asyCov {metaSEM}

Compute Asymptotic Covariance Matrix of a Correlation/Covariance Matrix

Description

It computes the asymptotic sampling covariance matrix of a correlation/covariance matrix under the assumption of multivariate normality.

Usage

asyCov(x, n, cor.analysis = TRUE, as.matrix = TRUE,
       acov=c("weighted", "individual", "unweighted"), ...)
asyCovOld(x, n, cor.analysis = TRUE, dropNA = FALSE, as.matrix = TRUE,
       acov=c("individual", "unweighted", "weighted"),
       suppressWarnings = TRUE,  silent = TRUE, run = TRUE, ...)

Arguments

x

A correlation/covariance matrix or a list of correlation/covariance matrices. NA on the variables or other values defined in na.strings will be removed before the analysis. Note that it only checks the diagonal elements of the matrices. If there are missing values, make sure that the diagonals are coded with NA or values defined in na.strings.

n

Sample size or a vector of sample sizes

cor.analysis

Logical. The output is either a correlation or covariance matrix.

dropNA

Logical. If it is TRUE, the resultant dimensions will be reduced by dropping the missing variables. If it is FALSE, the resultant dimensions are the same as the input by keeping the missing variables.

as.matrix

Logical. If it is TRUE and x is a list of correlation/covariance matrices with the same dimensions, the asymptotic covariance matrices will be column vectorized and stacked together. If it is FALSE, the output will be a list of asymptotic covariance matrices. Note that if it is TRUE, dropNA will be FALSE automatically. This option is useful when passing the asymptotic covariance matrices to meta

acov

If it is individual (the default), the sampling variance-covariance matrices are calculated based on the individual correlation/covariance matrix. If it is either unweighted or weighted, the average correlation/covariance matrix is calculated based on the unweighted or weighted mean with the sample sizes. The average correlation/covariance matrix is used to calculate the sampling variance-covariance matrices.

suppressWarnings

Logical. If TRUE, warnings are suppressed. It is passed to mxRun.

silent

Logical. An argument to be passed to mxRun

run

Logical. If FALSE, only return the mx model without running the analysis.

...

It is ignored in asyCov. The additional arguments will be passed to mxRun in asyCovOld.

Value

An asymptotic covariance matrix of the vectorized correlation/covariance matrix or a list of these matrices. If as.matrix=TRUE and x is a list of matrices, the output is a stacked matrix.

Note

Before 1.2.6, asyCov used an SEM approach based on Cheung and Chan (2004). After 1.2.6, asyCov was rewritten based on Olkin and Siotani (1976) for correlation matrix and Yuan and Bentler (2007, p. 371) for covariance matrix. Arguments such as dropNA, suppressWarnings, silent, and run were dropped. The original version was renamed to asyCovOld for compatibility.

Author(s)

Mike W.-L. Cheung <[e-mail]>

References

Cheung, M. W.-L., & Chan, W. (2004). Testing dependent correlation coefficients via structural equation modeling. Organizational Research Methods, 7, 206-223.

Olkin, I., & Siotani, M. (1976). Asymptotic distribution of functions of a correlation matrix. In S. Ideka (Ed.), Essays in probability and statistics (pp. 235-251). Shinko Tsusho.

Yuan, K.-H., & Bentler, P. M. (2007). Robust procedures in structural equation modeling. In S.-Y. Lee (Ed.), Handbook of Latent Variable and Related Models (pp. 367-397). Elsevier/North-Holland.

Examples

C1 <- matrix(c(1,0.5,0.4,0.5,1,0.2,0.4,0.2,1), ncol=3)  
asyCov(C1, n=100)

## Data with missing values
C2 <- matrix(c(1,0.4,NA,0.4,1,NA,NA,NA,NA), ncol=3)  
C3 <- matrix(c(1,0.2,0.2,1), ncol=2)

## Output is a stacked matrix of asymptotic covariance matrices
asyCov(list(C1,C2), n=c(100,50), as.matrix=TRUE)

## Output is a stacked matrix of asymptotic covariance matrices
asyCov(list(C3,C3), n=c(100,50), as.matrix=TRUE)

## Output is a list of asymptotic covariance matrices using the old version
asyCovOld(list(C1,C2,C3), n=c(100,50,50), dropNA=TRUE, as.matrix=FALSE)