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A semiparametric stochastic mixed effects model for bivariate cyclic longitudinal data
Author(s) -
Ji Kexin,
Dubin Joel A.
Publication year - 2020
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11543
Subject(s) - bivariate analysis , nonparametric statistics , mathematics , estimator , smoothing , smoothing spline , random effects model , mixed model , statistics , parametric statistics , parametric model , joint probability distribution , autocorrelation , semiparametric regression , econometrics , medicine , meta analysis , bilinear interpolation , spline interpolation
We propose a flexible semiparametric stochastic mixed effects model for bivariate cyclic longitudinal data. The model can handle either single cycle or, more generally, multiple consecutive cycle data. The approach models the mean of responses by parametric fixed effects and a smooth nonparametric function for the underlying time effects, and the relationship across the bivariate responses by a bivariate Gaussian random field and a joint distribution of random effects. The proposed model not only can model complicated individual profiles, but also allows for more flexible within‐subject and between‐response correlations. The fixed effects regression coefficients and the nonparametric time functions are estimated using maximum penalized likelihood, where the resulting estimator for the nonparametric time function is a cubic smoothing spline. The smoothing parameters and variance components are estimated simultaneously using restricted maximum likelihood. Simulation results show that the parameter estimates are close to the true values. The fit of the proposed model on a real bivariate longitudinal dataset of pre‐menopausal women also performs well, both for a single cycle analysis and for a multiple consecutive cycle analysis. The Canadian Journal of Statistics 48: 471–498; 2020 © 2020 Statistical Society of Canada