Modeling preference evolution in discrete choice models: A Bayesian state-space approach

We develop discrete choice models that account for parameter driven preference dynamics. Choice model parameters may change over time because of shifting market conditions or due to changes in attribute levels over time or because of consumer learning. In this paper we show how such preference evolution can be modeled using hierarchial Bayesian state space models of discrete choice. The main feature of our approach is that it allows for the simultaneous incorporation of multiple sources of preference and choice dynamics. We show how the state space approach can include state dependence, unobserved heterogeneity, and more importantly, temporal variability in preferences using a correlated sequence of population distributions. The proposed model is very general and nests commonly used choice models in the literature as special cases. We use Markov chain monte carlo methods for estimating model parameters and apply our methodology to a scanner data set containing household brand choices over an eight-year period. Our analysis indicates that preferences exhibit significant variation over the time-span of the data and that incorporating time-variation in parameters is crucial for appropriate inferences regarding the magnitude and evolution of choice elasticities. We also find that models that ignore time variation in parameters can yield misleading inferences about the impact of causal variables. This paper is based on the first author's doctoral dissertation.     

Bayesian estimation of multivariate-normal models when dimensions are absent

Multivariate economic and business data frequently suffer from a missing data phenomenon that has not been sufficiently explored in the literature: both the independent and dependent variables for one or more dimensions are absent for some of the observational units. For example, in choice based conjoint studies, not all brands are available for consideration on every choice task. In this case, the analyst lacks information on both the response and predictor variables because the underlying stimuli, the excluded brands, are absent. This situation differs from the usual missing data problem where some of the independent variables or dependent variables are missing at random or by a known mechanism, and the “holes” in the data-set can be imputed from the joint distribution of the data. When dimensions are absent, data imputation may not be a well-poised question, especially in designed experiments. One consequence of absent dimensions is that the standard Bayesian analysis of the multi-dimensional covariances structure becomes difficult because of the absent dimensions. This paper proposes a simple error augmentation scheme that simplifies the analysis and facilitates the estimation of the full covariance structure. An application to a choice-based conjoint experiment illustrates the methodology and demonstrates that naive approaches to circumvent absent dimensions lead to substantially distorted and misleading inferences.