Mingyung Kim, Eric Bradlow, Raghuram Iyengar (Under Review), A Bayesian Dual-Network Clustering Approach for Selecting Data and Parameter Granularities.
Abstract: While there are well-established methods for model selection (e.g., BIC, marginal likelihood), they generally condition on an a priori selected data (e.g., SKU-level data) and parameter granularity (e.g., brand-level parameters). That is, researchers think they are doing model selection, but what they are really doing is model selection conditional on their choices of data and parameter granularities. In this research, we propose a Bayesian dual-network clustering method as a novel way to make these two decisions simultaneously. To accomplish this, the method represents data and parameters as two separate networks with nodes being the unit of analysis (e.g., SKUs). The method then (a) clusters the two networks using a covariate-driven distance function which allows for a high degree of interpretability and (b) infers the data and parameter granularities that offer the best in-sample fit, akin to standard model selection methods. We apply our method to SKU-level demand analysis. The results show that the choices of data and parameter granularities based on our method as compared to those from extant approaches (e.g., latent class analysis) impact the demand elasticities and the optimal pricing of SKUs. We conclude by highlighting the generalizability of our framework to a broad array of marketing problems.
