Modeling Growth When Measurement Properties Change Between Persons and Within Persons Over Time: A Bayesian Regularized Second-Order Growth Curve Model

A common interest in educational and psychological measurement is to examine change over time through longitudinal assessments. To accurately capture true change in an underlying construct of interest, we must also account for changes in the way the construct manifests itself over time. One essential approach is longitudinal measurement models that analyze construct change over time and evaluate item characteristics at each wave. However, limitations exist for traditional longitudinal measurement and second-order growth models, such as an inability to incorporate time-varying covariates (TVC) that possess different values among individuals at a given wave. We propose an alternative model drawing on the advantages of regularized moderated nonlinear factor analysis (MNLFA; Bauer et al., 2019). This setup follows the MNLFA framework in using covariate moderation on item parameters to represent differential item functioning (DIF). Time and other TVC effects are incorporated explicitly as level-1 item moderation and level-2 trait moderation effects. The proposed model is more parsimonious than the traditional second-order growth model and one of the first setups to estimate DIF effects from both time-varying and time-invariant covariates. Additionally, this model can evaluate DIF effects from multiple covariates simultaneously without imposing a priori item equality constraints. It does so by applying Bayesian regularization to DIF effects and identifying the model without using anchor items (Chen et al., 2022). The current study evaluates the performance of the proposed regularized longitudinal MNLFA model through a simulation and empirical data. Performance outcomes include DIF detection rates and accuracy in recovering growth parameters. An empirical example on adolescent delinquency and early alcohol use is presented. This study demonstrates the feasibility and importance of including both time-varying and -invariant covariate effects in longitudinal measurement evaluation and growth modeling.