Evaluating Longitudinal Measurement Invariance in Latent Transition Models

• In Event: New Twists on Latent Transition Analysis: Unique Adaptations and Applications

Abstract

Latent transition analysis is mainly used for examining longitudinal discrete-state processes wherein the within-individual state change from time period to time period is captured by the latent class transitions. As with longitudinal autoregressive models for continuous outcomes, there is no part of the general model specification that requires longitudinal measurement invariance; that is, the number and meaning of the latent classes may be different for every time period. However, there are certain circumstances for which a reasonably high level of longitudinal measurement invariance is necessary for the substantive utility of the latent transition model. For example, if we were modeling stages of cognitive development and we wanted to investigate early predictors of stage transitions, we would need the “stages” (latent classes) to be invariant across time so that a transition, say, from Class 1 in time period 1 to Class 2 in time period 2 represented the same developmental transition as a transition from Class 1 in time period 3 to Class 2 in time period 4. Other concepts, such as “staying” in a particular class over time versus “moving” to a different class, also presuppose invariant classes across time.
Although there is much in the factor analysis and IRT literature related to statistical detection and testing of longitudinal non-invariance, there is comparatively little in the LTA literature. Current practices rely primarily on a descriptive heuristic for evaluating longitudinal measurement invariance of the latent classes; most commonly, assuming the same number of classes at each time period, estimating a LTA model allowing the latent class measurement parameters to freely vary across time, and then making a subjective determination about whether the resultant latent classes for each time period have the same meaning, substantively-speaking, and whether the same class labels could be reasonably applied the latent class variables across all the time periods.
The purpose of this paper is to present a new statistical procedure for the detection of longitudinal measurement non-invariance in LTA, borrowing principled practices from IRT linkage analysis. In short, an unconditional LTA model is fit assuming complete measurement invariance across the time periods. Then, the “observed” class-specific item response probabilities for each time period, based on the modal class assignment from the full invariance model, are compared to evaluate if the expected item response, given class membership, is associated with time. A significant time effect on the conditional item responses signals an area of non-invariance. The performance of this approach is evaluated through a limited simulation study and is illustrated using a real data example involving transitions across latent classes of social competence during elementary school from a prospective longitudinal study of school-aged children.

Author

• Katherine E. Masyn, Harvard University