**by Jukka Corander**

**Research Report
1999:6**

Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden

**Abstract**

A class of log-linear models, referred to as local graphical models, is introduced for multinomial data. These models generalize graphical models, by allowing conditional independence restrictions to be valid only in subsets of a sample space. Certain local models are non-hierarchical log-linear models, which illustrates that such models may have a simple interpretation in terms of conditional independence. Identification of plausible models is considered using a decision theoretic framework, where the utility of a model is determined by its predictive performance and relative complexity. Real data sets are used to illustrate that local graphical models may provide a simpler interpretation of a dependence structure than graphical models.

**Key words**: Bayesian
model determination, Graphical models, Local graphical models, Non-hierarchical
log-linear models, Reference analysis, Utility.

*Last update: 2000-02-15/CE*