Bootstrapping Goodness-of-Fit Measures in Structural Equation Models

1992/11/01 by Kenneth A. Bollen, Robert A. Stine · 1,789 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #Bootstrapping (finance) #Computer science #Econometrics #Goodness of fit #LISREL #Mathematics #Psychometric Methodologies and Testing #Resampling #Statistic #Statistical hypothesis testing #Statistical model #Statistics #Structural equation modeling

paper · doi:10.1177/0049124192021002004

published in Sociological Methods & Research 21(2), 205-229 (SAGE Publishing)

openalex publication_date 1992/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Assessing overall fit is a topic of keen interest to structural equation modelers, yet measuring goodness of fit has been hampered by several factors. First, the assumptions that underlie the chi-square tests of model fit often are violated. Second, many fit measures (e.g., Bentler and Bonett's [1980] normed fit index) have unknown statistical distributions so that hypothesis testing, confidence intervals, or comparisons of significant differences in these fit indices are not possible. Finally, modelers have little knowledge about the distribution and behavior of the fit measures for misspecified models or for nonnested models. Given this situation, bootstrapping techniques would appear to be an ideal means to tackle these problems. Indeed, Bentler's (1989) EQS 3.0 and Jöreskog and Sörbom's (forthcoming) LISREL 8 have bootstrap resampling options to bootstrap fit indices. In this article the authors (a) demonstrate that the usual bootstrapping methods will fail when applied to the original data, (b) explain why this occurs, and, (c) propose a modified bootstrap method for the chi-square test statistic for model fit. They include simulated and empirical examples to illustrate their results.

Cited by

• Pitfalls of hypothesis tests and model selection on bootstrap samples: Causes and consequences in biometrical applications
• Direct Discrepancy Dynamic Fit Index Cutoffs for Arbitrary Covariance Structure Models
• Mental Health of Lesbian, Gay, and Bisexual Youth and Young Adults: Differential Effects of Age, Gender, Religiosity, and Sexual Orientation
• Eight Myths About Causality and Structural Equation Models
• Using an Adapted Job Demands–Resources Model to Examine the Use of Legal, Prescription, and Illegal Drugs for Cognitive Enhancement in the Working Population in Germany
• The adolescent Internet Adaptability Scale: Development and psychometric properties
• Precluding Interpretational Confounding in Factor Analysis with a Covariate or Outcome via Measurement and Uncertainty Preserving Parametric Modeling
• Translation of scales in cross‐cultural research: issues and techniques
• New testing procedures for Structural Equation Modeling
• A critical evaluation of alternative methods and paradigms for conducting mediation analysis in operations management research
• Exploring the performance implications of precarious work
• When disgust leads to dysphoria: A three-wave longitudinal study assessing the temporal relationship between self-disgust and depressive symptoms
• The correlation space of Gaussian latent tree models and model selection without fitting
• Examining Structural Relationships among Brand Experience, Existential Authenticity, and Place Attachment in Slow Tourism Destinations
• The body unbound: Vestibular–motor hallucinations and out-of-body experiences
• Are business users social? A design experiment exploring information sharing in enterprise social systems
• Reliability and validity of age band 1 of the Movement Assessment Battery for Children – Second Edition
• 5. Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data

Related

• Applying the Bollen-Stine Bootstrap for Goodness-of-Fit Measures to Structural Equation Models with Missing Data
• New testing procedures for Structural Equation Modeling
• Sample Fit Reliability
• Alternative Ways of Assessing Model Fit
• Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics