A Bayesian Dual Clustering Approach for Selecting Data and Parameter Granularities

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.

History: Olivier Toubia served as the senior editor.

Funding: This work was supported by the American Statistical Association and Institute for Operations Research and the Management Sciences. Researcher(s) own analyses calculated (or derived) based in part on data from Nielsen Consumer LLC and marketing databases provided through the NielsenIQ Datasets at the Kilts Center for Marketing Data Center at The University of Chicago Booth School of Business. The conclusions drawn from the NielsenIQ data are those of the researcher(s) and do not reflect the views of NielsenIQ. NielsenIQ is not responsible for, had no role in, and was not involved in analyzing and preparing the results reported herein.

Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mksc.2024.1018.