dot-simulate_cfm_mvn: Draw multivariate-normal data from a population correlation...
In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

.simulate_cfm_mvn

R Documentation

Draw multivariate-normal data from a population correlation matrix.

Description

Internal helper called from efa_simulate(). Draws N cases from a p-variate normal with correlation (or covariance) R by post-multiplying a matrix of standard normal deviates by a matrix square root M of R (with M' M = R, so the rows of Z * M are N(0, R)). This is the same Z * M rule used by the NEST reference simulation (.simulate_cfm_eigen): there M is the transposed factor-score matrix, here it is a Cholesky or eigen square root. A positive-definite R is factored by Cholesky; a positive-semidefinite but singular R (which makes the Cholesky fail although it is still a valid covariance, e.g. a no-factor block or a smoothed factor intercorrelation matrix) falls back to a symmetric eigen square root.

Usage

.simulate_cfm_mvn(R, N, tol = 1e-08)

Arguments

`R`	numeric matrix. Population correlation/covariance matrix.
`N`	integer. Number of cases to draw.
`tol`	numeric. Eigenvalues below `-tol` mark `R` as indefinite.