Understanding Choice Intensity: A Poisson Mixture Model with Logit-based Random Utility Selective Mixing

In this paper we introduce a new Poisson mixture model for count panel data where the underlying Poisson process intensity is determined endogenously by consumer latent utility maximization over a set of choice alternatives. This formulation accommodates the choice and count in a single random utility framework with desirable theoretical properties. Individual heterogeneity is introduced through the random coefficient framework with a flexible semiparametric distribution. We deal with the analytical intractability of the resulting mixture by recasting the model as an embedding of infinite sequences of scaled moments of the mixing distribution, and newly derive their cumulant representations along with bounds on their rate of numerical convergence. We further develop an efficient recursive algorithm for fast evaluation of the model likelihood within a Bayesian Gibbs sampling scheme. We apply our model to a recent household panel of supermarket visit counts. We estimate the nonparametric density of three key variables of interest – price, driving distance, and total expenditure – while controlling for a range of consumer demographic characteristics. We use this econometric framework to assess the opportunity cost of time and analyze the interaction between store choice, trip frequency, household characteristics and store characteristics. JEL: C11, C13, C14, C15, C23, C25