ON ASSESSING GOODNESS-OF-FIT OF GENERALIZED LINEAR-MODELS TO SPARSE DATA

Approximations to the first three moments of Pearson's statistic are o btained for noncanonical generalized linear models, extending the resu lts of McCullagh. A first-order modification to Pearson's statistic is proposed which induces local orthogonality with the regression parame ters, resulting in substantial simplifications and increased power. Ac curate and easily computed approximations to the moments of the modifi ed Pearson statistic conditional on the estimated regression parameter s are obtained for testing goodness of fit to sparse data. Both the Pe arson statistic and its modification are shown to be asymptotically in dependent of the regression parameters. Simulation studies and example s are given.