adfCor {fungible}

Asymptotic Distribution-Free Covariance Matrix of Correlations

Description

Function for computing an asymptotic distribution-free covariance matrix of correlations.

Usage

adfCor(X, y = NULL)

Arguments

X

Data matrix.

y

Optional vector of criterion scores.

Value

adfCorMat

Asymptotic distribution-free estimate of the covariance matrix of correlations.

Author(s)

Jeff Jones and Niels Waller

References

Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62–83.

Steiger, J. H. and Hakstian, A. R. (1982). The asymptotic distribution of elements of a correlation matrix: Theory and application. British Journal of Mathematical and Statistical Psychology, 35, 208–215.

Examples

## Generate non-normal data using monte1
set.seed(123)
## we will simulate data for 1000 subjects
N <- 1000

## R = the desired population correlation matrix among predictors
R <- matrix(c(1, .5, .5, 1), 2, 2)

## Consider a regression model with coefficient of determination (Rsq): 
Rsq <- .50

## and vector of standardized regression coefficients
Beta <- sqrt(Rsq/t(sqrt(c(.5, .5))) %*% R %*% sqrt(c(.5, .5))) * sqrt(c(.5, .5))

## generate non-normal data for the predictors (X)
## x1 has expected skew = 1 and kurtosis = 3
## x2 has expected skew = 2 and kurtosis = 5
X <- monte1(seed = 123, nvar = 2, nsub = N, cormat = R, skewvec = c(1, 2), 
            kurtvec = c(3, 5))$data
            
## generate criterion scores            
y <- X %*% Beta + sqrt(1-Rsq)*rnorm(N)

## Create ADF Covariance Matrix of Correlations
adfCor(X, y)

#>             12           13           23
#> 12 0.0012078454 0.0005331086 0.0004821594
#> 13 0.0005331086 0.0004980130 0.0002712080
#> 23 0.0004821594 0.0002712080 0.0005415301