Selection Tests for possibly misspecified hierarchical multinomial marginal models

Hierarchical marginal models have been proposed for categorical data to overcome some limitations of the log-linear approach in modeling marginal distributions. These models can easily satisfy marginal conditional independence conditions and describe with great flexibility the dependence of marginal distributions on covariates. As the richness of the family of hierarchical marginal models leads to comparing models that do not satisfy a nesting relationship, statistical tests for model selection from non-nested, possibly mis- specified marginal models are introduced.