A method of moments technique for fitting interaction effects in structural equation models.

Area of Science:

• Social Sciences
• Statistics
• Epidemiology

Background:

• Structural equation models (SEMs) with interaction terms are widely used in social sciences.
• Existing methods for fitting these models often have limitations, particularly regarding distributional assumptions.

Purpose of the Study:

• To present a practical technique for fitting structural equation models with cross-product interaction terms.
• To provide a method that does not require normality assumptions for the underlying factors.
• To detail the implementation, including standard error estimation, for this specific model type.

Main Methods:

• Utilizes factor score estimates for the cross-product structural model.
• Employs closed-form moments-type estimators.
• Extends the general polynomial structural model technique by Wall and Amemiya (2000).

Main Results:

• The proposed method provides a practical implementation for cross-product models, including standard error estimation.
• A simulation study compared the method of moments for the cross-product model against three alternative procedures.
• The technique was applied to a social/behavioural epidemiology example, demonstrating its utility.

Conclusions:

• The presented technique offers a flexible and practical approach for fitting structural equation models with cross-product interactions.
• The method is advantageous as it does not necessitate normality assumptions for the latent factors.
• The approach is valuable for researchers in social sciences and epidemiology needing to model complex interactions.