Inference and diagnostics in overdispersed generalized partial nonlinear models

Statistical procedures are proposed in overdispersed generalized partial nonlinear models (OGPNLM). An adaptation of the iteratively re-weighted least squares procedure based on the backfitting algorithm is derived for the parameter estimation, under (penalized) maximum likelihood estimation. Derivations of effective degrees of freedom, standard errors of the estimates and some hypothesis tests are given. Diagnostic methods based on known techniques, such as leverage measures, residual analysis and local influence graphics, under different perturbation schemes, are proposed. Finally, in order to apply the proposed techniques to real-world studies, two motivating datasets are analyzed by the method developed in the paper.