Anderson J A, Pemberton J D
Biometrics. 1985 Dec;41(4):875-85.
The grouped continuous model for multivariate ordered categorical data is described. This is based on partitioning an underlying multivariate normal distribution. Straightforward maximum likelihood estimation is really feasible only for one- and two-way tables. We introduce an estimation system based on maximum likelihood estimation in the one- and two-way marginal tables of higher-order tables. This is computationally feasible and an example involving aspects of bird colouring is given. The approach is extended to provide a regression model for multivariate ordered categorical data, with an estimation scheme again based on the one- and two-way marginal tables. The above example is developed to investigate the covariate effect of time. The asymptotic efficiency of these sampling schemes is discussed; it appears that they have high efficiency.
描述了多变量有序分类数据的分组连续模型。该模型基于对潜在多变量正态分布的划分。直接的最大似然估计仅对单向和双向表真正可行。我们引入了一种基于高阶表的单向和双向边际表中的最大似然估计的估计系统。这在计算上是可行的，并给出了一个涉及鸟类着色方面的示例。该方法被扩展以提供多变量有序分类数据的回归模型，其估计方案同样基于单向和双向边际表。对上述示例进行拓展以研究时间的协变量效应。讨论了这些抽样方案的渐近效率；结果表明它们具有很高的效率。
