Elegant correlation table using xtable R package

Correlation matrix analysis

The following R code computes a correlation matrix using mtcars data. Click here to read more.

mcor<-round(cor(mtcars),2)
mcor

       mpg   cyl  disp    hp  drat    wt  qsec    vs    am  gear  carb
mpg   1.00 -0.85 -0.85 -0.78  0.68 -0.87  0.42  0.66  0.60  0.48 -0.55
cyl  -0.85  1.00  0.90  0.83 -0.70  0.78 -0.59 -0.81 -0.52 -0.49  0.53
disp -0.85  0.90  1.00  0.79 -0.71  0.89 -0.43 -0.71 -0.59 -0.56  0.39
hp   -0.78  0.83  0.79  1.00 -0.45  0.66 -0.71 -0.72 -0.24 -0.13  0.75
drat  0.68 -0.70 -0.71 -0.45  1.00 -0.71  0.09  0.44  0.71  0.70 -0.09
wt   -0.87  0.78  0.89  0.66 -0.71  1.00 -0.17 -0.55 -0.69 -0.58  0.43
qsec  0.42 -0.59 -0.43 -0.71  0.09 -0.17  1.00  0.74 -0.23 -0.21 -0.66
vs    0.66 -0.81 -0.71 -0.72  0.44 -0.55  0.74  1.00  0.17  0.21 -0.57
am    0.60 -0.52 -0.59 -0.24  0.71 -0.69 -0.23  0.17  1.00  0.79  0.06
gear  0.48 -0.49 -0.56 -0.13  0.70 -0.58 -0.21  0.21  0.79  1.00  0.27
carb -0.55  0.53  0.39  0.75 -0.09  0.43 -0.66 -0.57  0.06  0.27  1.00

The result is a table of correlation coefficients between all possible pairs of variables.

Lower and upper triangular part of a correlation matrix

To get the lower or the upper part of a correlation matrix, the R function lower.tri() or upper.tri() can be used. The formats of the functions are :

lower.tri(x, diag = FALSE)
upper.tri(x, diag = FALSE)

- x : is the correlation matrix - diag : if TRUE the diagonal are not included in the result.

The two functions above, return a matrix of logicals which has the same size of a the correlation matrix. The entries is TRUE in the lower or upper triangle :

upper.tri(mcor)

       [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11]
 [1,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
 [2,] FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
 [3,] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
 [4,] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
 [5,] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
 [6,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
 [7,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
 [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
 [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
[10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
[11,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

# Hide upper triangle
upper<-mcor
upper[upper.tri(mcor)]<-""
upper<-as.data.frame(upper)
upper

       mpg   cyl  disp    hp  drat    wt  qsec    vs   am gear carb
mpg      1                                                         
cyl  -0.85     1                                                   
disp -0.85   0.9     1                                             
hp   -0.78  0.83  0.79     1                                       
drat  0.68  -0.7 -0.71 -0.45     1                                 
wt   -0.87  0.78  0.89  0.66 -0.71     1                           
qsec  0.42 -0.59 -0.43 -0.71  0.09 -0.17     1                     
vs    0.66 -0.81 -0.71 -0.72  0.44 -0.55  0.74     1               
am     0.6 -0.52 -0.59 -0.24  0.71 -0.69 -0.23  0.17    1          
gear  0.48 -0.49 -0.56 -0.13   0.7 -0.58 -0.21  0.21 0.79    1     
carb -0.55  0.53  0.39  0.75 -0.09  0.43 -0.66 -0.57 0.06 0.27    1

#Hide lower triangle
lower<-mcor
lower[lower.tri(mcor, diag=TRUE)]<-""
lower<-as.data.frame(lower)
lower

     mpg   cyl  disp    hp  drat    wt  qsec    vs    am  gear  carb
mpg      -0.85 -0.85 -0.78  0.68 -0.87  0.42  0.66   0.6  0.48 -0.55
cyl              0.9  0.83  -0.7  0.78 -0.59 -0.81 -0.52 -0.49  0.53
disp                  0.79 -0.71  0.89 -0.43 -0.71 -0.59 -0.56  0.39
hp                         -0.45  0.66 -0.71 -0.72 -0.24 -0.13  0.75
drat                             -0.71  0.09  0.44  0.71   0.7 -0.09
wt                                     -0.17 -0.55 -0.69 -0.58  0.43
qsec                                          0.74 -0.23 -0.21 -0.66
vs                                                  0.17  0.21 -0.57
am                                                        0.79  0.06
gear                                                            0.27
carb                                                                

Use xtable R package to display nice correlation table in html format

library(xtable)
print(xtable(upper), type="html")

Combine matrix of correlation coefficients and significance levels

Custom function corstars() is used to combine the correlation coefficients and the level of significance. The R code of the function is provided at the end of this article. It requires 2 packages :

• The Hmisc R package to compute the matrix of correlation coefficients and the corresponding p-values.
• The xtable R package for displaying in HTML or Latex format.

corstars(mtcars[,1:7], result="html")

p < .0001 ‘****’; p < .001 ‘***’, p < .01 ‘**’, p < .05 ‘*’

The code of corstars function (The code is adapted from the one posted on this forum and on this blog ):

# x is a matrix containing the data
# method : correlation method. "pearson"" or "spearman"" is supported
# removeTriangle : remove upper or lower triangle
# results :  if "html" or "latex"
  # the results will be displayed in html or latex format
corstars <-function(x, method=c("pearson", "spearman"), removeTriangle=c("upper", "lower"),
                     result=c("none", "html", "latex")){
    #Compute correlation matrix
    require(Hmisc)
    x <- as.matrix(x)
    correlation_matrix<-rcorr(x, type=method[1])
    R <- correlation_matrix$r # Matrix of correlation coeficients
    p <- correlation_matrix$P # Matrix of p-value 
    
    ## Define notions for significance levels; spacing is important.
    mystars <- ifelse(p < .0001, "****", ifelse(p < .001, "*** ", ifelse(p < .01, "**  ", ifelse(p < .05, "*   ", "    "))))
    
    ## trunctuate the correlation matrix to two decimal
    R <- format(round(cbind(rep(-1.11, ncol(x)), R), 2))[,-1]
    
    ## build a new matrix that includes the correlations with their apropriate stars
    Rnew <- matrix(paste(R, mystars, sep=""), ncol=ncol(x))
    diag(Rnew) <- paste(diag(R), " ", sep="")
    rownames(Rnew) <- colnames(x)
    colnames(Rnew) <- paste(colnames(x), "", sep="")
    
    ## remove upper triangle of correlation matrix
    if(removeTriangle[1]=="upper"){
      Rnew <- as.matrix(Rnew)
      Rnew[upper.tri(Rnew, diag = TRUE)] <- ""
      Rnew <- as.data.frame(Rnew)
    }
    
    ## remove lower triangle of correlation matrix
    else if(removeTriangle[1]=="lower"){
      Rnew <- as.matrix(Rnew)
      Rnew[lower.tri(Rnew, diag = TRUE)] <- ""
      Rnew <- as.data.frame(Rnew)
    }
    
    ## remove last column and return the correlation matrix
    Rnew <- cbind(Rnew[1:length(Rnew)-1])
    if (result[1]=="none") return(Rnew)
    else{
      if(result[1]=="html") print(xtable(Rnew), type="html")
      else print(xtable(Rnew), type="latex") 
    }
} 

Conclusions

Infos

This analysis was performed using R (ver. 3.3.2).