  We propose a latent topic model with a Markovian transition for process data,
which consist of time-stamped events recorded in a log file. Such data are
becoming more widely available in computer-based educational assessment with
complex problem solving items. The proposed model can be viewed as an extension
of the hierarchical Bayesian topic model with a hidden Markov structure to
accommodate the underlying evolution of an examinee's latent state. Using topic
transition probabilities along with response times enables us to capture
examinees' learning trajectories, making clustering/classification more
efficient. A forward-backward variational expectation-maximization (FB-VEM)
algorithm is developed to tackle the challenging computational problem. Useful
theoretical properties are established under certain asymptotic regimes. The
proposed method is applied to a complex problem solving item in 2012 Programme
for International Student Assessment (PISA 2012).
