Three Corrected Score Tests for Generalized Linear Models with Dispersion Covariates

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Abstract
We develop three corrected score tests for generalized linear models with dispersion covariates, thus generalizing the results of Cordeiro,FerrariandPaula(1993)and Cribari‐NetoandFerrari(1995). We present, in matrix notation, general formulae for the coefficients which define the corrected statistics. The formulae only require simple operations on matrices and can be used to obtain analytically closed‐form corrections for score test statistics in a variety of special generalized linear models with dispersion covariates. They also have advantages for numerical purposes since our formulae are readily computable using a language supporting numerical linear algebra. Two examples, namely, iid sampling without covariates on the mean or dispersion parameter oand one‐way classification models, are given. We also present some simulations where the three corrected tests perform better than the usual score test, the likelihood ratio test and its Bartlett corrected version. Finally, we present a numerical example for a data set discussed by SimonoffandTsai(1994).

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