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The following fit indices were used: the comparative fit index (CFI; Bender, 1990), the root mean square error of approximation (RMSEA; Steiger, 1990), and the standardized root mean square residual.
Therefore, several disparate indices were used, as suggested by Tanaka (1993) to converge on an overall assessment, including the Root Mean Squared Error of Approximation (RMSEA) as discussed by Steiger (1990), Non-Normed Fit Index (Bentler & Bonett, 1980), Incremental Fit Index (Bollen, 1989), Comparative Fit Index (Bentler, 1990), and Goodness-of-Fit Index (Joreskog & Sorbom, 1981).
how much better the model fits compared to a baseline model, usually the independence model' (Joreskog, Sorbom 1993: 125), and this is assessed using the Non-Formed Fit Index (NNFI) and the Comparative Fit Index (CFI).
If values of [chi square]/degree of freedom ([chi square]/df), goodness-of-fit index (GFI), comparative fit index (CFI), and root mean square error of approximation (RMSEA) exceed their recommended levels, then constructs are valid (Joreskog and Sorbom 1993).
These indices include [chi square], the goodness-of-fit index (GFI), the adjusted goodness-of-fit index (AGFI), the comparative fit index (CFI), the root mean squared residual (RMSR), the root mean square error of approximation (RMSEA), the normed fit index (NFI), the non-normed fit index or Tucker Lewis index (NNFI) and the parsimonious fit index (PNFI).
Finally, comparative fit statistics assess the fit of the model specified with a null model--typically one where the covariances among all indicators are fixed to zero (variances are not constrained; Brown, 2006), with the most popular being the comparative fit index (CFI).
In performing the current analyses, six statistics reflecting fit were reported: the chi-square test statistic; the ratio of chi-square statistic to degrees of freedom; the root mean square error of approximation; the Tucker Lewis Index, also known as the Non Normed Fit Index; Weighted Root Mean Square Residual; and the Comparative Fit Index as appropriate.
The resulting Comparative Fit Index (CFI) is equal to the discrepancy function adjusted for sample size and usually ranges from 0 to 1, with a larger indicating better value fit.