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    Area of Science:

    • Statistics
    • Psychometrics
    • Quantitative Psychology

    Background:

    • Cross-validation is crucial for assessing the predictive validity of statistical models.
    • Estimating cross-validation coefficients often requires large sample sizes.
    • Existing methods for covariance structure analysis can be computationally intensive.

    Purpose of the Study:

    • To develop and evaluate single sample approximations for cross-validation coefficients.
    • To propose an adjustment for predictive validity applicable to various discrepancy functions.
    • To investigate the relationship between the proposed coefficient and the Akaike Information Criterion.

    Main Methods:

    • The study focuses on single sample approximations for cross-validation coefficients.
    • An adjustment for predictive validity is proposed for use with any correctly specified discrepancy function.
    • Maximum likelihood estimation under normality assumptions is considered.

    Main Results:

    • A novel single sample approximation for the cross-validation coefficient is presented.
    • The proposed adjustment enhances predictive validity assessment.
    • Under normality and maximum likelihood estimation, the coefficient is a linear function of the Akaike Information Criterion.

    Conclusions:

    • Single sample approximations offer a viable alternative for cross-validation coefficient estimation.
    • The proposed adjustment is flexible and broadly applicable.
    • The findings simplify model selection by linking cross-validation to information criteria.