Available extensions of generalized estimating equations for longitudinal ordinal response require a conversion of the ordinal response to a vector of binary category indicators. That leads to a rather complicated working correlation structure and to large matrices when the number of categories and dimension of the clusters are large. Weighted scores estimating equations are constructed to overcome the aforementioned problems. Similar to generalized estimating equations which construct unbiased equations weighting the residuals, the weighted scores weight the univariate score functions. To specify the weight matrices, the weighted scores estimating equations use a working dependence model, namely the multivariate normal (MVN) copula model with univariate ordinal probit or logit regressions as the marginals. There is no need to convert the ordinal response to binary indicators, thus the weight matrices have smaller dimensions. Composite likelihood information criteria are further proposed as an intermediate step for selecting both the covariates in the mean function modelling and the structure of the latent correlation matrix induced by the MVN latent variables. The weighted scores estimating equations and composite likelihood information criteria are illustrated by analysing a rheumatoid arthritis clinical trial. Our modelling framework is implemented in the package weightedScores within the open source statistical environment R.

中文翻译：

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纵向有序响应的加权分数估计方程和 CL1 信息标准

纵向序数响应的广义估计方程的可用扩展需要将序数响应转换为二元类别指标的向量。当聚类的类别和维度的数量很大时，这会导致相当复杂的工作相关结构和大型矩阵。构建加权分数估计方程以克服上述问题。类似于构建对残差加权的无偏方程的广义估计方程，加权分数对单变量分数函数进行加权。为了指定权重矩阵，加权分数估计方程使用工作依赖模型，即多变量正态 (MVN) copula 模型，以单变量序数概率或 logit 回归作为边际。无需将序数响应转换为二元指标，因此权重矩阵具有更小的维度。复合似然信息标准被进一步提出作为中间步骤，用于选择均值函数建模中的协变量和由 MVN 潜在变量引起的潜在相关矩阵的结构。通过分析类风湿性关节炎临床试验来说明加权分数估计方程和复合似然信息标准。我们的建模框架在开源统计环境 R 中的 weightedScores 包中实现。复合似然信息标准被进一步提出作为中间步骤，用于选择均值函数建模中的协变量和由 MVN 潜在变量引起的潜在相关矩阵的结构。通过分析类风湿性关节炎临床试验来说明加权分数估计方程和复合似然信息标准。我们的建模框架在开源统计环境 R 中的 weightedScores 包中实现。复合似然信息标准被进一步提出作为中间步骤，用于选择均值函数建模中的协变量和由 MVN 潜在变量引起的潜在相关矩阵的结构。通过分析类风湿性关节炎临床试验来说明加权分数估计方程和复合似然信息标准。我们的建模框架在开源统计环境 R 中的 weightedScores 包中实现。