Optimal Scaling of Interaction Effects in Generalized Linear Models.

Area of Science:

• Statistics
• Social Sciences

Background:

• Multiplicative interaction models, like Goodman's RC(M) association models, are valuable for analyzing interaction effects.
• Existing models are often limited to two or three predictor variables, restricting their application.

Purpose of the Study:

• To present an optimal scaling model for analyzing interaction effects in generalized linear models.
• To provide a parsimonious, one-dimensional multiplicative interaction model applicable to any number of categorical predictors.
• To demonstrate visual interpretation of interaction effects using the proposed model.

Main Methods:

• Developed an optimal scaling model for interaction effects within generalized linear models.
• Explored extensions of the one-dimensional model.
• Applied the model to two real-world data sets: Student/Teacher Achievement Ratio project and General Social Survey data.

Main Results:

• The optimal scaling of interactions model offers a flexible approach to analyzing interaction effects with multiple categorical predictors.
• The model facilitates visual interpretation of interaction effects.
• Demonstrated practical application and interpretation of results using empirical data.

Conclusions:

• The optimal scaling of interactions model extends the utility of multiplicative interaction models to complex datasets.
• The model provides a parsimonious and interpretable method for understanding interaction effects in generalized linear models.
• The approach is applicable to diverse research areas, including education and social attitudes.