# adfCov: Asymptotic Distribution-Free Covariance Matrix of Covariances In fungible: Psychometric Functions from the Waller Lab

## Asymptotic Distribution-Free Covariance Matrix of Covariances

### Description

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

### Usage

``````adfCov(X, y = NULL)
``````

### Arguments

 `X` Data matrix. `y` Optional vector of criterion scores.

### Value

 `adfCovMat` Asymptotic distribution-free estimate of the covariance matrix of covariances

### 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.

### 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 Covariances