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Adjusting Incremental Fit Indices for Nonnormality.

Patricia E Brosseau-Liard1, Victoria Savalei2

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Summary
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This study introduces a novel nonnormality correction for structural equation modeling fit indices, specifically the comparative fit index and Tucker-Lewis index. The proposed method enhances model fit assessment accuracy when data deviates from normality assumptions.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Structural equation modeling (SEM) relies on various fit indices to evaluate model adequacy.
  • Commonly used fit indices derived from normal theory maximum likelihood are sensitive to nonnormality in observed data.
  • This sensitivity can lead to inaccurate assessments of model fit in real-world applications.

Purpose of the Study:

  • To develop and present a nonnormality correction for two widely used incremental fit indices: the comparative fit index (CFI) and the Tucker-Lewis index (TLI).
  • To propose a correction method that modifies the sample estimate of fit indices without altering their population values.
  • To demonstrate the superiority of this approach over existing methods that adjust population values.

Main Methods:

  • A novel nonnormality correction was developed for the CFI and TLI.
  • The correction utilizes the Satorra-Bentler scaling constant to adjust the sample estimates.
  • A simulation study was conducted to evaluate the performance of the proposed correction under diverse conditions.

Main Results:

  • The proposed nonnormality correction effectively modifies the sample estimates of the CFI and TLI.
  • The correction demonstrated robust performance across various sample sizes, model types, and degrees of misspecification.
  • The simulation results support the efficacy of the Satorra-Bentler scaling constant approach for handling nonnormality.

Conclusions:

  • The presented nonnormality correction offers a superior method for assessing model fit in structural equation modeling when data is nonnormal.
  • This approach provides more accurate fit index estimates compared to methods that alter population values.
  • The correction is recommended for researchers seeking reliable model fit evaluations with nonnormal data.