Mostly Harmless Direct Effects: A Comparison of Different Latent Markov Modeling Approaches

Abstract

We evaluate the performance of the most common estimators of latent Markov (LM) models with covariates in the presence of direct effects of the covariates on the indicators of the LM model. In LM modeling it is common practice not to model such direct effects, ignoring the consequences that might have on the overall model fit and the parameters of interest. However, in the general literature about latent variable modeling it is well known that unmodeled direct effects can severely bias the parameter estimates of the model at hand. We evaluate how the presence of direct effects influences the bias and efficiency of the 3 most common estimators of LM models, the 1-step, 2-step, and 3-step approaches. Furthermore, we propose amendments (that were thus far not used in the context of LM modeling) to the 2- and 3-step approaches that make it possible to account for direct effects and eliminate bias as a consequence. This is done by modeling the (possible) direct effects in the first step of the stepwise estimation procedures. We evaluate the proposed estimators through an extensive simulation study, and illustrate them via a real data application. Our results show, first, that the augmented 2-step and 3-step approaches are unbiased and efficient estimators of LM models with direct effects. Second, ignoring the direct effects leads to biased estimates with all existing estimators, the 1-step approach being the most sensitive.

Keywords:

• direct effects
• latent Markov model
• model comparison
• stepwise modeling

Notes

¹ In principle, both modal and proportional assignment rules can be used. Yet, proportional assignment could become infeasible with larger number of time points, as nonzero weights are allocated to all possible latent state patterns of each observation.

² A larger number of states was also tried, but in all cases we observed that a number approximately twice as large as the number of states in the latent variable of interest was enough to approximate the distribution of the noise.

³ See https://www.icpsr.umich.edu/icpsrweb/ICPSR/series/28/studies/7398?archive=ICPSR sort.