Machine Learning Diagnosis and Local Shrinkage of Covariance-Level Pathologies in SEM

Non-convergence in small-sample structural equation modeling (SEM) is frequently driven by localized pathologies in the sample covariance matrix—specific covariance patterns that, for a given model specification, substantially elevate the risk of non-convergence. We propose a diagnose–localize–shrinkage framework in which a machine learning classifier predicts SEM non-convergence and SHAP values localize the covariance pairs that drive this prediction. Sample covariance matrices are generated independently of the fitted SEM and modified through controlled pathology injection. A fixed SEM is then fitted to each matrix, and the resulting convergence status is used as the prediction target. The classifier is trained on the unique off-diagonal elements of the corresponding correlation matrix. The SHAP-identified covariance pairs are then used to construct a local shrinkage step toward a well-conditioned model-based target matrix to evaluate whether SEM convergence can be restored with limited distortion of the original covariance pattern. We demonstrate the proposed method using an illustrative example.