Make Some Noise: Generating Data from Imperfect Factor Models

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Covariance structure models are essential in statistical analysis.
• Simulating model misfit is crucial for evaluating model performance.
• Existing methods like TKL, CB, and WB have limitations in reproducing multiple fit indices.

Purpose of the Study:

• To introduce a novel multiple-target TKL method for generating error-perturbed data.
• To enable the reproduction of specific Root Mean Square Error of Approximation (RMSEA) and Comparative Fit Index (CFI) values.
• To provide researchers with a tool for precise control over simulated model misfit.

Main Methods:

• Developed a multiple-target Tucker, Koopman, and Linn (TKL) method.
• Simulated error-perturbed correlation matrices for factor analysis models.
• Compared the multiple-target TKL method against Cudeck and Browne (CB) and Wu and Browne (WB) methods.

Main Results:

• The multiple-target TKL method produced RMSEA and CFI values closer to target values than CB and WB methods.
• The new method successfully reproduced target RMSEA and CFI values individually and simultaneously.
• Simulations demonstrated the superior accuracy of the multiple-target TKL approach.

Conclusions:

• The multiple-target TKL method is a valuable tool for generating error-perturbed correlation matrices.
• This method offers precise control over model misfit simulation for researchers.
• The `fungible` library provides access to the functions described in this study.