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Obtaining robust practical fit indices with multiply imputed nonnormal data in structural equation modeling.

Fan Jia1, Terrence D Jorgensen2, Wei Wu3

  • 1Department of Psychological Sciences, University of California, 5200 N. Lake Road, Merced, CA, 95343, USA. fjia3@ucmerced.edu.

Behavior Research Methods
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Summary
This summary is machine-generated.

Robust estimators like MLM and MLMV improve structural equation model fit evaluation with missing, nonnormal data. Pooling strategies D4 and D3 offer better accuracy and lower failure rates for fit indices like RMSEA and CFI.

Keywords:
CFIMultiple ImputationPooling StrategiesRMSEARobust Fit Indices

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Evaluating structural equation model (SEM) fit with missing, nonnormal data is complex.
  • Multiple imputation (MI) is often used, but requires careful handling of model fit indices.
  • Robust estimators and pooling strategies are needed for accurate SEM fit assessment.

Purpose of the Study:

  • To investigate the performance of robust estimators (MLR, MLM, MLMV) and MI pooling strategies (D2, D3, D4 extensions) for SEM fit indices.
  • To compare the accuracy of Type I error rates and practical fit indices (RMSEA, CFI) under various missing data conditions.
  • To assess the impact of nonnormal and missing data on robust SEM fit estimation.

Main Methods:

  • A comprehensive simulation study was conducted.
  • Evaluated combinations of Maximum Likelihood with Robust standard errors (MLR, MLM, MLMV) and MI pooling strategies (D2, D3, D4 extensions).
  • Assessed Root Mean Squared Error of Approximation (RMSEA) and Comparative Fit Index (CFI) performance.

Main Results:

  • MLM and MLMV provided more accurate Type I error rates than MLR with minimal differences in practical fit indices.
  • Pooling strategies D4 and D3 extensions showed superior Type I error rates and lower failure rates compared to D2.
  • Robust CFI estimates were less affected than RMSEA under missing completely at random (MCAR) and missing at random (MAR) conditions, excluding long-tailed distributions.

Conclusions:

  • MLM and MLMV are recommended for SEM with missing, nonnormal data due to better Type I error control.
  • Pooling strategies D4 and D3 extensions are preferable for improved accuracy and reduced failure rates in fit index estimation.
  • Robust CFI may offer more stable estimates than RMSEA under certain missing data scenarios, but caution is advised.