Models for contingency tables specified by linear contraints on two types of odds ratios

A class of models for multi-way contingency tables obtained from a log-linear model by imposing non linear constraints on the interaction parameters are presented. In particular the constraints will regard measures of bivariate association between a pair of categorical variables based on the local-continuation and continuation-local odds ratios.The contribution of this work, according to the author's knowledge, is the simultaneous constraining of more than one type of odds ratio and the approach to manage the row and the column effect of the dependence relationship between categorical variables.