Hierarchical Interaction Models
David Edwards · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1990
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.