A Simulation Study on the Robustness of Parametric Inference in a Nonlinear Mixed Modelling Context

This paper presents simulation results on the robustness of normal parametric inference in non-linear mixed models. A linearization approach to inference is compared with two two-stage methods (standard two-stage, STS, and global two-stage, GTS). When the assumptions of normality of the residuals and/or the random effects are not met, some aspects of these inferential approaches are not entirely reliable, especially with respect to the coverage of the confidence intervals for the fixed effects and for the covariance estimates of the random effects. When the true distribution of the random effects is asymmetrical, the true coverage is markedly lower than the nominal one. Breast cancer data are used to illustrate the methods and motivate the simulation scenarios