Specification tests for probabilistic choice models: Fid-Bau Portal

Specification tests for probabilistic choice models

Horowitz, Joel

Abstract Probabilistic choice models, such as logit and probit models, are highly sensitive to a variety of specification errors, including the use of incorrect functional forms for the systematic component of the utility function, incorrect specification of the probability distribution of the random component of the utility function, and incorrect specification of the choice set. Specification errors can cause large forecasting errors, so it is of considerable importance to have means of testing for the presence of these errors. A number of tests based on the likelihood ratio statistic have been developed. These tests and available information on their power are summarized in this paper. The likelihood ratio test can entail considerable computational diffuculty, owing to the need to evaluate the likelihood function for both the null and alternative hypotheses. Substantial gains in computational efficiency can be achieved through the use of a test that requires evaluating the likelihood function only for the null hypothesis. A Lagrangian multiplier test that has this property is described, and numerical examples of its computational properties are given. An important disadvantage of conventional specification tests is that they do not permit comparisons of models that belong to different parametric families in order to determine which model best explains the available data. Thus, these tests cannot be used to compare models whose utility functions have substantially different functional forms or models that are based on different behavioral paradigms. Several methods for dealing with this problem, including the construction of hybrid models and the Cox test of separate families of hypotheses, are described.