Plain Answers to Several Questions about Association/Independence Structure in Complete/Incomplete Contingency Tables

In this paper, we develop some results based on Relational model (Klimova, et al. 2012) which permits a decomposition of logarithm of ex- pected cell frequencies under a log-linear type model. These results imply plain answers to several questions in the context of analyzing of contingency tables. Moreover, determination of design matrix and hypothesis-induced matrix of the model will be discussed. Properties of maximum likelihood estimators of the model parameters are obtained. Some new model resid- uals and an alternative symmetric chi-square criterion are given. Two real examples illustrate the method.