Generating correlation matrices with model error for simulation studies in factor analysis: a combination of the...

Area of Science:

• Statistics
• Psychometrics
• Computational Statistics

Background:

• Traditional factor analysis simulations use the common-factor model to generate correlation matrices.
• The common-factor model assumes a perfect fit, which is unrealistic for real-world phenomena.
• Model error is crucial for realistic simulations, as no model perfectly represents reality.

Purpose of the Study:

• To present a novel procedure for generating population and sample correlation matrices that incorporates model error.
• To enhance the realism of factor analysis simulation studies.
• To provide a practical implementation using SAS/IML.

Main Methods:

• Combining the Tucker-Koopman-Linn model with Wijsman's algorithm to generate correlation matrices.
• Incorporating model error into the matrix generation process.
• Developing a SAS/IML program for the described procedure.

Main Results:

• A procedure for generating correlation matrices with model error was successfully developed.
• The Tucker-Koopman-Linn model, combined with Wijsman's algorithm, offers a more realistic approach than the conventional common-factor model.
• A SAS/IML program and an example are provided for practical application.

Conclusions:

• The proposed method enhances the accuracy and realism of factor analysis simulations by including model error.
• This approach provides researchers with a more robust tool for conducting simulation studies in factor analysis.
• The availability of the SAS/IML program facilitates the application of this advanced simulation technique.