Random Coefficients Modeling

Abstract

Abstract In marketing, it is important to recognize interpersonal differences in model parameters such as brand preference and price sensitivity. In recent years, random coefficient modeling has significantly simplified our ability to characterize heterogeneity. A particularly useful aspect of random coefficient models is that each provides individual‐level inference. To model unobserved heterogeneity, one can assume that individual response coefficients (β i ) come from an underlying distribution. In the finite mixture approach, this distribution is discrete. If the true underlying distribution of preference is continuous, a simple approach to characterize heterogeneity may be to use a multivariate normal distribution. Because of its simplicity and conceptual appeal, the multivariate normal distribution of heterogeneity has experienced considerable popularity in marketing. An even more flexible approach may be to use a normal component mixture model that is capable of representing a wide variety of distributions of heterogeneity. To carry out estimation, finite mixture models use maximum likelihood methods. For continuous distributions of heterogeneity, Markov chain Monte Carlo (MCMC) estimation methods are commonly used. A particular advantage of MCMC methods is that they offer significant flexibility in specifying the functional form of the heterogeneity distribution.