Structural Equation Models of Factorial Invariance in Parallel Proportional Profiles and Oblique Confactor Problems.

Area of Science:

• Psychometrics
• Quantitative Psychology
• Statistical Modeling

Background:

• Discusses challenges in multiple group factor rotation using Cattell's methods.
• Highlights the historical context of "parallel proportional profiles" and "confactor rotation."

Purpose of the Study:

• To explore the relationship between classic factor rotation techniques and modern structural equation modeling (SEM).
• To demonstrate the utility of the Confactor approach within SEM frameworks.
• To examine alternative structural modeling solutions for factor analysis.

Main Methods:

• Relates the Confactor approach to Meredith's selection model.
• Applies standard SEM techniques (e.g., LISREL) to fit the Confactor model.
• Examines mathematical and statistical properties using a four-group problem example.

Main Results:

• The Confactor approach is shown to be a parsimonious model for multiple group factor analysis.
• SEM techniques provide a viable method for fitting the Confactor model.
• Alternative solutions like reference variable selection and invariant orthogonal structure rotation are discussed.

Conclusions:

• The Confactor approach, when fitted using SEM, offers a valuable tool for oblique factor resolution.
• The study identifies benefits and limitations of this structural modeling approach.
• Opportunities for future research in advanced structural modeling are suggested.