Testing for heterogeneous factor loadings using mixtures of confirmatory factor analysis models.

The current study assessed the viability of mixture confirmatory factor analysis (CFA) for measurement invariance testing by evaluating the ability of mixture CFA models to identify differences in factor loadings across populations with identical mean structures. Using simulated data from a model with known parameters, convergence rates, parameter recovery, and the power of the likelihood-ratio test were investigated as impacted by sample size, latent class proportions, magnitude of factor loading differences, percentage of non-invariant factor loadings, and pattern of non-invariant factor loadings. Results suggest that mixture CFA models may be a viable option for testing the invariance of factor loadings; however, without differences in latent means and measurement intercepts, results suggest that larger sample sizes, more non-invariant factor loadings, and larger amounts of heterogeneity are needed to successfully estimate parameters and detect differences across latent classes.