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Smoothing spline estimation of generalised varying-coefficient mixed model. (English) Zbl 1172.62009

Summary: The generalised varying-coefficient model with longitudinal data faces the challenge that the data are correlated, as multiple observations are measured from each individual. 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.

MSC:

62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
62J12 Generalized linear models (logistic models)
62F15 Bayesian inference
62H12 Estimation in multivariate analysis

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[1] DOI: 10.2307/2290687 · Zbl 0775.62195 · doi:10.2307/2290687
[2] Hastie T., J. Roy. Statist. Soc. Ser. B 55 pp 757– (1993)
[3] DOI: 10.1093/biomet/85.4.809 · Zbl 0921.62045 · doi:10.1093/biomet/85.4.809
[4] DOI: 10.1198/016214501753168280 · Zbl 1018.62034 · doi:10.1198/016214501753168280
[5] DOI: 10.1111/1467-9868.00233 · Zbl 04558573 · doi:10.1111/1467-9868.00233
[6] DOI: 10.1093/biomet/89.1.111 · Zbl 0998.62024 · doi:10.1093/biomet/89.1.111
[7] DOI: 10.1081/STA-120029828 · Zbl 1114.62318 · doi:10.1081/STA-120029828
[8] Zhang R., Varying-coefficient Model (2004)
[9] DOI: 10.2307/2669476 · Zbl 0996.62078 · doi:10.2307/2669476
[10] DOI: 10.1111/j.1467-9868.2006.00539.x · Zbl 1110.62053 · doi:10.1111/j.1467-9868.2006.00539.x
[11] DOI: 10.1111/1467-9868.00183 · Zbl 0915.62062 · doi:10.1111/1467-9868.00183
[12] Green P. J., Nonparametric Regression and Generalized Linear Models (1994) · Zbl 0832.62032
[13] DOI: 10.2307/2287970 · Zbl 0587.62067 · doi:10.2307/2287970
[14] Gu C., Smoothing Spline ANOVA Models (2002) · Zbl 1051.62034
[15] DOI: 10.2307/2286796 · Zbl 0373.62040 · doi:10.2307/2286796
[16] Wahba G., J. Roy. Statist. Soc. B 40 pp 364– (1978)
[17] DOI: 10.1214/aos/1176349743 · Zbl 0596.65004 · doi:10.1214/aos/1176349743
[18] DOI: 10.1093/biomet/80.1.75 · Zbl 0771.62027 · doi:10.1093/biomet/80.1.75
[19] Wahba G., J. Roy. Statist. Soc. B 45 pp 133– (1983)
[20] DOI: 10.2307/2291720 · Zbl 0882.62059 · doi:10.2307/2291720
[21] Weiss R. E., Modeling Longitudinal Data (2005) · Zbl 1076.62071
[22] DOI: 10.2307/2529876 · Zbl 0512.62107 · doi:10.2307/2529876
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