Interpreting Fit Indices in the CFA Table
There are some fit indices reported in the CFA table. Here is more information on how to interpret them. Note that it is generally recommended not to rely on a single measure when evaluating model fit, but to look at several indices.
- CFI (Comparative Fit Index) and Tucker-Lewis Index (TLI) should be close to or higher than .95 (Hu & Bentler, 1999), but sometimes values above .90 are also considered acceptable (Iacobucci, 2010).
- SRMR (Standardized Root Mean square Residual) indicates how poorly your model fits. This value should be below .08 to be considered acceptable, although some argue that using a cutoff value of .05 is better (Jaccard & Wan, 1996).
- RSMEA (Root Mean Square Error of Approximation) also indicates how poorly your model fits the data. This should be less than .06 but below .08 is also considered acceptable (Browne & Cudeck, 1993)
- The ratio of the chi-squared to degrees of freedom should be less than 3 (Iacobucci, 2010)
The table then compares the proposed model with nested models where two factors are combined into one, and a single-factor model, where all items load on the same factor. The latter is sometimes referred to as Harman's one factor model.
References
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). Beverly Hills, CA: Sage.
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.
Iacobucci, D. (2010). Structural equations modeling: Fit indices, sample size, and advanced topics. Journal of Consumer Psychology, 20, 90-98.
Jaccard, J., & Wan, C.K. (1996). LISREL approaches to interaction effects in multiple regression. Thousand Oaks, CA: Sage Publications.