Testing for factor loading differences in mixture simultaneous factor analysis: A Monte Carlo simulation-based perspective

Factor analysis is ubiquitously applied in behavioral sciences for capturing covariances of observed variables by latent variables (factors). When factor-analyzing data from many groups of subjects, mixture simultaneous factor analysis (MSFA) determines which groups have the same factor model by clustering them based on their factor loadings, factor (co)variances and residual variances. Two Monte Carlo simulations are performed to investigate the power and type I error of Wald tests for factor loading differences in MSFA, as affected by characteristics of the data (sample size in terms of number and size of groups), factor models (item communality levels, sizes and types of loading differences) and clustering (cluster size, classification error and uncertainty). The results were better in case of equal cluster sizes, strongly overdetermined factors, high communalities, and larger primary loading differences.