On diagnostics in double generalized linear models

The aim of this paper is to propose some diagnostic methods in double generalized linear models (DGLMs) for large samples. A review of DGLMs is given, including the iterative process for the estimation of the mean and precision coefficients as well as some asymptotic results. Then, a variety of diagnostic tools, such as leverage measures and curvatures of local influence under some usual perturbation schemes, the standardized deviance component, and Pearson residuals, are proposed. The diagnostic plots are constructed for the mean and precision models, and an illustrative example, in which the texture of four different forms of light snacks is compared across time with the texture of a traditional one, is analyzed under appropriate double gamma models. Some of the diagnostic procedures proposed in the paper are applied to analyze the fitted selected model.