Abstract: Although there are well-established model selection methods (e.g., Bayesian Information Criterion (BIC)), they commonly condition on a priori selected data and parameter granularities. That is, researchers think they are doing model selection, but what they are really doing is model selection conditional on their chosen granularities. We propose a new method, Bayesian dual clustering (BDC), that infers both data and parameter granularities by sampling over their posterior distribution. BDC represents data and parameters as two separate collections of nodes (e.g., stock keeping unit (SKU)) with each node being the unit of analysis. The method then clusters the nodes in each collection and infers the corresponding data and parameter granularities while providing a high degree of interpretability regarding why certain granularities are selected. Notably, BDC can handle large collections, accommodate parameter restrictions (e.g., data need to be at least as granular as parameters) using a split-merge sampler, and relate to other extant methods (e.g., latent-class analysis). We apply BDC to a frequently purchased grocery category. The results show that BDC inferred granularities differ from those from extant approaches, which, in turn, leads to different demand elasticities and optimal actions. We conclude by highlighting the generalizability of BDC to a broad array of marketing problems.

Abstract: Firms employ temporal data for predicting sales and making managerial decisions accordingly. To use such data appropriately, managers need to make two major analysis decisions: (a) the temporal granularity (e.g., weekly, monthly) and (b) an accompanying demand model. In most empirical contexts, however, model selection, sales forecasts, and managerial decisions are vulnerable to both of these choices.   While extant literature has proposed methods that can select the best-fitted model (e.g., BIC) or provide predictions robust to model misspecification (e.g., weighted likelihood), most methods assume that the granularity is either correctly specified or pre-specify it. Our research fills this gap by proposing a method, the scaled power likelihood with multiple weights (SPLM), that not only identifies the best-fitted granularity-model combination jointly, but also conducts doubly (granularity and model) robust prediction against their potentially incorrect selection. An extensive set of simulations shows that SPLM has higher statistical power than extant approaches for selecting the best-fitted granularity-model combination and provides doubly robust prediction in a wide variety of mis-specified conditions. We apply our framework to predict sales for a scanner dataset and find that similar to our simulations, SPLM improves sales forecasts due to its ability to select the best-fitted pair via SPLM’s dual weights.