Assessing and comparing models for sequence data by microsimulation (with Supplementary Material)

We consider the study of the occurrence of different states over (discrete) time for a set of subjects, focusing on the resulting trajectories as a whole rather than on the occurrence of specific events. Such situation occurs commonly in a variety of settings, for example in the social and biomedical sciences. Model based approaches, such as multi-state models or hidden Markov models, designed to study the transitions across states, are being used increasingly to analyze trajectories and to study their relationships with a set of explanatory variables. Comparing the performance of competing models, typically based upon different assumptions, is an open problem. To accomplish this task, we introduce a novel approach based on microsimulation, i.e. the model-based generation of trajectories, and on dissimilarities. In particular, we discuss some criteria to compare competing models with respect to their ability to generate trajectories similar to the ones in the data. We illustrate the methods using life course trajectories arising from the Fertility and Family Survey study.