Perturbation diagnostics of autocorrelation coefficients in non linear mixed-effects models with AR(1) errors based on M-estimation

ABSTRACT

In this work we propose and analyze non linear mixed-effects models for longitudinal data, which are widely used in the fields of economics, biopharmaceuticals, agriculture, and so on. A robust method to obtain maximum likelihood estimates for the parameters is presented, as well as perturbation diagnostics of autocorrelation coefficient in non linear models based on robust estimates and influence curvature. The obtained results are illustrated by plasma concentrations data presented in Davidian and Giltinan, which was analyzed under the non robust situation.

KEYWORDS:

• Autocorrelation coefficient
• influence curvature
• M-estimation
• non linear mixed-effects models
• perturbation diagnostics.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J02

Funding

This project was supported by NSFC11202180, NSFC11171065, and National Statistical Science Research Project of China (2014LZ14 and 2015LZ27).