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

## Description

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

## Usage

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34``` ```## 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 Sept. 29, 2021, 1:06 a.m.