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.
Highlights
In this paper we introduce a new type of model for discrete variables called restricted or coloured graphical log-linear model (RGLL model ), which combines symmetry with discrete graphical models
Symmetry is considered through specific parameter restrictions not used before, but inspired by those used in the continuous case
We have introduced RGLL models mainly as a way of generalizing symmetry in graphical log-linear models
Summary
In this paper we introduce a new type of model for discrete variables called restricted or coloured graphical log-linear model (RGLL model ), which combines symmetry with discrete graphical models. In SQS graphical models, the main effects restrictions are similar to those for RGLL models, and in SQS and QS models there are restrictions of the kind uXY (ij) = uRS(ij) for all i, j = 1, ..., L (considering L levels in each variable), for elements in the same class; including restrictions uXY (ij) = uXY (ji) for all i, j = 1, ..., L, and uRS(ij) = uRS(ji) for all i, j = 1, ..., L; and implying specific restrictions on the second-order interactions, i.e. on the parameters uXY Z(ijk). The first-order interaction restrictions in any SQS or QS graphical model are a particular case of the kind of restrictions defined for those terms in RGLL models. In the Appendix we provide a method for getting a numerical solution
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