dot-simulate_cfm_eigen: Reference eigenvalues for the efa_nest() simulation via the...

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Reference eigenvalues for the efa_nest() simulation via the shared kernel.

Description

Internal helper called from efa_nest(). Simulates nreps datasets from an (nf - 1)-factor reference model, given that model's loadings Lambda and uniquenesses Psi, and returns the nf-th largest eigenvalue of each simulated correlation matrix. The data are drawn with the shared Z * M rule (see .simulate_cfm_mvn()) using the factor-score square root ⁠M = t([Lambda | diag(sqrt(Psi))])⁠, so a row randn(1, nf - 1 + p) * M is N(0, Lambda Lambda' + diag(Psi)). Drawing nf - 1 + p standard normals and post-multiplying by the factor-score matrix is faster than forming the model- implied correlation matrix and drawing from it, and matches the position at which efa_nest() reads the reference eigenvalue.

Usage

.simulate_cfm_eigen(nf, N, Lambda, Psi, nreps = 1000L)

Arguments

nf	integer. Position of the empirical eigenvalue being tested (1-based); the nf-th largest simulated eigenvalue is returned per replicate.
N	integer. Number of cases / observations per simulated dataset.
Lambda	numeric matrix. Loadings of the (nf - 1)-factor reference model (⁠p x (nf - 1)⁠); pass a ⁠p x 0⁠ matrix for the nf == 1 null (identity) model.
Psi	numeric vector. Uniquenesses (1 - h2) of the reference model.
nreps	integer. Number of datasets to simulate.

EFAtools documentation built on Aug. 21, 2026, 5:16 p.m.