Latent Variable Regression: A Technique for Estimating Interaction and Quadratic Coefficients

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Estimating regression coefficients for latent variables with interaction and quadratic terms presents challenges.
• Existing methods may require a priori error estimates, limiting their applicability.

Purpose of the Study:

• To propose a novel technique for estimating regression coefficients for interaction and quadratic latent variables.
• To combine regression analysis with the measurement model of structural equation analysis.

Main Methods:

• The proposed technique integrates regression analysis with the measurement model of structural equation analysis (e.g., CALLS, EQS, LISREL).
• Parameter estimates from the measurement model are used to correct the variance-covariance matrix in regression analysis.

Main Results:

• The method provides accurate coefficient estimates for regression models.
• It is applicable to both existing measures and new measures lacking a priori error estimates.

Conclusions:

• This technique offers a robust approach to estimating regression coefficients for complex latent variable models.
• It enhances the utility of structural equation modeling in various scientific disciplines.