Testing of homogeneity of variance and autocorrelation coefficients of nonlinear mixed models with AR(1) errors based on M-estimation

ABSTRACT

Homogeneity of between-individual variance and autocorrelation coefficients is one of assumptions in the study of longitudinal data. However, the assumption could be challenging due to the complexity of the dataset. In the paper we propose and analyze nonlinear mixed models with AR(1) errors for longitudinal data, intend to introduce Huber's function in the log-likelihood function and get robust estimation, which may help to reduce the influence of outliers, by Fisher scoring method. Testing of homogeneity of variance among individuals and autocorrelation coefficients on the basis of Huber's M-estimation is studied later in the paper. Simulation studies are carried to assess performance of score test we proposed. Results obtained from plasma concentrations data are reported as an illustrative example.

KEYWORDS:

• Autocorrelation coefficient
• heteroscedasticity
• nonlinear mixed-effects models
• AR(1)errors
• M-estimation
• hypothesis testing

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J02

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This study is supported by the National Natural Science Foundation of China [Grant No. 11202180 and No. 11171065] and the National Statistical Science Research Project of China [Grant No. 2014LZ14 and 2015LZ27].