Improving the Evaluation of Construct Change Over Time: Advantages of Longitudinal Moderated Nonlinear Factor...

Conventional growth curve models, often fitted to sum or mean scores of scale responses, do not account for potential changes in item measurement unrelated to construct growth (i.e. differential item functioning; DIF). An untested assumption is that the construct is stably measured over time. When this assumption is incorrect, estimates of construct change obtained from conventional growth models may be biased. To address this issue, we recently proposed a new, flexible second-order growth model based upon a longitudinal extension of moderated nonlinear factor analysis (MNLFA; Chen & Bauer, 2024) that allows for DIF from categorical or continuous covariates that may or may not vary over time (e.g. sex, age, age $\times$ sex). Further, we applied Bayesian regularization to evaluate DIF effects across multiple sources simultaneously without imposing item equality assumptions (i.e. anchor items). In this paper, we present a simulation study to validate the model's performance in detecting DIF over time and between groups. Results indicate that the proposed approach effectively detects DIF without predetermined anchor items and avoids the biased growth estimates consistently observed for conventional models fitted to mean scores. We demonstrate the utility of the method in an empirical example on child externalizing behaviors.