Robust Model Testing Research — Robust SEM and Structural Model Evaluation
Robust Model Testing Research Design · Also known as: robust SEM, robust structural model testing, robust fit evaluation, robust model evaluation research
Robust model testing research applies structural or path models to data while explicitly accounting for violations of multivariate normality and other distributional assumptions. Rather than discarding non-normal data or forcing transformations, it uses corrected estimators — most notably the Satorra-Bentler scaled chi-square and Yuan-Bentler robust standard errors — to produce trustworthy fit indices and parameter estimates even when classical maximum likelihood assumptions are breached.
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When to use it
Use robust model testing research when you are testing a theoretically specified structural or measurement model with multivariate data that show evidence of non-normality (elevated kurtosis or skewness, bounded or Likert-type scales, outlier-prone distributions). It is the appropriate default in applied social science, educational measurement, and health research where Likert scales are common. Do NOT use it as a substitute for re-specifying a poorly fitting model — robustness corrects for distributional violations, not for misspecified theory. It is also unnecessary if data genuinely satisfy multivariate normality (verified by Mardia's test), where standard ML is efficient and adequate.
Strengths & limitations
- Produces valid fit statistics and standard errors even when multivariate normality is violated, preventing false model rejections.
- Widely implemented in major software (R lavaan, Mplus, EQS, LISREL) making replication straightforward.
- Retains the interpretive richness of full SEM — latent variables, measurement error correction, and path coefficients — while adding distributional robustness.
- Applicable to a broad range of data types including continuous non-normal, bounded scale, and mixed-format data.
- The Satorra-Bentler correction is theoretically well-grounded and extensively validated in simulation studies.
- Does not resolve model misspecification — if the theoretical model is wrong, robust estimators will still indicate poor fit.
- Satorra-Bentler corrections assume a sufficiently large sample; with n < 200 the corrections may themselves be unstable.
- Nested model comparison requires the special Satorra-Bentler chi-square difference formula; naive subtraction of scaled chi-squares yields incorrect p-values.
- Does not address missing data — a separate missing data strategy (FIML or multiple imputation) must be applied before or alongside robust estimation.
Frequently asked
What is the difference between MLM and MLR in Mplus?
Both use the Satorra-Bentler scaling idea but differ in their corrections. MLM applies a mean adjustment to the chi-square statistic only, leaving standard errors as standard ML estimates. MLR applies both mean and variance adjustments, producing robust standard errors and confidence intervals in addition to the scaled chi-square. MLR is generally preferred because it also corrects standard errors, which affects significance tests for individual parameters.
How do I compare two nested models when using robust estimation?
You cannot simply subtract one scaled chi-square from another. You must use the Satorra-Bentler scaled difference test, which divides the difference in scaled chi-squares by a correction factor computed from the scaling factors of each model. Mplus produces this automatically with the DIFFTEST option. Failing to use this correction commonly leads to erroneous conclusions about whether adding or removing a path improves fit.
Can I use robust estimation with ordinal (Likert) data?
For purely ordinal data, WLSMV (weighted least squares mean and variance adjusted, the default for categorical indicators in Mplus) is generally preferred over MLR because it treats ordinal variables as categorical, estimating polychoric correlations. MLR with ordinal data assumes the variables are continuous approximations, which can be acceptable for five or more response categories but is technically misspecified for truly ordinal scales.
Does robust estimation require a larger sample than standard ML?
Robust estimators are asymptotically valid and therefore perform better in large samples. As a practical guide, n >= 200 is commonly recommended for robust SEM, compared to n >= 100–150 for standard ML with well-behaved data. In small samples the scaling corrections themselves become unstable; bootstrapped confidence intervals or Bayesian SEM are better options below n = 150.
If robust fit indices indicate good fit but modification indices are large, should I re-specify the model?
Good global fit does not mean the model is uniquely correct — a misspecified model can still yield acceptable fit indices while systematically mis-representing specific relationships. Inspect residuals and modification indices as diagnostics, but make re-specifications only when they are theoretically justified. Post-hoc modifications driven purely by modification indices constitute capitalisation on chance and must be disclosed and cross-validated.
Sources
- Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Sage. link ↗
- Yuan, K.-H., & Bentler, P. M. (1998). Robust mean and covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 51(1), 63–88. DOI: 10.1111/j.2044-8317.1998.tb00667.x ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Model Testing Research Design. ScholarGate. https://scholargate.app/en/research-design/robust-model-testing-research
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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