Model selection for mixture hidden Markov models: an application to clickstream data

In a clickstream analysis setting, Mixture Hidden Markov Models (MHMMs) can be used to examine categorical sequences assuming they evolve according to a mixture of latent Markov processes, each related to a different subpopulation. These models involve identifying both the number of subpopulations and hidden states. This study proposes a model selection criterion based on an integrated completed likelihood approach that accounts for the two latent classes in the model. We implemented a Monte Carlo simulation study to compare selection criteria performance. In scenarios characterised by categorical short length sequences, our proposed measure outperforms the most commonly used model selection criteria in identifying components and states. The paper presents a case study on clickstream data collected from the website of a company operating in the hospitality industry and modelled by an MHMM selected by the proposed score.