Label- and Level-Invariant Graphical Log-Linear Models

摘要

We introduce two types of graphical log-linear models: label- and level-invariant models for triangle-free graphs. These models generalise symmetry concepts in graphical log-linear models and provide a tool with which to model symmetry in the discrete case. A label-invariant model is category-invariant and is preserved after permuting some of the vertices according to transformations that maintain the graph, whereas a level-invariant model equates expected frequencies according to a given set of permutations. These new models can both be seen as instances of a new type of graphical log-linear model termed the restricted graphical log-linear model, or RGLL, in which equality restrictions on subsets of main effects and first-order interactions are imposed. Their likelihood equations and graphical representation can be obtained from those derived for the RGLL models.