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    Area of Science:

    • Statistics
    • Econometrics
    • Psychometrics

    Background:

    • Influential observations can significantly distort results in statistical modeling.
    • Identifying these observations is crucial for robust analysis in complex models.
    • Nonlinear structural equation models (NLSEM) are widely used but sensitive to outliers.

    Purpose of the Study:

    • To propose a novel case-deletion procedure for detecting influential observations in NLSEM.
    • To develop diagnostic measures rooted in the EM algorithm's complete-data log-likelihood.
    • To enhance computational efficiency through an approximation technique.

    Main Methods:

    • A case-deletion diagnostic procedure is developed for NLSEM.
    • Diagnostic measures are derived from the conditional expectation of the complete-data log-likelihood within the EM algorithm.
    • An one-step pseudo approximation is employed to reduce computational load.
    • Key components are computed using observations from the MH algorithm.

    Main Results:

    • The proposed procedure effectively identifies influential observations in simulation studies.
    • The method demonstrates practical utility in an illustrative real-data example.
    • The one-step approximation successfully reduces computational burden without sacrificing performance.

    Conclusions:

    • The developed case-deletion procedure offers a reliable tool for influential observation detection in NLSEM.
    • The integration with the EM algorithm and MH algorithm provides a computationally feasible approach.
    • This method contributes to more robust and accurate analyses using nonlinear structural equation models.