.par

restore the graphic parameters when exiting

pval

scale the numbers by their pvals, categorizing them based upon the values of cuts

cuts

Scale the numbers by the categories defined by pval < cuts

scale

Should the size of the numbers be scaled by the significance level?

select

Select the subset of variables to plot

cex

Character size. Should be reduced a bit for large numbers of variables.

MAR

Allows for adjustment of the margins if using really long labels or big fonts

upper

Should the upper off diagonal matrix be drawn, or left blank?

diag

Should we show the diagonal?

symmetric

By default, if given a non-symmetric matrix, we find the correlations using pair.wise complete and then show them. If wanting to display a non-symmetric matrix, then specify that symmetric is FALSE

stars

For those people who like to show the 'significance' of correlations by using magic astricks, set stars=TRUE

adjust

If showing significance, should we adjust for multiple tests? The default is to show zero order probabilities below the diagonal and adjust these using the 'holm' correction above the diagonal. Use adjust = "none" if no adjustment is desired. adjust is also used in corPlotUpperLowerCI to show the nominal alpha confidence intervals (adjust =FALSE) or the Bonferonni adjusted confidence intervals (adjust=TRUE).

xlas

Orientation of the x axis labels (1 = horizontal, 0, parallel to axis, 2 perpendicular to axis)

ylas

Orientation of the y axis labels (1 = horizontal, 0, parallel to axis, 2 perpendicular to axis)

xaxis

By default, draw this below the figure. If xaxis=3, then it wil be drawn above the figure

gr

A color gradient: e.g., gr <- colorRampPalette(c("#B52127", "white", "#2171B5")) will produce slightly more pleasing (to some) colors. See next to last example.

alpha

The degree of transparency (0 = completely, 1= not). Default value of .75 makes somewhat moreor pleasing plots when using numbers.

min.length

If not NULL, then the maximum number of characters to use in row/column labels

...

Other parameters for axis (e.g., cex.axis to change the font size, srt to rotate the numbers in the plot)

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 `corr.test`

.

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 `corr.test`

, the upper off diagonal will be scaled by the corrected probability, the lower off diagonal the scaling is the uncorrected probabilities.

If using the output of `corr.test`

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 corr.test).

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 correlations will be found.

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.

# NOT RUN { 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 <- corr.test(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 <- corr.test(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 cor.plot.upperLowerCi(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) cor.plot.upperLowerCi(R=rs,numbers=TRUE,gr=gr) #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) # }