Lack-of-fit Tests Based On Partial Sums of Residuals

To evaluate the validity of the mean function in generalized linear models, Su and Wei (1991 Su, J.Q., Wei, L.T. (1991). A lack-of-fit test for the mean function in a generalized linear model. J. Amer. Statist. Assoc. 86:420–426.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a lack-of-fit test based on partial sums of residuals. They compute P values using an unusual bootstrapping simulation. However, the simulations can hardly be performed with more than a few predictor variables because it is prohibitively time consuming. We modify their test for linear models and propose another lack of fit test based on partial sums of residuals. We find the non normal limiting distributions for both tests thus enabling more direct calculation of P values. Finally, we examine how the nature of the simulation reduces the power of Su-Wei’s test.