Hierarchical Interaction Models
本文扩展了Lauritzen和Wermuth提出的图形关联模型，提出层次交互模型，给出了模型表示和估计算法，并探讨了边际化和条件化性质，适用于混合定性和连续数据的分析。
SUMMARY Lauritzen and Wermuth have proposed a class of models for mixed qualitative and continuous data, defined by two properties: that the continuous variables are normally distributed given the qualitative variables and that a set of conditional independence relations hold between specified pairs of variables. These models, called graphical association models, include graphical log-linear models for contingency tables and covariance selection models for correlation matrices. The present paper examines an extension to this class called hierarchical interaction models. A compact form for model representation is described and an estimation algorithm is given. Some properties of the models concerning marginalization and conditioning are examined. The class includes and generalizes hierarchical log-linear models, standard fixed effect analysis of variance (ANOVA), multivariate ANOVA and multivariate regression models. Two applications are given.