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Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements
Author(s) -
Ryu Duchwan,
Li Erning,
Mallick Bani K.
Publication year - 2011
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2010.01489.x
Subject(s) - covariate , markov chain monte carlo , random effects model , mathematics , bayesian probability , statistics , nonparametric regression , nonparametric statistics , econometrics , linear model , bayesian inference , semiparametric regression , medicine , meta analysis
Summary We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject‐specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply Bayesian nonparametric methods including cubic smoothing splines or P‐splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data‐augmentation schemes. The approach allows flexible covariance structures for the random effects and within‐subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the “naive” approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves.