psych (version 1.0-17)

mat.regress: Multiple Regression from matrix input

Description

This function extracts subsets of variables (x and y) from a correlation matrix (m) and then find the multiple correlation and beta weights of the (x) set predicting each member of the (y) set.

Usage

mat.regress(m, x, y,digits=2)

Arguments

m

a matrix of correlations

x

the column numbers of the x set (e.g., c(1,3,5)

y

the column numbers of the y set (e.g., c(2,4,6)

digits

round the answer to digits

Value

• beta
  the beta weights for each variable in X for each variable in Y
• R2
  The multiple R2 for each equation

Details

Although it is more common to calculate multiple regression from raw data, it is, of course, possible to do so from a set of correlations. The input to the function is a square covariance or correlation matrix, as well as the column numbers of the x (predictor) and y (criterion) variables. The output is a set of multiple correlations, one for each dependent variable in the y set. A typical use in the SAPA project is to form item composites by clustering or factoring (see ICLUST, principal), extract the clusters from these results (factor2cluster), and then form the composite correlation matrix using cluster.cor. The variables in this reduced matrix may then be used in multiple R procedures using mat.regress.

References

For an application of this procedure, see http://personality-project.org/revelle/publications/sapa.pdf

See Also

cluster.cor, factor2cluster,principal,ICLUST

Examples

test.data <- Harman74.cor$cov     #24 mental variables
#choose 3 of them to regress against another 4 -- arbitrary choice of variables
print(mat.regress(test.data,c(1,2,3),c(4,5,10,12)),digits=2)
#gives this output
#print(mat.regress(test.data,c(1,2,3),c(4,5,10,12)),digits=2)
#$beta
#                 Flags GeneralInformation Addition CountingDots
#VisualPerception 0.397               0.22    0.162        0.296
#Cubes            0.064               0.18    0.056        0.049
#PaperFormBoard   0.125               0.10   -0.158        0.005
#
#$R2
#             Flags GeneralInformation           Addition       CountingDots 
#             0.239              0.148              0.034              0.101 
#


## The function is currently defined as
function(m,x,y)  {
 #a function to extract subsets of variables (a and b) from a correlation matrix m
  #and find the multiple correlation beta weights + R2 of the a set predicting the b set
    
    #first reorder the matrix to select the right variables
         nm <- dim(m)[1]
        t.mat <- matrix(0,ncol=nm,nrow=nm)
        xy <- c(x,y)
         numx <- length(x)
     	numy <- length(y)
        nxy <- numx+numy
        for (i in 1:nxy) {
     	t.mat[i,xy[i]] <- 1 }
     	
     	reorder <- t.mat %*% m %*% t(t.mat)
     	a.matrix <- reorder[1:numx,1:numx]
     	b.matrix <- reorder[1:numx,(numx+1):nxy]
     	model.mat <- solve(a.matrix,b.matrix)       #solve the equation bY~aX
     	if (length(y) >1 ) { rownames(model.mat) <- rownames(m)[x]
     	 colnames(model.mat) <- colnames(m)[y]
     	 
     	R2 <- colSums(model.mat * b.matrix) }
     	 else { R2 <- sum(model.mat * b.matrix)
     	 names(model.mat) <- rownames(m)[x]
     	 names(R2) <- colnames(m)[y]}
     	mat.regress <- list(beta=model.mat,R2=R2)
     	return(mat.regress)
     	}