PARAMETER ESTIMATION OF PROBABILISTIC CHOICE MODELS

Probabilistic choice models are used by economists, psychologists, and marketing scientists in the analysis of choice behavior involving discrete, or quantal choice alternatives. The most widely-used of these is the multinomial logit model, which is a special case of the Luce model. These models are appealing for their simplicity and elegance, but have some severe flaws which have motivated continued research on more complex choice models. This has given rise to a need for efficient numerical algorithms for parameter estimation. One of the most important estimators is the maximum likelihood estimator, which historically has been avoided due to its computational difficulty.New algorithms for maximum likelihood estimation of choice models are developed which exploit the special structure inherent in the problem. The approach taken is to write the problem as a generalized regression problem; this gives rise to two formulations in which the Hessian is written as the sum of two matrices. The first is readily available from information already calculated for the gradient, and the second is expensive to calculate. The algorithms approximate the second piece by means of a least-change secant update, and solve the problem using a model/trust region approach involving model switching. Both approaches are successful, with one approach dominating the other in test examples using the multinomial logit, elimination-by-aspects, and Batsell-Polking models. Additional work includes a comparison of estimators in which it is demonstrated that the maximum likelihood and nonlinear least squares estimators have small-sample properties which are superior to other estimators proposed in the literature, especially those utilizing generalized least squares.