Model of Brand Choice with a No-Purchase Option Calibrated to Scanner-Panel Data

In usual practice, researchers specify and estimate brand-choice models from purchase data, ignoring observations in which category incidence does not occur (i.e., no-purchase observations). This practice can be problematic if there are unobservable factors that affect the no-purchase and the brand-choice decisions. When such a correlation exists, it is important to model simultaneously the no-purchase and the brand-choice decisions. The authors propose a model suitable for scanner-panel data in which the no-purchase decision depends on the price, feature, and display of each brand in the category and on household stock of inventory. They link the no-purchase model to the brand-choice outcome through marketing-mix covariates and through unobservables that affect both outcomes. The authors assume that model parameters are heterogeneous across households and allow for a flexible correlation structure between the coefficients in the no-purchase model and those in the brand-choice model. The model formulation is more general than what is possible from either a nested logit model or a translog utility model and from models in which the no-purchase outcome is an additional outcome with the deterministic component of its utility set equal to zero. The authors estimate the proposed model using Bayesian Markov chain Monte Carlo estimation methods. They then apply the estimation methods to scanner-panel data on the cola product category and compare the results with those from the widely used nested logit model.

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