Improving the Validity of Post-Selection Inference in Lasso-Regularized Structural Equation Modeling for Model Respecification

Regularization is increasingly used in structural equation modeling (SEM) to search for potential post hoc model modifications, yet the validity of statistical inference after selecting parameters/models via regularization has received limited attention. We propose selective discrepancy inference for lasso-regularized SEM, particularly when the lasso is used for model respecification. The framework views regularization not simply as selecting SEM parameters, but as selecting Jacobian-defined covariance-change directions along which a constrained model may fail to reproduce the covariance structure. The inferential target is therefore a selected covariance-discrepancy coefficient, which quantifies how much the misfit left by the constrained model is explained by the selected modification direction after accounting for other selected directions and baseline parameter readjustment. A simulation study shows that the resulting confidence intervals achieve target coverage rates. An empirical example regarding measurement invariance testing illustrates how the approach evaluates lasso-selected model modifications. Example R code is provided.