Abstract: A modified geometric framework is proposed for nonlinear reproductive dispersion mixed models (NRDMMs) based on the Laplace approximate marginal likelihood. Three improved approximate confidence regions of parameters and subset paramters are investigated for NRDMMs based on the proposed curvatures. The results for nonlinear regression models and exponential family nonlinear models are extended to the complicated nonlinear reproductive dispersion mixed models including exponential family nonlinear models and nonlinear reproductive dispersion models as their special cases.

Key words: Nonlinear reproductive dispersion mixed models, Laplace approximation, Curvatures, Score statistic, Confidence region