Local influence of nonlinear mixed effects model based on M-estimation

Abstract

In this work we mainly study the local influence in nonlinear mixed effects model with M-estimation. A robust method to obtain maximum likelihood estimates for parameters is presented, and the local influence of nonlinear mixed models based on robust estimation (M-estimation) by use of the curvature method is systematically discussed. The counting formulas of curvature for case weights perturbation, response variable perturbation and random error covariance perturbation are derived. Simulation studies are carried to access performance of the methods we proposed. We illustrate the diagnostics by an example presented in Davidian and Giltinan, which was analyzed under the non-robust situation.

Keywords:

• Perturbation diagnostics
• Nonlinear mixed-effects models
• M-estimation
• Local influence analysis
• Masking effects

Additional information

Funding

This work is supported by the National Statistical Science Research Project of China (Grant No. 2018LY40), the Natural Science Foundation of Jiangsu Province (Grants No. BK20181058), the National Natural Science Foundation of China (Grants Nos. 11871001, 11901508) and the National Social Science Foundation of China (Grant No. 17BTJ026).