Using Adjusted Crosstabulations to Interpret Log-Linear Relationships

This paper extends the utility of log-linear analysis by presenting a new way to interpret its parameters. We focus on explaining and trying to solve the interpretational problems arising from the difficulty of distinguishing between absolute and relative comparisons that are embedded in a set of log-linear parameters as well as in odds ratios constructed from the parameters. As a solution, we propose a technique for calculating adjusted crosstabulations from log-linear results. Our solution provides a more intuitive and comprehensible method for presenting and discussing results, especially for resolving the issue of absolute versus relative comparisons. As an illustration, we analyze a data set on unemployment, using polytomous dependent and independent variables. We utilize these results to highlight some of the problems of common odds-ratio interpretations of parameters and to describe in detail the application and interpretation of the method of constructing adjusted crosstabulations.