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Equivalence Testing Based Fit Index: Standardized Root Mean Squared Residual.

Nataly Beribisky1, Robert A Cribbie1

  • 1Quantitative Methods Program, Department of Psychology, York University, Toronto, Canada.

Multivariate Behavioral Research
|August 18, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces equivalence-testing based fit tests for the standardized root mean squared residual (SRMR) in structural equation modeling (SEM). Certain new ESRMR tests effectively identify poor-fitting models and detect good-fitting ones.

Keywords:
Equivalence testingfit indicesnegligible effect testingstandardized root mean squared residualstructural equation modeling

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Quantitative Psychology

Background:

  • Standardized root mean squared residual (SRMR) is a common structural equation modeling (SEM) fit index.
  • Equivalence testing, a method for evaluating model fit, has not been previously applied to SRMR.

Purpose of the Study:

  • To propose and evaluate novel equivalence-testing based fit tests for SRMR (ESRMR).
  • To compare the performance of ESRMR tests against traditional SEM fit evaluation methods.

Main Methods:

  • Development of several ESRMR test variations with different equivalence bounds and confidence interval computations.
  • A Monte Carlo simulation study to compare ESRMR tests with existing fit indices.
  • An illustrative example using real data to demonstrate ESRMR application.

Main Results:

  • Certain ESRMR tests utilizing analytic confidence intervals demonstrated effectiveness.
  • These ESRMR tests accurately rejected poorly fitting models.
  • The tests showed good power in identifying well-fitting models.

Conclusions:

  • Equivalence-testing based fit tests for SRMR (ESRMR) offer a valuable addition to SEM model fit evaluation.
  • ESRMR tests should be reported alongside traditional fit indices for comprehensive model assessment.
  • The proposed ESRMR methods provide a robust approach to assessing model fit in SEM.