BSEM Measurement Invariance Analysis

This paper concerns measurement invariance analysis for situations with many groups or time points. A BSEM (Bayesian Structural Equation Modeling) approach is proposed for detecting non-invariance that is similar to modification indices with maximum-likelihood estimation, but unlike maximum-likelihood is applicable also for high-dimensional latent variable models for categorical variables. Under certain forms of non-invariance, BSEM gives proper comparisons of factor means and variances using only approximate measurement invariance and without relaxing the invariance specifications or deleting non-invariant items. To ensure correct estimation, a two-step Bayesian analysis procedure is proposed, where step 1 uses BSEM to identify non-invariant parameters and step 2 frees those parameters.