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Abstract:
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We propose and consider inference for a semiparametric stochastic mixed model for bivariate periodic repeated measures data. The bivariate model uses parametric fixed effects for modelling covariate effects and periodic smooth nonparametric functions for each of the two underlying time effects. In addition, the between-subject and within-subject correlations are modelled using separate but correlated random effects and a bivariate Gaussian random field, respectively. We derive estimators for both the fixed effects regression coefficients and the nonparametric time functions using maximum penalized likelihood, where the resulting estimator for the nonparametric time function is a smoothing spline. The smoothing parameters and all variance components are estimated simultaneously using restricted maximum likelihood. We investigate the proposed methodology through simulation. We also illustrate the model by analyzing bivariate longitudinal female hormone data collected daily over multiple consecutive menstrual cycles.
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