A random coefficients mixture hidden Markov model for marketing research

The hidden Markov model (HMM) provides a framework to model the time-varying effects of marketing mix variables. When employed in a panel data context, it is important to properly account for unobserved heterogeneity across individuals. We propose a new random coefficients mixture HMM (RCMHMM) that allows for flexible patterns of unobserved heterogeneity in both the state-dependent and transition parameters. The RCMHMM nests all HMMs found in the marketing literature. Results of two simulation studies demonstrate that 1) averaging across a large number of different data generating processes, the RCMHMM outperforms all its nested versions using both in-sample and out-of-sample performance and 2) the RCMHMM is more robust than its nested versions when underlying model assumptions are violated. In addition, we apply the RCMHMM to an empirical application where we examine the effectiveness of in-game promotions in increasing the short-term demand for Major League Baseball (MLB) attendance. We find that the effectiveness of four promotional categories varies over the course of the season and across teams and that the RCMHMM performs best.