Nonparametric Bayesian modeling for multivariate ordinal data
Nonparametric Bayesian modeling for multivariate ordinal data
复制标题
DOI：
10.1198/106186005x63185
复制
发表时间：
2005-09-01
影响因子：
2.4
通讯作者：
Quintana, F
中科院分区：
文献类型：
--
作者：
Kottas, A;Müller, P;Quintana, F
本文提出了一种卡伯维有序结果的概率模型，即考虑对具有序数因子的卡伯维列联表中记录的数据进行推断。该方法建立在完全后验推断的基础上，采用灵活的表格单元概率先验概率模型。我们使用传统多变量概率模型的一种变体，用潜在分数来决定观测数据。在我们的模型中，混合正态先验取代了通常的单一多元正态模型中的潜在变量。通过将先验模型扩展到法线的混合，我们以两种重要的方式推广了推理。首先，我们考虑到列联表中不同的局部依赖结构。其次，序数多变量概率模型中的推理受到与这些潜在变量定义的截止值的选择和重采样有关的问题的困扰。我们展示了所提出的混合模型方法如何完全消除这些问题。我们用两个例子来说明该方法，一个是模拟数据集，另一个是评价者间协议的数据集。
This article proposes a probability model for kappa-dimensional ordinal outcomes, that is, it considers inference for data recorded in kappa-dimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contingency table cell probabilities. We use a variation of the traditional multivariate probit model, with latent scores that determine the observed data. In our model, a mixture of normals prior replaces the usual single multivariate normal model for the latent variables. By augmenting the prior model to a mixture of normals we generalize inference in two important ways. First, we allow for varying local dependence structure across the contingency table. Second, inference in ordinal multivariate probit models is plagued by problems related to the choice and resampling of cutoffs defined for these latent variables. We show how the proposed mixture model approach entirely removes these problems. We illustrate the methodology with two examples, one simulated dataset and one dataset of interrater agreement.