Average most powerful tests for a segmented regression

To improve the goodness of fit between a regression model and observations, the model can be complicated; however, that can reduce the statistical power when the complication does not lead significantly to an improved model. In the context of two-phase (segmented) logistic regressions, the model evaluation needs to include testing for simple (one-phase) versus two-phase logistic regression models. In this article, we propose and examine a class of likelihood ratio type tests for detecting a change in logistic regression parameters that splits the model into two-phases. We show that the proposed tests, based on Shiryayev-Roberts type statistics, are on average the most powerful. The article argues in favor of a new approach for fixing Type I errors of tests when the parameters of null hypotheses are unknown. Although the suggested approach is partly based on Bayes-Factor-type testing procedures, the classical significance levels of the proposed tests are under control. We demonstrate applications of the average most powerful tests to an epidemiologic study entitled Time to pregnancy and multiple births.