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
adfCov(X, y)

#>         11       12       13       22       23       33
#> 11 3.438760 2.317159 2.269080 2.442003 1.962584 1.688631
#> 12 2.317159 3.171722 2.278212 3.349173 2.692097 2.028701
#> 13 2.269080 2.278212 2.303659 2.395033 2.149316 2.106310
#> 22 2.442003 3.349173 2.395033 6.275088 4.086652 2.687647
#> 23 1.962584 2.692097 2.149316 4.086652 3.287088 2.501094
#> 33 1.688631 2.028701 2.106310 2.687647 2.501094 2.818664

fungible documentation built on May 29, 2024, 8:28 a.m.