A multivariate hidden semi-Markov model of customer-multichannel engagement

In multichannel retailing, customers often use a mix of a firm's online and physical stores for their search and buy activities. We define the customer's “channel engagement” as a latent attitude or predisposition towards the firm's online and offline channels which dynamically transitions between states of “high” and “low”. We propose that when in a “high” engagement state with a channel, a customer is likely to visit and purchase from that channel. Using customer level data on web visits, online and in-store purchases from a multichannel firm, we simultaneously model the customer's online and offline channel engagement in a discrete time multivariate hidden semi-Markovian framework. An important implication of the semi-Markovian framework is that we can explicitly model the latent engagement state duration using any distribution. We examine the distributional properties of the state duration by comparing between Poisson and geometric processes under alternative state transition specifications. We find that the proposed Poisson duration model predicts the online visits and purchases better than the geometric, with slight over-prediction of offline purchases. The model's ability to explicitly infer the state duration can assist marketers to target customers with channel specific interventions and to mitigate attrition risk