Multinomial Poisson Models subject to inequality constraints

Multinomial-Poisson Homogeneous (MPH) models and Homogeneous Linear Predictor (HLP) Multinomial-Poisson models include as special cases many models for contingency table analysis that have been introduced in the effort to overcome well known limitations of the log-linear models. Here the definitions of MPH and HLP models are extended to include inequality constraints. It is shown that inequality constrained MPH and HLP models are a very flexible and rich family of models for contingency table analysis. The inequality constrained Hierarchical Multinomial Marginal models which are an important sub-class of MPH models are also examined