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Biometrika 1999 86(3):531-539; doi:10.1093/biomet/86.3.531
© 1999 by Biometrika Trust
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A chi-squared goodness-of-fit test for logistic regression models based on case-control data

B Zhang

Department of Mathematics, The University of Toledo, Toledo, OH 43606, USA bzhang@math.utoledo.edu

We propose a chi-squared-type statistic to test the validity of the logistic regression model based on case-control data by adapting the goodness-of-fit test of Nikulin-Rao-Robson-Moore. The proposed test statistic requires a high-dimensional matrix inversion, but is otherwise easy to compute and has an asymptotic chi-squared distribution. This test statistic is an alternative to the Kolmogorov-Smirnov-type statistic of Qin & Zhang (1997) and does not need to employ a bootstrap method to evaluate its critical values. We present some results on simulation and on analysis of two real datasets.

Key Words: Biased sampling problem; Case-control data; Chi-squared statistic; Gaussian process; Generalised inverse; Local alternative; Mixture sampling


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