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Abstract

It is claimed by some authors that the distribution of the sum of weighted squared residuals, used as a goodness of fit measure in binary choice models, behaves for large n as a x2n_k_i distribution. This claim seems to be based on a false analogy with the well-known Pearson x2 statistic for frequency tables with a fixed number of cells and cell sizes tending to infinity. We derive the asymptotic (normal) distribution and show that the approximation by the x2 distribution in general will not be valid. A new x2 test is proposed based on the asymptotic normality of the measure.

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