TESTING THE FIT OF A REGRESSION-MODEL VIA SCORE TESTS IN RANDOM EFFECTS MODELS

This paper considers testing the goodness of fit of regression models. Emphasis is on a goodness-of-fit test for generalized linear models w ith canonical link function and known dispersion parameter. The test i s based on the score test for extra variation in a random effects mode l. By choosing a suitable form for the dispersion matrix, a goodness-o f-fit test statistic is obtained which is quite similar to test statis tics based on non-parametric kernel methods. We consider the distribut ion of the test statistic and discuss the choice of the dispersion mat rix. The testing method can handle models with continuous and discrete covariates. Corrections for bias when parameters are estimated are av ailable and extensions to models with unknown dispersion parameters, a nd more general nonlinear models are discussed. The proposed goodness- of-fit method is demonstrated in a simulation study and on real data o f bone marrow transplant patients. The individual contributions of obs ervations to the test statistic are used to perform residual analyses.