WEAI/AERE 2009 - Individual Paper Abstract
Title: Specifying, Estimating, and Simulating, Multivariate Extreme Value (GEV) Discrete Choice Models in Fisheries
Author(s): David Layton, University of Washington, dflayton@u.washington.edu; Alan Haynie, National Marine Fisheries Service
Abstract:
We build upon and extend the formulation of Fougeres et. al. (2007) to generate estimable Generalized Extreme Value (GEV) spatial discrete choice models. In the statistics literature, the term Generalized Extreme Value is used differently, and these models are termed multivariate extreme value. Fougeres et. al. (2007) showed how a class of multivariate extreme value distributions could be generated using a stable mixture approach. This approach is based upon the idea that if the scale terms of conditionally independent extreme value distributions are randomly distributed then one generates a dependent multivariate distribution. If the scale components are distributed as positive alpha-stable, then the resulting unconditional distributions will be multivariate extreme value.
This result can be extended to allow the scale components to depend upon sums of positive alpha-stable random variables. We show how one can adjust their formulation so that the resulting multivariate distribution satisfies McFadden's (1978) homogeneity property. The homogeneity property facilitates a closed form expression for the discrete choice probability, so that we in turn arrive at closed form probabilities for GEV models. This approach can be utilized to generate McFadden's (1978) nested logit models and the class of cross-nested GEV models. The class can also be further extended.
We then explore a variety of random effects structures that provide for correlation in zonal discrete choice models. These include pair-wise correlation models that are part of the cross-nested family, and new models that interact inter-zonal distances with the positive alpha-stable scale components, thus inducing correlated zonal utilities (profits) in an economical manner. The random effects structure and our extension of it was motivated in part by earlier work in simulating multivariate extreme value random variables (Stephenson 2003). This link yields easily simulated multivariate extreme value random variables with spatial dependence structures, thus allowing for Monte Carlo studies, and for simulation of spatial correlation and other quantities such as the distribution of welfare measures. The model is applied to the Bering Sea pollock fishery.