Chao Wei-Hsiung, Chen Su-Hua
Department of Applied Mathematics, National Dong Hwa University, Shoufeng, Hualien 97401, Taiwan.
Biom J. 2009 Aug;51(4):571-87. doi: 10.1002/bimj.200800254.
A predictive continuous time model is developed for continuous panel data to assess the effect of time-varying covariates on the general direction of the movement of a continuous response that fluctuates over time. This is accomplished by reparameterizing the infinitesimal mean of an Ornstein-Uhlenbeck processes in terms of its equilibrium mean and a drift parameter, which assesses the rate that the process reverts to its equilibrium mean. The equilibrium mean is modeled as a linear predictor of covariates. This model can be viewed as a continuous time first-order autoregressive regression model with time-varying lag effects of covariates and the response, which is more appropriate for unequally spaced panel data than its discrete time analog. Both maximum likelihood and quasi-likelihood approaches are considered for estimating the model parameters and their performances are compared through simulation studies. The simpler quasi-likelihood approach is suggested because it yields an estimator that is of high efficiency relative to the maximum likelihood estimator and it yields a variance estimator that is robust to the diffusion assumption of the model. To illustrate the proposed model, an application to diastolic blood pressure data from a follow-up study on cardiovascular diseases is presented. Missing observations are handled naturally with this model.
针对连续面板数据开发了一种预测性连续时间模型，以评估随时间变化的协变量对随时间波动的连续响应变量运动总体方向的影响。这是通过根据其平衡均值和一个漂移参数对奥恩斯坦-乌伦贝克过程的无穷小均值进行重新参数化来实现的，该漂移参数评估过程恢复到其平衡均值的速率。平衡均值被建模为协变量的线性预测值。该模型可被视为一个具有协变量和响应变量的时变滞后效应的连续时间一阶自回归回归模型，与离散时间类似模型相比，它更适合不等距面板数据。考虑了最大似然法和拟似然法来估计模型参数，并通过模拟研究比较了它们的性能。建议采用更简单的拟似然法，因为它产生的估计量相对于最大似然估计量具有较高的效率，并且产生的方差估计量对模型的扩散假设具有稳健性。为了说明所提出的模型，给出了一个应用于心血管疾病随访研究中舒张压数据的实例。该模型能够自然地处理缺失观测值。
