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Home Statistical Analysis Interpretation of Confirmatory Factor Analysis Results

Interpretation of Confirmatory Factor Analysis Results

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Interpretation of Confirmatory Factor Analysis Results


Fit Indices – Brown (2006) recommends reporting at least one index from each category below:


A.     Absolute Fit – indices that evaluate how close the observed variance-covariance matrix is to the estimated matrix


1.      Chi-Square (χ2)

§         Desire a result that is not statistically significant (i.e., observed covariance matrix equal to estimated matrix)

§         Sensitive to sample size (large samples may result in significant χ2)

§         Sensitive to multivariate nonnormality of the data


2.      Standardized root mean square residual (SRMR)

§         Ranges from 0 – 1.0 (1.0 indicates perfect fit)

§         Recommend SRMR≤.08 (Hu & Bentler, 1999)


3.      Standardized Residuals

§          Not technically a fit index, but can provide information about closely the estimated matrix corresponds to the observed matrix (i.e., how well the data fits the model)

§         Desire standardized residuals closer to 0 (i.e., little or no difference between observed covariance matrix and estimated matrix)


B.    Parsimony Correction – “similar to absolute fit indices, but incorporate a penalty function for poor model parsimony” (Kalinowski, 2006, p. 13)


1.      Root Mean Square Error of Approximation (RMSEA)

§         Ranges from 0 - +∞

§         Recommend RMSEA≤.06 (Hu & Bentler, 1999; Thompson, 2004)


C.    Comparative Fit – evaluate the fit of the hypothesized model to null model (i.e., covariances = 0)


1.      Comparative Fit Index (CFI)

§         Ranges from 0 – 1 (1.0 indicates perfect fit)

§         Recommend CFI≥.95 (Hu & Bentler, 1999; Thompson, 2004)


2.      Tucker-Lewis Index (TLI)

§         Usually interpreted within the range of 0 – 1.0

§         Recommend TLI≥.95 (Hu & Bentler, 1999)


3.      Normed Fit Index (NFI)

§         Ranges from 0 – 1.0

§         Recommend NFI≥.95 (Thompson, 2004)





Brown, T.A. (2006). Confirmatory factor analysis for applied research. New York, NY: The Guildford Press.

Bryant, F.B., & Yarnold, P.R. (1995). Principal-components analysis and exploratory and confirmatory factor analysis. In L. Grimm & P. Yarnold (Eds.), Reading and understanding multivariate statistics (pp. 99-136). Washington, D.C.: American Psychological Association.

Gorsuch, R.L. (1983). Factor analysis (2nd ed.) Hillsdale, NY: Erlbaum.

Hu, L., & Bentler, P.M. (1999). Cutoff criteria for fit indices in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.

Kalinowski, K.E. (2006). Using structural equation modeling to conduct confirmatory factor analysis.

Schumacker, R.E., & Lomax, R.G. (2004). A beginner’s guide to structural equation modeling (2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.

Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington, D.C.: American Psychological Association.



Source: http://www.coe.unt.edu/cira/historical_papers/CFA%20Interpretation.doc   2008_10_8

Last Updated on Tuesday, 16 February 2010 17:14