Investigating the Impacts of Longitudinal Measurement Non-Invariance in Latent Transition Analysis

• In Event: Advancing Mixture Modeling Methodology: Model Specification, Class Enumeration, and Measurement Invariance for Complex Data Structures

Abstract

In recent years, researchers in education and the social sciences have increasingly used longitudinal person-centered approaches such as latent transition analysis (LTA) to examine individual differences in developmental patterns of cognition and behavior. While longitudinal measurement invariance (LMI) is not required in specifying LTA models, imposing LMI constraints offers statistical and interpretive advantages (Nylund-Gibson, 2023) and should be tested when theory supports parameter invariance (Masyn, 2017). However, LMI is frequently assumed in LTA applications without empirical evaluation (Maassen et al., 2023), and the impact of ignoring longitudinal measurement non-invariance (LMNI), when present in data, has been notably unexplored in the LTA literature (cf., Talley, 2020).
Talley (2020) initiated methodological inquiry into the consequences of violating configural invariance in LTA. Building on this work, the current simulation study systematically examines the impacts of ignoring LMNI in LTA by evaluating the accuracy, precision, and coverage of parameter estimates—specifically, latent class proportions, transition probabilities, and class-specific item response probabilities—when LMI is incorrectly assumed.
We conducted a Monte Carlo simulation study generating populations with varying magnitudes and types of LMNI (e.g., full LMI, uniform LMNI in one or multiple waves, nonuniform LMNI in one or multiple waves). Realistic parameter sets for data generation were identified through a review of recently published applied LTA studies in education and psychology. Population models included three configurally-invariant latent classes at each of three waves, with six binary latent class indicators per wave. Sample size was varied as a design factor. Analytic models applied to each simulation replication include LTA models with full LMI constraints and no LMI constraints, as well as the correctly-specified model (corresponding to the specific population model). In addition to assessing the accuracy and precision in the measurement and structural parameter estimates across the analytic models, we also examined the performance of the likelihood ratio test comparing the full-LMI model to the no-LMI model in detecting the presence of LMNI, as this is the most common statistical test of LMI used in LTA applications in the rare instances when an empirical evaluation of LMI is done. The presentation provides an overview and synthesis of the study results with implications for researchers using LTA in real data settings.
A parallel investigation was initiated to examine LMNI in the emerging Random Intercept LTA (RI-LTA; Muthén & Asparouhov, 2022) model using the same population parameters and design factors but incorporating a random intercept in both data generation and analytic models.
This study is significant in three ways. First, it provides empirical evidence quantifying the impacts of ignoring LMNI in LTA, underscoring the need for improved methods to detect LMNI. Second, it offers practical guidance for applied researchers by identifying conditions under which parameter estimates become biased, helping to prevent erroneous conclusions about developmental change. Finally, by encouraging more rigorous methodological practices, this research enhances the validity of findings in education and social science studies using LTA to inform theory and practice.

Authors

• Boshi Wang, Georgia State University

• Katherine E. Masyn, Georgia State University