Abstract
We present, in matrix notation, general Bartlett correction formulae for several hypotheses in generalized linear models with dispersion covariates. These results generalize previous work by Cordeiro (1983, 1993) who obtained Bartlett corrections for generalized linear models with known dispersion parameter and for multiplicative heteroscedastic normal models, respectively. The formulae derived are simple enough to be used analytically to obtain several closed form Bartlett corrections in a variety of important tests when the information matrix has a closed form. They also have advantages for numerical purposes since our formulae are readily computable using a language supporting numerical linear algebra. We give applications to some special models and discuss improved likelihood ratio tests.
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