1,224
Views
42
CrossRef citations to date
0
Altmetric
Original Articles

Using the Bollen-Stine Bootstrapping Method for Evaluating Approximate Fit Indices

&

REFERENCES

  • Barrett, P. (2007). Structural equation modeling: Adjudging model fit. Personality and Individual Differences, 42, 815–824.
  • Beauducel, A., & Wittmann, W. (2005). Simulation study on fit Indices in confirmatory factor analysis based on data with slightly distorted simple structure. Structural Equation Modeling, 12, 41–75.
  • Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238–246.
  • Bentler, P.M., & Bonett, D.G. (1980). Significance tests and goodness of fit in the analysis of covariance structures, Psychological Bulletin, 88, 588–606.
  • Bollen, K.A., & Stine, R.A. (1993). Bootstrapping goodness-of-fit measures in structural equation models. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 111–135). Newbury Park, CA: Sage.
  • Browne, M.W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.
  • Chen, F., Curran, P.J., Bollen, K.A., Kirby, J., & Paxton, P. (2008). An empirical evaluation of the use of fixed cutoff points in RMSEA test statistic in structural equation models. Sociological Methods & Research, 36, 462–494.
  • Child and Family Center. (2003). Early Steps Coder Impressions (ESCOIMP). Available from the Child and Family Center, 195 West 12th Avenue, Eugene, OR 97401.
  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
  • Curran, P.J., West, S.G., & Finch, J.F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16–29.
  • Dishion, T.J., Shaw, D., Connell, A., Gardner, F., Weaver, C., & Wilson, M. (2008). The Family Check-Up with high-risk indigent families: Preventing problem behavior by increasing parents’ positive behavior support in early childhood. Child Development, 79, 1395–1414.
  • Enders, C.K. (2002). Applying the Bollen-Stine bootstrap for goodness-of-fit measures to structural equation models with missing data. Multivariate Behavioral Research, 37, 359–377.
  • Enders, C.K. (2005). An SAS macro for implementing the modified Bollen-Stine bootstrap for missing data: Implementing the bootstrap using existing structural equation modeling software. Structural Equation Modeling, 12, 620–641.
  • Fan, X., & Sivo, S.A. (2005). Sensitivity of fit indices to misspecified structural or measurement model components: Rationale of the two-index strategy revisited. Structural Equation Modeling, 12, 343–367.
  • Holzinger, K.J., & Swineford, F.A. (1939). A study in factor analysis: The stability of a bi-factor solution. Supplementary Education Monographs, No. 48. Chicago, IL: University of Chicago.
  • Hu, L., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55.
  • Jöreskog, K.G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183–202.
  • Jöreskog, K.G., & Sörbom, D. (1981). LISREL V: Analysis of linear structural relationships by the method of maximum likelihood. Chicago, IL: National Educational Resources.
  • Lei, M., & Lomax, R.G. (2005). The effect of varying degrees of nonnormality in structural equation modeling. Structural Equation Modeling, 12, 1–27.
  • Marsh, H.W., Hau, K., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling, 11, 320–341.
  • Millsap, R.E. (2007). Structural equation modeling made difficult. Personality and Individual Differences, 42, 875–881.
  • Millsap, R.E. (2012). A simulation paradigm for evaluating model fit. In M. Edwards & R. MacCallum (Eds.), Current issues in the theory and application of latent variable models (pp. 165--182). New York, NY: Routledge.
  • Mulaik, S. (2007). There is a place for approximate fit in structural equation modeling. Personality and Individual Differences, 42, 883–891.
  • Muthén, L.K., & Muthén, B.O. (1998–2012). Mplus user's guide (7th ed.). Los Angeles, CA: Author.
  • Nevitt, J., & Hancock, G.R. (2000). Improving the root mean square error of approximation for nonnormal conditions in structural equation modeling. The Journal of Experimental Education, 68, 251–268.
  • Ory, D.T., & Mokhtarian, P.L. (2010). The impact of non-normality, sample size and estimation technique on goodness-of-fit measures in structural equation modeling: Evidence from ten empirical models of travel behavior. Quality & Quantity, 44, 427–445.
  • Pornprasertmanit, S., Miller, P., Schoemann, A., Quick, C., & Jorgensen, T. (2013). Manual for package “simsem.” Retrieved from http://www.simsem.org/
  • R Core Team. (2012). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0. . Retrieved from http://www.R-project.org/
  • Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. http://www.jstatsoft.org/v48/i02/
  • Satorra, A., & Saris, W.E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 83–90.
  • Savalei, V. (2012). The relationship between root mean square error of approximation and model misspecification in confirmatory factor analysis models. Educational and Psychological Measurement, 72, 910–932.
  • Savalei, V., & Yuan, K.-H. (2009). On the model-based bootstrap with missing data: Obtaining a p value for a test of exact fit. Multivariate Behavioral Research, 44, 741–763.
  • Steiger, J.H. (1989). EzPATH: A supplementary module for SYSTAT and SYGRAPH [Computer program manual]. Evanston, IL: Systat.
  • Tucker, L.R, & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 1–10.
  • Wang, L., Fan, X., & Wilson, V.L. (1996). Effects of nonnormal data on parameter estimates and fit indices for a model with latent and manifest variables: An empirical study. Structural Equation Modeling, 3, 228–247.
  • Yuan, K.H. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40, 115–148.
  • Yuan, K.H., & Bentler, P.M. (2000). Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data. In M.E. Sobel & M.P. Becker (Eds.), Sociological methodology 2000 (pp. 165–200). Washington, DC: American Sociological Association.
  • Yung, Y.F., & Bentler, P.M. (1996). Bootstrap techniques in analysis of mean and covariance structures. In G.A. Marcoulides & R.E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 195–226). Mahwah, NJ: Erlbaum.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.