Testing measurement and structural invariance in latent moderated mediation models

Testing measurement and structural invariance in latent mediation models – A comparison of IPCR and Bayesian MNLFA

Moderated mediation models are frequently used in psychological research to examine direct, indirect, and total effects across an external moderating variable. When these models involve latent variables, measurement invariance should be tested first to ensure that measures function equivalently across subpopulations. If measurement invariance is violated, conclusions drawn about the moderation effects can be biased. However, measurement invariance is seldom tested across the moderator variable itself, especially if it is continuous. Individual parameter contribution regression (IPCR) and moderated nonlinear latent factor analysis (MNLFA) are two appraoches that allow testing measurement and structural invariance simultaneously and across continuous covariates. With data from N = 383 couples in the German Family Panel (pairfam, Brüderl et al., 2022), we show both approaches and how MNLFA can be estimated in a Bayesian framework. Within the Bayesian MNLFA analysis, we explain model selection with posterior predictive model checks and leave-one-out cross-validation (Vehtari et al., 2017). Based on the empirical application and a simulation study, we provide recommendations for applied researchers working with latent moderated mediation models.