A0196
Title: Scalable estimation of multinomial response models with uncertain consideration sets
Authors: Kenichi Shimizu - University of Alberta (Canada) [presenting]
Abstract: A standard assumption in fitting unordered multinomial response models for J mutually exclusive nominal categories on cross-sectional or longitudinal data is that the responses arise from the same set of J categories between subjects. However, when responses measure a choice made by the subject, it is more appropriate to assume that the distribution of multinomial responses is conditioned on a subject-specific consideration set, where this consideration set is drawn from the power set of the set of J categories. Because the cardinality of this power set is exponential in J, estimation is infeasible in general. An approach to overcoming this problem is provided. A key step in the approach is a probability model over consideration sets based on a general representation of probability distributions on contingency tables, which results in mixtures of independent consideration models. Although the support of this distribution is exponentially large, the posterior distribution over consideration sets given parameters is typically sparse and is easily sampled in an MCMC scheme. Posterior consistency of the parameters of the conditional response model and the distribution of consideration sets are shown. The methodology's effectiveness is documented in simulated longitudinal data sets with $J=100$ categories and real data from the cereal market with $J=68$ brands.
