A Framework to Interpret Nonstandard Log-Linear Models

The formulation of log-linear models within the framework of
Generalized Linear Models offers new possibilities in modeling categorical
data. The resulting models are not restricted to the analysis of contingency
tables in terms of ordinary hierarchical interactions. Such models are considered
as the family of nonstandard log-linear models. The problem that
can arise is an ambiguous interpretation of parameters. In the current paper
this problem is solved by looking at the effects coded in the design matrix
and determining the numerical contribution of single effects. Based on these
results, stepwise approaches are proposed in order to achieve parsimonious
models. In addition, some testing strategies are presented to test such (eventually
non-nested) models against each other. As a result, a whole interpretation
framework is elaborated to examine nonstandard log-linear models in depth.