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Understanding individual customers' sensitivities to prices, promotions, brands, and other marketing mix elements is fundamental to a wide swath of marketing problems. An important but understudied aspect of this problem is the dynamic nature of these sensitivities, which change over time and vary across individuals. Prior work has developed methods for capturing such dynamic heterogeneity within product categories, but neglected the possibility of correlated dynamics across categories. In this work, we introduce a framework to capture such correlated dynamics using a hierarchical dynamic factor model, where individual preference parameters are influenced by common cross-category dynamic latent factors, estimated through Bayesian nonparametric Gaussian processes. We apply our model to grocery purchase data, and find that a surprising degree of dynamic heterogeneity can be accounted for by only a few global trends. We also characterize the patterns in how consumers' sensitivities evolve across categories. Managerially, the proposed framework not only enhances predictive accuracy by leveraging cross-category data, but enables more precise estimation of quantities of interest, like price elasticity.

Automating the customer analytics process is crucial for companies that manage distinct customer bases. In such data-rich and dynamic environments, visualization plays a key role in understanding events of interest. These ideas have led to the popularity of analytics dashboards, yet academic research has paid scant attention to these managerial needs. We develop a probabilistic, nonparametric framework for understanding and predicting individual-level spending using Gaussian process priors over latent functions that describe customer spending along calendar time, interpurchase time, and customer lifetime dimensions. These curves form a dashboard that provides a visual model-based representation of purchasing dynamics that is easily comprehensible. The model flexibly and automatically captures the form and duration of the impact of events that influence spend propensity, even when such events are unknown a-priori. We illustrate the use of our Gaussian Process Propensity Model (GPPM) on data from two popular mobile games. We show that the GPPM generalizes hazard and buy-till-you-die models by incorporating calendar time dynamics while simultaneously accounting for recency and lifetime effects. It therefore provides insights about spending propensity beyond those available from these models. Finally, we show that the GPPM outperforms these benchmarks both in fitting and forecasting real and simulated spend data.