Measurement Invariance in Latent Transition Models

• In Event: Issues of Measurement Invariance in Mixture Models for Educational Data

Abstract

Latent transition analysis (LTA) provides an opportunity for the study of development in discrete states over time, providing a flexible modeling framework for educational researchers to address pressing research questions. Most applications of the LTA model found in the literature make the assumption of measurement invariance-- that is, they assume that both the number and type of latent classes that emerge across measurement occasions are the same. While the assumption of measurement invariance (MI) certainly makes interpretation of transition probabilities more straightforward, it is not a necessary assumption for model identification or valid interpretation, and is often used in applications without an empirical or theoretical justification. Additionally, MI significantly reduces the number of measurement parameters estimated at each time point, significantly increasing model estimating time and complexity.
While there are certainly practical reasons why the assumption of MI would be appealing, the implications of wrongly assuming MI across occasions without empirical support will have detrimental effects to other parts of the model. Importantly, it’s not just a statistical misspecification, but it has important implications on the ability to make meaningful substantive interpretation of the LTA results.
The purpose of this paper is to highlight the modeling flexibility that allows for the empirical evaluation of longitudinal measurement invariance with LTA. This same flexibility introduces the possibility of partial invariance which could accommodate the deletion and insertion of latent class indicators over time in the LTA specification without having to delete indicators not used across all time points (as is typically done). Similarly, developmental changes in the functioning of some items as indicators of the latent classes can also be accommodated. To facilitate an understanding of MI in LTA, in this paper we propose a modeling framework for testing MI, with specific modeling steps for use by researchers, to test for measurement invariance in the LTA context. Our hope is that by providing a better understanding of the implications and providing a specific framework to test for MI that the empirical investigation of longitudinal invariance in LTA will become part of standard practices for applied researchers.

Authors

• Karen L. Nylund-Gibson, University of California - Santa Barbara

• Katherine E. Masyn, Georgia State University