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In CFA and SEM, fit indices indicate how well a model fits the data
and whether there is sufficient evidence that the model should
or should not be rejected. It is known that most fit indices
are sensitive to different conditions (e.g., sample size, model
complexity, or model misspecification). The X2 statistic is
extremely sensitive to large sample size (Byrne, 2010; Kline,
2005; Vandenberg & Lance, 2000). Some goodness-of-fit indices
(e.g., Tucker-Lewis Index and Comparative Fit Index) are overly
sensitive to complex models, that is, those with more than three
factors or with hierarchical structure (Cheung & Rensvold, 2002).
The most popular index, the root mean square error of
approximation (RMSEA), is sensitive to complex models and
specification error (Fan & Sivo, 2007). In contrast, the standardized
root mean square residual (SRMR) and gamma hat have been
shown to be relatively resistant to the impact of large samples,
complex models, and model misspecification (Fan & Sivo, 2007).
Nonetheless, it is recommended that multiple fit indices are
reported when assessing model fit (Fan & Sivo, 2005; Hu & Bentler,
1999). In this study, the following values for the various fit indices
are used to test a model fit: the X2 package including X2, df, X2/df,
SRMR, RMSEA with 90% CI, CFI, and gamma hat. For the X2 package,
perfect fit occurs when X2 is roughly equal to its df and good fit is
inferred when the ratio of X2 to df has p>.05. When RMSEA and
SRMR are ??05 fit is good and when ??08, it is acceptable (Browne &
Cudeck, 1989; Byrne, 2010; Hu & Bentler, 1999). When the 90% CI
for RMSEA falls in the range from .050 to .080, fit is acceptable
(Kenny, 2008). For goodness-of-fit indicators, when CFI and gamma
hat are ??95, fit is good and when they are >.90, fit is acceptable
(Byrne, 2010; Hoyle, 1995).

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