An improved likelihood ratio test for varying dispersion in exponential family nonlinear models

This paper considers the issue of testing for varying dispersion in exponential family nonlinear models. We obtain a Bartlett correction to the modified profile likelihood ratio test given by Wei et al. [Testing for varying dispersion in exponential family nonlinear models. Ann. Inst. Statist. Math. 50 (1998) 277–294.]. Our results generalize those in Ferrari et al. [An improved test for heteroskedasticity using adjusted modified profile likelihood-inference. J. Statist. Plann. Inf. 124 (2004) 423–4376.] which are confined to normal linear regression models. Our numerical results show that the corrected test we propose displays reliable finite sample behavior and outperforms the ordinary and the modified profile likelihood ratio tests.