Restricted graphical log-linear models

Abstract

We introduce a new type of graphical log-linear model called restricted graphical log-linear model. This model is obtained by imposing equality restrictions on subsets of main effects and of first-order interactions. These restrictions are obtained through partitions of the variable and first-order interaction sets. The vertices or variables in the same class have the same main effects in all their categories and the first-order interactions in the same class are equal. We study its properties and derive its associated likelihood equations and give some applications. A graphical representation is possible through a coloured graph.