Selecting Data Granularity and Model Specification Using the Scaled Power Likelihood with Multiple Weights

• Published in: Marketing science (Providence, R.I.) R.I.), 2022-07, Vol.41 (4), p.848-866
• Main Authors: Kim, Mingyung, Bradlow, Eric T., Iyengar, Raghuram
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Corporate planning; data granularity; Decision making; doubly robust prediction; granularity-model selection; Marketing; Sales; Sales forecasting; Simulation; Specification; Statistical power
• ISSN: 0732-2399; 1526-548X
• DOI: 10.1287/mksc.2021.1340

This paper proposes a selection tool that jointly identifies the best-fitted granularity-model pair that can be used for out-of-sample forecasting. 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. Whereas extant literature has proposed methods that can select the best-fitted model (e.g., Bayesian information criterion) or provide predictions robust to model misspecification (e.g., weighted likelihood), most methods assume that the granularity is either correctly specified or prespecify 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 misspecified conditions. We apply our framework to predict sales for a scanner data set 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.