Misspecification of longitudinal measurement invariance within the latent transition analysis framework

Assessing the impact of violations to longitudinal measurement invariance (LMI) within a mixture modeling context is not well-covered territory in current methodological research, and is notably unexplored in latent transition analyses (LTA). At a minimum, it can be assumed that any substantial departure from LMI within the LTA framework would thwart unambiguous interpretations of the latent classes as well as the probabilities of transitioning in and out of each latent class over time. The intent of this dissertation is to initiate the conversation by providing some thoughts and examples of how LMI can manifest in LTA models, followed by a statistical assessment of the most straightforward violation to LMI in LTA: configural non-invariance, or unequal numbers of latent classes emerging at each time point in the population. Monte Carlo simulation methods were used to generate data exhibiting varying degrees of departure from configural LMI, then class enumeration decisions and parameter recovery were explored under LTA models that assume configural invariance. The conditions manipulated in this simulation include the pattern of non-invariance (i.e., classes merging or splitting over time), class homogeneity and separation, class prevalence splits in the non-invariant class, overall sample size, and the transition matrix design (i.e., ordered or unordered movement). By imposing a configurally invariant LTA model on data that are non-invariant in nature, the researcher is risking a complete misestimation of the number and type of latent classes that exist at a particular time point, particularly in terms of both under- and overestimated values of within-class agreement. For this reason, it is recommended that researchers make class enumeration decisions at each measurement occasion, based on time-specific latent class analyses (LCA), before fitting the overall LTA model to the data. Any non-invariance discovered at the LCA level can be substantively explored and modeled with a non-symmetrical LTA. However, if the best-fitting class solution must be made at the LTA level, results from this study suggest that the AIC and ABIC indices are preferable for their overfitting tendencies. It seems reasonable to prefer an overfitted lens for analyzing non-invariant data, due to the added flexibility of the additional parameters estimated, but the parsimony of an underfitted model may be preferable in certain situations. As per usual, larger sample sizes (in this study, N = 1,000) are protective against parameter bias and convergence issues.