The Impact of Space on the Application Of Discrete Choice Models

Kingsley E Haynes,A Stewart Fotheringham

doi:10.52324/001c.9194

Abstract

In spatial analysis, the 1980’s could be characterized as the decade of discrete choice modeling and, more generally, categorized data analysis. Subsequent to the pioneering work undertaken in economics, marketing and transportation, it was quickly recognized that most spatial decisions are discrete (for example, the selection of a city in which to live or a store at which to shop) and the discrete choice framework was adopted enthusiastically. One of the most popular statistical models for the analysis of discrete choices has been the multinomial logit model (MNL). In this paper we describe the added complexities space introduces into Discrete Choice Modeling and then discuss how they can be incorporated into the framework to produce more realistic spatial choice models. Our discussion is centered around the MNL model, because of its popularity, and on the role of the Independence from Irrelevant Alternatives (IIA) assumption which is shown to be a key factor in highlighting the differences between aspatial and spatial choice. We also demonstrate that in certain models where IIA is relaxed the subtleties of space are not captured sufficiently and that these subtleties can only be captured by developing models from spatial theory. Some promising beginnings in this direction are reported.

Highlights

In spatial analysis, the 1980's could be characterized as the decade of discrete choice modeling and, more generally, categorized data analysis (Williams, 1977; Wilson, 1981; Wrigley, 1982; 1985; Wrigley and Longley, 1984)
In this paper we describe the added complexities space introduces into OCM and discuss how they can be incorporated into the framework to produce more realistic spatial choice models
Our discussion is centered around the MNL model, because of its popularity, and on the role of the Independence from Irrelevant Alternatives (IIA) assumption which is shown to be a key factor in highlighting the differences between aspatial and spatial choice

Summary

Introduction

The 1980's could be characterized as the decade of discrete choice modeling and, more generally, categorized data analysis (Williams, 1977; Wilson, 1981; Wrigley, 1982; 1985; Wrigley and Longley, 1984). Two possible strategies are available for remedying this situation: explicitly incorporating attributes of other alternatives into the observable component of the utility function or relaxing the assumption of simple scalability and zero error covariances The applicability of these altemative approaches in spatial choiceanalysis will depend to a large extent on the particular structure of the choices in any given context. In clusters ofaspatial alternatives there is an alternative and are each independent across alternatives, implicit assumption of randomness in the arrangement of the only way that equal substitutability can hold for the full alternatives which within a cluster, are assumed to beequal choice set is if the e..'s have zero variance. Band B and C are substitutes, because of their greater spatial separation, there is no guarantee that A and C are substitutes

Variation and Location

The Nested Logit Model

The Multinomial Probit Model