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.

翻译：理解个体消费者对价格、促销、品牌及其他营销组合要素的敏感性，是解决众多营销问题的基础。该问题一个重要但尚未被充分研究的方面是这些敏感性的动态特性——它们随时间变化且因人而异。先前研究已开发出捕捉产品类别内此类动态异质性的方法，但忽略了跨类别关联动态的可能性。本研究引入一个采用分层动态因子模型的框架来捕捉此类关联动态，其中个体偏好参数受跨类别动态潜因子影响，这些因子通过贝叶斯非参数高斯过程进行估计。我们将模型应用于杂货购买数据，发现仅用少数全局趋势就能解释惊人的动态异质性程度。同时，我们刻画了消费者敏感性在跨类别演变中的模式。在管理应用层面，该框架不仅通过利用跨类别数据提升了预测准确性，还能实现对价格弹性等关注量的更精确估计。