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

中文翻译：

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二元循环纵向数据的半参数随机混合效应模型

我们为双变量循环纵向数据提出了一种灵活的半参数随机混合效应模型。该模型可以处理单个周期的数据，或更一般而言，可以处理多个连续的周期数据。该方法通过参数固定效应和平滑的非参数函数对底层时间效应建模响应的平均值，并通过双变量高斯随机场和随机效应的联合分布跨双变量响应建立关系。所提出的模型不仅可以对复杂的个人资料进行建模，而且还可以使主题内和响应间的关联更加灵活。使用最大惩罚似然估计固定效应回归系数和非参数时间函数，其中非参数时间函数的最终估计量为三次平滑样条。使用限制的最大似然率同时估计平滑参数和方差分量。仿真结果表明参数估计值接近真实值。无论是单周期分析还是多个连续周期分析，建议的模型在绝经前妇女的真实双变量纵向数据集上的拟合效果也很好。加拿大统计杂志48：471-498；加拿大统计局。2020©2020加拿大统计学会