Methodological evaluation reveals aberrant behavior of Wald's test in binomial logit models, indicating severe power loss when parameter estimates diverge far from null values.
For tests of a single parameter in the binomial logit model, Wald's test is shown to behave in an aberrant manner. In particular, the test statistic decreases to zero as the distance between the parameter estimate and null value increases, and the power of the test, based on its large-sample distribution, decreases to the significance level for alternatives sufficiently far from the null value.
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Hauck et al. (1977) studied this question.
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