Comparing frequentist and Bayesian methods for factorial invariance with latent distribution heterogeneity

Factorial invariance is critical for ensuring consistent relationships between measured variables and latent constructs across groups or time, enabling valid comparisons in social science research. Detecting factorial invariance becomes challenging when varying degrees of heterogeneity are present in the distribution of latent factors. This simulation study examined how changes in latent means and variances between groups influence the detection of noninvariance, comparing Bayesian and maximum likelihood fit measures. The design factors included sample size, noninvariance levels, and latent factor distributions. Results indicated that differences in factor variance have a stronger impact on measurement invariance than differences in factor means, with heterogeneity in latent variances more strongly affecting scalar invariance testing than metric invariance testing. Among model selection methods, goodness-of-fit indices generally exhibited lower power compared to likelihood ratio tests (LRTs), information criteria (ICs; except BIC), and leave-one-out cross-validation (LOO), which achieved a good balance between false and true positive rates.