A Bounded-Size Likelihood Test for Non- Nested Probabilistic Discrete Choice Models Estimated from Choice-Based Samples

Abstract

Discrete-choice models of the hierarchical logit form enable the analyst to configure tree structures and to investigate the relative statistical and behavioural strengths of alternative hierarchies. The alternative tree structures can be nested or nonnested in a specification sense, and the underlying sample of observations can be exogenous or endogenous. When the sample is endogenous (i.e. choice based) and alternative tree structures are non-nested in a statistically comparative sense, the conventional likelihood ratio tests for comparisons of exogenously sampled nested hierarchical models are not appropriate. This paper presents a bounded-size likelihood ratio test for non-nested discrete choice models estimated from choice-based samples. The tests are presented with and without correction for sample size. We apply the test using a sample of four transport modes for long distance non-business travel in Australia.