标题： 分级数组先验用于交叉分类数据的方差分析分解 显示英文标题

标题： Hierarchical array priors for ANOVA decompositions of cross-classified data

摘要： 方差分析（ANOVA）分解是一种描述和估计多类别因子水平下响应变量均值异质性的标准方法。 在这样的分解中，所有主要效应和交互项的完整集合可以看作是一组共享由因子水平定义的不同索引集的向量、矩阵和数组。 对于许多类型的分类因子而言，ANOVA 分解在效应的阶数上表现出某种一致性是有道理的，即具有相似主要效应系数的因子水平在更高阶交互项中也可能具有相似的系数。 在这种情况下，通过从主要效应和低阶交互中借用信息，可以改进高阶交互项的估计。 为了利用这些模式，本文介绍了一类用于交互数组集合的分层先验分布，能够适应这些交互的存在。 这些先验分布基于一种多元数组正态分布，为每个因子估计一个协方差矩阵。 该先验能够适应因子水平之间潜在的相似性，并将此类信息整合到涉及该因子的效果估计中。 在存在这种相似性的情况下，此先验能够从估计良好的主要效应和低阶交互中借用信息，以辅助估计数据信息有限的高阶项。 显示英文摘要

摘要： ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matrices and arrays that share various index sets defined by the factor levels. For many types of categorical factors, it is plausible that an ANOVA decomposition exhibits some consistency across orders of effects, in that the levels of a factor that have similar main-effect coefficients may also have similar coefficients in higher-order interaction terms. In such a case, estimation of the higher-order interactions should be improved by borrowing information from the main effects and lower-order interactions. To take advantage of such patterns, this article introduces a class of hierarchical prior distributions for collections of interaction arrays that can adapt to the presence of such interactions. These prior distributions are based on a type of array-variate normal distribution, for which a covariance matrix for each factor is estimated. This prior is able to adapt to potential similarities among the levels of a factor, and incorporate any such information into the estimation of the effects in which the factor appears. In the presence of such similarities, this prior is able to borrow information from well-estimated main effects and lower-order interactions to assist in the estimation of higher-order terms for which data information is limited.