Latent Class Analysis with Measurement Invariance Testing: Simulation Study to Compare Overall Likelihood Ratio vs Residual Fit Statistics Based Model Selection

A standard assumption of latent class (LC) analysis is conditional independence, that is the items of the LC are independent of the covariates given the LCs. Several approaches have been proposed for identifying violations of this assumption. The recently proposed likelihood ratio approach is compared to residual statistics (bivariate residuals [BVR] and expected parameter change [EPC] statistics) for identifying nonuniform direct effect of covariates on the items of the LC model. The simulation study results show that the likelihood ratio (LR) test correctly identifies direct effects more often than the BVR statistics, showing comparable results to the EPC statistic in many situations- this at the price of having also a higher false positive rate than BVR. A real data example illustrates the use of the three procedures. Overall the combined use of residual statistics and LR testing is recommended for applied research.