Hierarchical Log-linear Models for Contingency Tables

Log-linear models are widely used for qualitative data in multidimensional contingency tables. Hierarchical log-linear models are models that include all lower-order terms composed from variables contained in a higher-order model term. The starting point is a saturated model, then homogenous associations, conditional independence and complete independence. There are several statistics that help to choose the best model. The first is the likelihood ratio approach, next is AIC and BIC information criteria. In R software there is loglm() function in MASS library and glm in stats library. The first approach is presented in this paper