adfCor | R Documentation |

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

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

`X` |
Data matrix. |

`y` |
Optional vector of criterion scores. |

`adfCorMat` |
Asymptotic distribution-free estimate of the covariance matrix of correlations. |

Jeff Jones and Niels Waller

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.

```
## 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
```

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