Alternative Strategies for Cross-Validation of Covariance Structure Models.

Area of Science:

• Psychometrics
• Statistics
• Structural Equation Modeling

Background:

• Evaluating covariance structure models requires cross-validation to assess overall model fit.
• Overall discrepancy combines approximation and estimation discrepancies.
• Existing cross-validation strategies include tight and partial approaches.

Purpose of the Study:

• To describe and investigate alternative two-sample cross-validation strategies for covariance structure models.
• To compare tight versus partial cross-validation strategies regarding model complexity and sample size.
• To provide justification for specific partial cross-validation strategies.

Main Methods:

• Two-sample cross-validation strategies were defined based on parameter constraints (tight vs. partial).
• A sampling study using empirical data was conducted.
• Model fit was evaluated by re-fitting a calibration sample solution to a validation sample covariance matrix.

Main Results:

• Tight cross-validation strategies favored simpler models in smaller samples.
• Partial cross-validation strategies supported more complex models, even with small sample sizes.
• The choice of cross-validation strategy impacts model selection decisions.

Conclusions:

• Partial cross-validation offers a viable alternative to tight strategies, especially when model complexity is a concern.
• The findings have implications for model comparison and evaluation in structural equation modeling.
• Consideration of sample size and model complexity is crucial when selecting cross-validation approaches.