Modeling Construct Change Over Time Amidst Potential Changes in Construct Measurement: A Longitudinal Moderated Factor Analysis Approach

In analyzing longitudinal data with growth curve models, a critical assumption is that changes in the observed measures reflect construct change and not changes in the manifestation of the construct over time. However, growth curve models are often fit to a repeated measure constructed as a sum or mean of scale items, making an implicit assumption of constancy of measurement. This practice risks confounding actual construct change with changes in measurement (i.e., differential item functioning; DIF), threatening the validity of conclusions. An improved method that avoids such confounding is the second-order growth curve model (SGC). It specifies a measurement model at each occasion of measurement that can be evaluated for invariance over time. The applicability of SGC is hindered by key limitations: (1) SGC treats time as continuous when modeling construct growth but as discrete when modeling measurement, reducing interpretability and parsimony; (2) the evaluation of DIF becomes increasingly error-prone given multiple timepoints and groups; (3) DIF associated with continuous covariates is difficult to incorporate. Drawing on moderated nonlinear factor analysis (MNLFA), we propose an alternative approach that provides a parsimonious framework for including many timepoints and DIF from different types of covariates. We implement this model through Bayesian estimation, allowing for incorporation of regularizing priors to facilitate efficient evaluation of DIF. We demonstrate a two-step workflow of measurement evaluation and growth modeling, with an empirical example examining changes in adolescent delinquency over time.