Markov chain model selection by misclassitied model probabilities

This study presents a probability measure based on model classification concept to evaluate the adequacy of Markov chain models with incomplete observations. We first define predictive indicators based on transition probabilities and use a square loss function to quantify the discrepancies between those predictive indicators and their correspondence transition probabilities. We then derive misclassified model probabilities from the distribution of the loss function and propose a decision rule to select proper Markov chain models. A simulation study shows that the proposed approach works well under different sizes of sample and different rates of missing data. We use an HIV cohort study to illustrate the usefulness of the method.