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Three Corrected Score Tests for Generalized Linear Models with Dispersion Covariates
Author(s) -
Cordeiro Gauss M.,
Botter Denise A.,
Barroso Lúcia P.,
Ferrari Silvia L. P.
Publication year - 2003
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00237
Subject(s) - mathematics , covariate , statistics , generalized linear model , score test , dispersion (optics) , notation , linear model , statistical hypothesis testing , physics , arithmetic , optics
We develop three corrected score tests for generalized linear models with dispersion covariates, thus generalizing the results of Cordeiro , Ferrari and Paula (1993) and Cribari‐Neto and Ferrari (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 Simonoff and Tsai (1994).