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.