Simulation-cum-ROC Fit Evaluation in Sparse Ordinal CFA Under Category Collapsing

Global fit indices are routinely used in confirmatory factor analysis, but sparse ordinal categories and category-collapsing decisions can alter diagnostic performance. Using a Monte Carlo simulation-cum-ROC framework, we examined how RMSEA, SRMR, CFI, and TLI discriminated correctly specified ordinal CFA models from a local misspecification, operationalized as an omitted cross-loading, and a structural misspecification, operationalized as combining two correlated factors. Analyses compared WLSMV, MLR, and MLMV across sample size, loading magnitude, sparsity, number of sparse-pattern items, collapsing intensity, and a no-collapse baseline. Discrimination varied substantially by condition. Local misspecification was difficult to detect under moderate loadings, smaller samples, and aggressive collapsing, whereas structural misspecification was detected well except under extreme sparsity and aggressive collapsing. Mild and moderate collapsing produced small average changes relative to the original response scale. Findings support treating ROC-derived cutoffs as condition-specific operating points. Researchers should justify collapsing decisions and verify discrimination before interpreting cutoffs.