Designs for discrimination between binary response models

Abstract

Abstract We propose a test statistic for discrimination between alternative univariate binary response models which is asymptotically equivalent to the likelihood ratio statistic and Pearson's goodness of fit statistic. We propose an optimal design procedure. Under certain conditions we prove that the maximum value of the power can be obtained when the degrees of freedom of the test statistic is one. Several mathematical properties of the incomplete gamma function ratio and the non-central chi-squared distribution are required in the discussion and these are established.