Correlated Disturbances in Discrete Choice Models: A Comparison of Multinomial Probit Models and Logit Models

Abstract

In political science, there are many cases where individuals make discrete choices from more than two alternatives. This paper uses Monte Carlo analysis to examine several questions about one class of discrete choice models - those involving both alternative specific and individual-specific variables on the right-hand side - and demonstrates several findings. First, the use of estimation techniques assuming uncorrelated disturbances across alternatives in discrete choice models can lead to significantly biased parameter estimates. This point is tempered by the observation that probability estimates based on the full choice set generated from such estimates are not likely to be biased enough to lead to incorrect inferences. However, attempts to infer the impact of altering the choice set - such as by removing one of the alternatives - will be less successful. Second, the Generalized Extreme Value (GEV) model is extremely unreliable when the pat tern of correlation among the disturbances is not as restricted as the GEV model assumes. GEV estimates may suggest grouping among the choices that is in fact not present in the data. Third, in samples the size of many typical political science applications – 1000 observations - Multinomial Probit (MNP) is capable of recovering precise estimates of the parameters of the systemic component of the model, though MNP is not likely to generate precise estimates of the relationship among the disturbances in samples of this size. Paradoxically, MNP's primary benefit is its ability to uncover relationships among alternatives and to correctly estimate the effect of removing an alternative from the choice set. Thus this paper suggests the increased use of MNP by political scientists examining discrete choice problems when the central question of interest is the effect of removing an alternative from the choice set. We demonstrate that for other questions, models positing in dependent disturbances may be 'close enough.'

Files

Additional details