Application scenarios for nonstandard log-linear models

In this article, the authors have 2 aims. First, hierarchical, nonhierarchical, and nonstandard log-linear models are defined. Second, application scenarios are presented for nonhierarchical and nonstandard models, with illustrations of where these scenarios can occur. Parameters can be interpreted in regard to their formal meaning and in regard to their magnitude. The interpretation of the meaning of parameters is the main focus of this article. Design matrices are used to describe the hypotheses tested in models and to illustrate cases in which parameters are interpretable. Also, design matrices are used to show where and how nonstandard models differ from standard hierarchical models. Coding schemes are discussed, in particular, dummy coding and effects coding. Data examples are given with data and models discussed in the literature.