A Factorial Hidden Markov Model for the Analysis of Temporal Change in Choice Models

Consumers’ preferences for various product attributes change over time. Modeling such temporal changes through a single process assumes that all the attributes’ preferences change together with the same dynamics; however, this assumption is not appropriate when there are several processes with distinct characteristics. We propose a new non-homogeneous factorial hidden Markov model (FHMM) for choice models to dynamically segment consumers into distinct states while each preference parameter may follow a distinct Markov process. The transition probabilities are modeled as time-varying at the individual level, affected by covariates of a feedback term of the consumer’s previous purchase decision, specific to each Markov process. We motivate the proposed approach by an application to a scanner panel choice dataset and find two processes with entirely different characteristics governing the shifts in two preference attributes. Model fit and prediction power based on Brier scores show the superiority of the proposed non-homogeneous FHMM in capturing temporal changes in preferences compared to a traditional hidden Markov model as well as a benchmark comparison model.