Some aspects of random utility, extreme value theory and multinomial logit models

In this paper, we survey some aspects of the relationship between random utility, extreme value theory and multinomial logit models. In particular, we study the robustness of the assumption of a Gumbel distributed random utility. These ideas are well known within the field of spatial economics, but do not appear to be common knowledge to researchers in probability theory. The purpose of this paper is to try to bridge this gap.

[1]  Sven Erlander,et al.  Cost-Minimizing Choice Behavior in Transportation Planning: A Theoretical Framework for Logit Models , 2010 .

[2]  J. Norris.  Appendix: probability and measure , 1997 .

[3]  Kurt Jörnsten,et al.  Modeling freight markets for coal , 2008 .

[4]  Moshe Ben-Akiva,et al.  Discrete Choice Analysis: Theory and Application to Travel Demand , 1985 .

[5]  John K. Dagsvik.  Probabilistic models for qualitative choice behavior : an introduction , 2000 .

[6]  An asymptotic foundation for logit models , 1998 .

[7]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[8]  N. F. Stewart,et al.  The Gravity Model in Transportation Analysis - Theory and Extensions , 1990 .

[9]  G Leonardi,et al.  THE STRUCTURE OF RANDOM UTILITY MODELS IN THE LIGHT OF THE ASYMPTOTIC THEORY OF EXTREMES , 1984 .

[10]  Alan Wilson,et al.  A statistical theory of spatial distribution models , 1967 .

[11]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[12]  A. Anas.  Discrete choice theory, information theory and the multinomial logit and gravity models , 1983 .

[13]  L. Bregman.  The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[14]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[15]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[16]  A. Karlqvist,et al.  Spatial interaction theory and planning models , 1978 .

[17]  C. Manski.  The structure of random utility models , 1977 .