Maximally selected chi-square statistics and binary splits of nominal variables.
We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a birth data set.
Boulesteix
Anne-Laure
AL
Department of Medical Statistics and Epidemiology, Technical University of Munich, Ismaningerstr. 22, D-81675 Munich, Germany. anne-laure.boulesteix@tum.de
D001699:Biometry / Q000379:methods*; D002585:Cesarean Section; D016009:Chi-Square Distribution; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D036801:Parturition / Q000502:physiology; D011247:Pregnancy