Nested Cross-Validation for Model Selection in Structural Equation Modeling

Yoonsik Chae

doi:10.1080/10705511.2026.2731583

Nested Cross-Validation for Model Selection in Structural Equation Modeling

2026-10-20

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DOI：10.1080/10705511.2026.2731583

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Model selection in structural equation modeling (SEM) commonly relies on in-sample fit indices, which use the same data for estimation and assessment and are therefore vulnerable to overfitting. Although cross-validation provides an alternative, standard K-fold Cross-Validation can still be affected by selection bias when the same procedure informs both model selection and evaluation. This study examines Nested Cross-Validation (NCV) as a model selection framework for SEM that separates these stages. Simulations based on the design of Hu and Bentler (Citation1999) compared NCV with 5-fold and 10-fold CV and conventional in-sample fit indices across sample sizes and factor loading conditions. NCV generally achieved higher true model selection rates, particularly when the candidate set included over-specified alternatives. Under low factor loadings combined with small samples (N ≤ 250), however, higher non-convergence rates within NCV’s inner loop reduced its selection rate below the corresponding rates of both K-fold CV variants. These findings support NCV as a useful approach for SEM model selection while underscoring the importance of sample size, measurement strength, and convergence. Further research is needed to examine the performance of NCV-based model evaluation.

Keywords:

Fit indices

generalizability

model selection

Nested cross-validation

overfitting

Nested Cross-Validation for Model Selection in Structural Equation Modeling

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