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)

References

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