Some simple log-linear models for the analysis of ordinal response data

A family of log-linear models are proposed to describe contingency tables in which one variable can be considered as the response to the remaining. The proposed models take into account the ordering nature of the response categories and have structure similar to that employed in polynomial regression. Stochastic ordering of the response distributions under the proposed models is discussed and the model-reduction techniques are developed. The proposed models are applied to two data sets previously analysed in the literature.