Optimal Scaling of Interaction Effects in Generalized Linear Models

Abstract

Multiplicative interaction models, such as Goodman's (1981) RC(M) association models, can be a useful tool for analyzing the content of interaction effects. However, most models for interaction effects are suitable only for data sets with two or three predictor variables. Here, we discuss an optimal scaling model for analyzing the content of interaction effects in generalized linear models with any number of categorical predictor variables. This model, which we call the optimal scaling of interactions model, is a parsimonious, one-dimensional multiplicative interaction model. We discuss how the model can be used to visually interpret the interaction effects. Several extensions of the one-dimensional model are also explored. Finally, two data sets are used to show how the results of the model can be applied and interpreted. The first data set is based on the Student/Teacher Achievement Ratio project and is used to investigate the effects of class size on the performance of primary school students. The second data set comprises four questions from the 1994 General Social Survey (Davis & Smith, 1996) on attitudes of the labor roles of women.

ACKNOWLEDGMENTS

We thank two anonymous reviewers for helpful suggestions and the Vereniging Trustfonds Erasmus Universiteit Rotterdam for providing financial support.

Notes

¹ The figures in this article have been created using the programming language MATLAB. Programming code for creating such figures is included in the package that can be downloaded at http://people.few.eur.nl/groenen.