Kernel-based global MLE of partial linear random effects models for longitudinal data

ABSTRACT

Random effects models have been playing a critical role for modelling longitudinal data. However, there are little studies on the kernel-based maximum likelihood method for semiparametric random effects models. In this paper, based on kernel and likelihood methods, we propose a pooled global maximum likelihood method for the partial linear random effects models. The pooled global maximum likelihood method employs the local approximations of the nonparametric function at a group of grid points simultaneously, instead of one point. Gaussian quadrature is used to approximate the integration of likelihood with respect to random effects. The asymptotic properties of the proposed estimators are rigorously studied. Simulation studies are conducted to demonstrate the performance of the proposed approach. We also apply the proposed method to analyse correlated medical costs in the Medical Expenditure Panel Survey data set.

KEYWORDS:

• Longitudinal data
• random effects
• semi-parametric model
• pooled local maximum likelihood
• Gaussian quadrature

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by AHRQ R01 HS 020263, National Natural Science Foundation of China [Grant Nos. 11571340, U1430103], the President Fund of UCAS and the Open Project of Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences.