Abstract In longitudinal data with many replications, the high-order autoregressive (AR) structure of covariance matrix is required to capture the serial correlations between repeated outcomes. Thus, the high-order AR structure requires many parameters underlying the dynamic data dependence. In this paper, we proposed an autoregressive moving-average (ARMA) structure of covariance matrix involving multivariate linear models instead of the high-order AR structure of covariance matrix. We decomposed the covariance matrix using autoregressive moving-average Cholesky decomposition (ARMACD) to explain the correlations between responses at each time point, the correlation within separate responses over time, and the cross-correlation between different responses at different times. The ARMACD facilitates nonstationarity and heteroscedasticity of the covariance matrix, and the estimated covariance matrix is guaranteed to be positive definite. We illustrated the proposed methods using data derived from a study of nonalcoholic fatty liver disease.

中文翻译：

---

使用 ARMA Cholesky 和超球面分解分析多变量纵向数据

摘要 在具有多次重复的纵向数据中，需要协方差矩阵的高阶自回归（AR）结构来捕捉重复结果之间的序列相关性。因此，高阶 AR 结构需要许多作为动态数据依赖性基础的参数。在本文中，我们提出了一种涉及多元线性模型的协方差矩阵的自回归移动平均（ARMA）结构，而不是协方差矩阵的高阶 AR 结构。我们使用自回归移动平均 Cholesky 分解 (ARMACD) 分解协方差矩阵，以解释每个时间点响应之间的相关性、不同响应内随时间的相关性以及不同时间不同响应之间的互相关。ARMACD 有助于协方差矩阵的非平稳性和异方差性，并且估计的协方差矩阵保证是正定的。我们使用来自非酒精性脂肪性肝病研究的数据说明了所提出的方法。