Logit Specification Tests Using Grouped Data.
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA NAVAL PLANNING MANPOWER AND LOGISTICS DIV
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Despite its widespread usage, the logit model used to analyze discrete events has been criticized because it possesses the Independence of Irrelevant Alternatives IIA property. That is, the relative probabilities of any pair of choices are unaffected by the attributes of any third choice. For example, the relative probabilities of commuting by bus versus commuting by automobile are unaffected by the ticket price and travel time of commuting by train. This paper considers four logit specification tests for the case of grouped data. The first test, originally suggested by Cox, compares the covariance matrix of the regression residuals to the matrix that we expect under the logit model. The other three tests do address the IIA property directly. The second test compares the coefficient estimates from two distinct restricted sets of choices. Here this test is similar in spirit to the first of the Hausman and McFadden tests. The third test compares the logit model to the more general universal logit model, which allows each pair of relative probabilities to be affected by all variables in the model. Finally, the fourth test embeds the logit model within a grouped data version of the nested logit model.
- Statistics and Probability