  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.
