Modeling price response from store sales

Sales response models address the relationship between the sales quantity of a product and independent variables like the product's price or sales promotion activities that are assumed to influence the product's unit sales. Here, the main focus lies on the investigation of different approaches of modeling price response from store sales which allow for heterogeneous marketing mix effects across stores or groups of stores and/or which accommodate functional flexibility in price response. In the first part, a general heterogeneity model that derives segments of stores and allows for store-specific marketing mix effects within these segments is introduced. Well-known special cases of this model are the hierarchical Bayes, the latent class model and the homogeneous model. We compare the parametric heterogeneous model versions to a semiparametric model based on Bayesian P-splines and accounting for functional flexibility in price effects, as well as to the simple parametric homogeneous model. Subsequently, sales response models are compared that neither address store heterogeneity nor functional flexibility, allow for store heterogeneity only, or address functional flexibility only to a hierarchical Bayesian semiparametric model which simultaneously accounts for both features. In the third part, the general heterogeneity model is extended to a general heterogeneity seemingly unrelated regression (SUR) model which accounts for correlations between sales across brands. We further investigate a semiparametric SUR model based on Bayesian P-splines and again contrast the general heterogeneity SUR model as well as its heterogeneous special cases and the flexible model to the simple homogeneous SUR model.