Measurement Invariance

Invariance is given if RMSEA value is less than .08 and CFI and TFI values are higher than .90 (> .95 even better) (Byrne, 2008; Hu & Bentler, 1999; MacCallum, Browne, & Sugawara, 1996).

Considering the χ2 difference test’s sensitivity to sample size when comparing model fit, we follow Chen’s (31) model-comparison-specific recommended cutoff values: metric vs. configural, Δ*CFI < .010, Δ*SRMR < .030, Δ*RMSEA < .015; scalar vs. metric, Δ*CFI < .010, Δ*SRMR < .010, Δ*RMSEA < .015. As noted above, the asterisk before the fit index name denotes that the index is based on the robust chi-square, as produced using the robust estimation method in Mplus

Chen FF (2007) Sensitivity of goodness of fit indexes to lack of measurement invariance. Struct Equ Model. doi:10.1080/10705510701301834.

Invariance is given if values are equal to or smaller than -.01, as suggested by Cheung and Rensvold (2002).

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological methods, 1(2), 130.

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.

Byrne, B. M. (2008). Testing for multigroup equivalence of a measuring instrument: A walk through the process. Psicothema, 20, 872–882.