In order to analyze longitudinal ordinal data, researchers commonly use the cumulative logit random effects model. In these models, the random effects covariance matrix is used to account for both subject variation and serial correlation of repeated outcomes. However, the covariance matrix is assumed to be homoscedastic and restricted due to the high-dimensionality and positive-definiteness of the matrix. In order to relieve these assumptions, three Cholesky decomposition methods were proposed to model the random effects covariance matrix: modified Cholesky, moving average Cholesky, and autoregressive moving-average decompositions. We also use the three decompositions to model the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. In addition, Bayesian methods are presented for the parameter estimation of the proposed models, and Markov Chain Monte Carlo is conducted using the JAGS program. The proposed methods are illustrated using lung cancer data.

中文翻译：

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具有ARMA随机效应协方差矩阵的贝叶斯累积logit随机效应模型

为了分析纵向序数数据，研究人员通常使用累积logit随机效应模型。在这些模型中，随机效应协方差矩阵用于说明受试者差异和重复结果的序列相关性。但是，由于矩阵的高维和正定性，协方差矩阵被假定为等规且受限制。为了缓解这些假设，提出了三种Cholesky分解方法来对随机效应协方差矩阵建模：改进的Cholesky，移动平均Cholesky和自回归移动平均分解。我们还使用三个分解为纵向有序数据的累积logit随机效应模型中的随机效应协方差矩阵建模。此外，提出了贝叶斯方法用于所提出模型的参数估计，并且使用JAGS程序进行了马尔可夫链蒙特卡洛。使用肺癌数据说明了所提出的方法。