Beta‐logistic Models of Urban Shopping Center Choice

Abstract

This paper describes beta-logistic models of shopping center choice and presents an empirical application of the models to consumer behavior within a British city. Beta-logistic models are an extension of conventional logistic (logit) models dealing with choice patterns in panel data which incorporate heterogeneity, and they are appropriate when there are data on the outcome of a repeated choice process. The models have two major advantages. First, they provide predictions of both the mean probability of selecting a particular choice alternative and the distribution of the choice probabilities around the mean. Second, the models provide a convenient method of accounting for the effect of omitted variables (population heterogeneity) in the analysis of panel/event-history data (see Davies and Crouchley 1985; Davies and Pickles 1984). The relationship of beta-logistic to conventional logistic models for cross-sectional data was first drawn to the attention of social scientists by Heckman and Willis (1977). More recently, Davies (1984) and Davies and Pickles (1984) have introduced the models into the geographical/planning literature, generalized their form to incorporate timevarying exogenous variables and feedback effects, and then applied them to the study of residential mobility. In these previous applications, the models have been confined to dichotomous choice problems. However, Heckman and Willis (1977, p. 42) do suggest in a footnote to their paper that beta-logistic models can readily be extended to deal with polytomous (multiple category) choice problems and can therefore provide what are essentially paneldata/ heterogeneous-population extensions of the conventional multinomial logit models for cross-sectional data. They suggest that the multinomial extension involves replacing the beta distribution, which accounts for omitted variables/population heterogeneity in the dichotomous choice problem, by the multivariate beta or Dirichlet distribution. In this paper we derive the form of this multinomial Thanks are due to Andrew Ehrenberg, Christopher Chatfield, and Gerald Goodhardt for comments on earlier versions of this paper. This research was funded by the Economic and Social Research Council, United Kingdom, grants wO230010 and wO230033.