Regression-based specification tests for the multinomial logit model

Abstract

Diagnostic tests for omitted variables or functional misspecification in the multinomial logit (MNL) model can be performed conveniently by testing the significance of auxiliary regressions of residuals on included and excluded variables. In particular, Lagrange Multiplier (LM) and Hausman-McFadden (HM) tests of the Independence from Irrelevant Alternatives (IIA) Property of the MNL model can be carried out by the regression method using suitably defined excluded variables. Using this method, it is straightforward to test jointly against several sources of misspecification, and to diagnose the structure of deviations from the MNL model.