Smoothing spline estimation of generalised varying-coefficient mixed model

Abstract

The generalised varying-coefficient model with longitudinal data faces a challenge that the data are correlated, as multiple observations are measured from each individual. In this article we consider the generalised varying-coefficient mixed model (GVCMM) which uses a varying-coefficient model to fit mean functions, while accounting for overdispersion and correlation by adding random effects. Smoothing splines are used to estimate the smooth but arbitrary nonparametric coefficient functions. The usually intractable integration involved in evaluating the quasi-likelihood function is approximated by the Laplace method. This suggests that the GVCMM can be approximately represented by a generalised linear mixed model. Hence, the smoothing parameters and the variance components can be estimated by using the restricted maximum log-likelihood (REML) approach, where the smoothing parameters are treated as an extra variance component vector. We illustrate the performance of the proposed method through some simulation and an application to a real data set.

Keywords:

• varying-coefficient models
• generalised varying-coefficient mixed model
• smoothing spline
• restricted maximum likelihood

AMS Subject Classification :

• 62G05
• 62G08

Acknowledgements

Lu's research was supported by National Natural Science Foundation of China (NNSFC) grant 10501053. Zhang's research was supported by NNSFC grant 10781072. We would like to thank the editor and two referees for their careful reading of the original manuscript and for their comments that significantly improved the paper.