Year Old Unbiased Distribution Free Estimator Reliably Improves SEM Statistics for Nonnormal Data
Bibliographic Data
| ID | 21641729 |
|---|---|
| Authors | Han Du (0000-0001-7538-7789, University of California, Los Angeles, corresponding author), Peter M Bentler (0000-0002-9440-721X, University of California, Los Angeles) |
| Year | 2022 |
| Volume | 29 |
| Issue | 6 |
| Pages | 872-887 |
| Publication date | 2022-11-02 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Structural Equation Modeling: A Multidisciplinary Journal (JOURNAL) |
| Journal identifiers | ISSN: 1070-5511 • E-ISSN: 1532-8007 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/10705511.2022.2063870 |
| OpenAlex | W4281734499 |
| Language | EN |
| Citations received | 4 |
| References cited | 52 |
In structural equation modeling, researchers conduct goodness-of-fit tests to evaluate whether the specified model fits the data well. With nonnormal data, the standard goodness-of-fit test statistic T does not follow a chi-square distribution. Comparing T to χdf2 can fail to control Type I error rates and lead to misleading model selection conclusions. To better evaluate model fit, researchers have proposed various robust test statistics, but none of them consistently control Type I error rates under all examined conditions. To improve model fit statistics for nonnormal data, we propose to use an unbiased distribution free weight matrix estimator (Γ^DFU) in robust test statistics. Specifically, using normal theory based parameter estimates with Γ^DFU, we calculate various robust test statistics and robust standard errors. We conducted a simulation study to compare 63 existing robust statistic combinations with the 4 proposed robust statistics with Γ^DFU. The Satorra–Bentler statistic TSB based on Γ^DFU (TSBU) provided acceptable Type I error rates at α=.01,.05, or .1 across all conditions (except a few cases with α=.01), regardless of the sample size and the distribution. TSBU or TMVA2U typically provided the smallest Anderson-Darling test values, showing the smallest distances between p-values and Uniform(0,1). We use a real data example to compare statistics with Γ^DFU and that with Γ^ADF
Econometrics · Estimator · Goodness of fit · Normal distribution · Robust statistics · Standard error · Statistic · Statistical hypothesis testing · Statistics · Test statistic · Type I and type II errors · Bayesian Modeling and Causal Inference · Mathematics · Psychometric Methodologies and Testing · Statistical Methods and Bayesian Inference
Robustness?
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Simulating Multivariate Nonnormal Distributions
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Distributionally-Weighted Least Squares in Growth Curve Modeling
Non-normal Data Simulation using Piecewise Linear Transforms
A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis
A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix
Evaluating Small Sample Approaches for Model Test Statistics in Structural Equation Modeling
The Noncentral Chi-square Distribution in Misspecified Structural Equation Models
A Note on Using and Unbiased Weight Matrix in the ADF Test Statistic
Generating Nonnormal Multivariate Data Using Copulas
Empirically Corrected Rescaled Statistics for SEM with Small N and Large p
Univariate and multivariate skewness and kurtosis for measuring nonnormality
Can test statistics in covariance structure analysis be trusted
Comparative fit indexes in structural models
| Unique citing works | 4 |
|---|---|
| Citations per year | 1,33 |
| Citation span | 2023 - 2025 (3) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 4 |