Sparse Ordinal CFA and Model-Fit Decisions
Category sparsity, category collapsing, and simulation-cum-ROC evaluation
Published SEM paper + accepted BRM extension Sparse ordinal CFA research program
Sparse ordinal categories can affect not only estimation, but also whether global fit indices can distinguish a correctly specified model from a misspecified one. This project treats fit evaluation as a discrimination problem before treating any cutoff as a decision rule.
Abstract
Using a Monte Carlo simulation-cum-ROC framework, the study evaluates how RMSEA, SRMR, CFI, and TLI distinguish correctly specified ordinal CFA models from two forms of misspecification under sparse response categories and category collapsing. A local misspecification is represented by an omitted cross-loading, while a structural misspecification combines two correlated factors. The analysis compares WLSMV, MLR, and MLMV across sample size, loading magnitude, sparsity, number of sparse-pattern items, collapsing intensity, and a no-collapse baseline.
Paper
Liu, L., Liu, J., Yi, H., & Okech, D. (2026). Simulation-cum-ROC fit evaluation in sparse ordinal CFA under category collapsing. Structural Equation Modeling: A Multidisciplinary Journal. Published online August 6, 2026.
Code
All results are based on simulated data. Analysis code for the simulation study is available on OSF:
The repository contains code supporting the simulation workflow, including data generation, model fitting, fit-index extraction, and ROC-based evaluation.
Simulation Design
RMSEA · SRMR · CFI · TLI
WLSMV · MLR · MLMV
omitted cross-loading · combined correlated factors
sample size, loadings, sparsity, sparse items, collapsing intensity
A no-collapse baseline makes it possible to separate the effect of sparse response structure itself from the additional information loss introduced by category collapsing. ROC analysis evaluates both overall diagnostic separation through AUC and condition-specific operating points through sensitivity and specificity.
Key Findings
- Discrimination varied substantially across conditions. Fit-index performance cannot be summarized well by a single universal cutoff.
- Local misspecification was harder to detect. Detection weakened under moderate loadings, smaller samples, and aggressive category collapsing.
- Structural misspecification was generally easier to detect. Performance remained strong in many conditions, with notable deterioration under extreme sparsity and aggressive collapsing.
- Mild and moderate collapsing produced relatively small average changes from the original response scale. The largest losses were concentrated in more aggressive collapsing and difficult information conditions.
- A cutoff is meaningful only when the index has adequate discrimination. The paper therefore treats ROC-derived cutoffs as condition-specific operating points rather than new universal rules.
Accepted Extension
Liu, L., Liu, J., & Okech, D. (accepted). Calibrating fit-index cutoffs for sparse ordinal CFA: Scenario-specific thresholds and operating characteristics. Behavior Research Methods.
This companion paper translates the discrimination results from the published SEM study into scenario-specific fit-index thresholds and operating characteristics for sparse ordinal CFA. The manuscript was accepted on October 7, 2026 and has entered Springer production.
Contribution to my research program
This project anchors my work on measurement under sparse and heterogeneous data. The broader program studies how response sparsity, estimator choice, category collapsing, and model-fit calibration affect the quality of measurement decisions.