Collective Response Spike Prediction for Mutually Interacting Consumers

Modeling how marketing actions in various channels influence or cause consumer purchase decisions is crucial for marketing decision-making. Marketing campaigns stimulate consumer awareness, interest and help drive interactions such as the browsing of product web pages, ultimately impacting an individual's purchase decision. In addition, some successful campaigns stimulate word-of-mouth and social trends among consumers, and such collective behavior of consumers result in concurrent and correlated responses over a short term. Though each consumer's response should be attributed with both the same individual's experiences and the collective factors, unobservability of most word-of-mouth events makes the estimation challenging. The authors propose a new continuous-time predictive model for time-dependent response rates of each consumer, which can incorporate both the individual and the collective factors without explicit word-of-mouth observations. The individual factor is modeled as staircase functions associated with the experienced events by each consumer, and provides a clear psychological interpretation about how marketing advertising communications impact short-term and mid-term memories of consumers. The collective factor is modeled with aggregate response frequencies for mutually-interacting groups that are automatically estimated from data. The key idea to mine the mutually-interacting groups exists in a three-step estimator, which initially performs a Poisson regression without the collective factor, then does clustering of the residual time-series in the initial regression, and finally performs another Poisson regression involving the collective factor. The proposed collective factor robustly incorporates the underlying trends even when causality from one consumer's event spikes to another consumer's response is weak. High predictive accuracy of the proposed approach is empirically validated using real-world data provided by an online retailer in Europe.