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Methodology 145
too large, but the researcher should carefully scrutinize any stan-
dardized residual exceeding |4.0| (below -4.0 or above 4.0) (Hair
et al. 2006) With regard to the SRMR values, Hu and Bentler
(1999 in Murovec et al. 2012) suggest that SRMR values of less
than 0.08 indicate an acceptable fit.
- RMSEA (Root Mean Square Error of Approximation) – another
measure that attempts to correct for the tendency of the χ2 go-
odness-of-fit test statistic to reject models with large samples or a
large number of observed variables. It differs from the RMSR in
that it has a known distribution. Thus, it better represents how
well a model fits a population, not just a sample used for estima-
tion. Lower RMSEA values indicate better fit; typically, “good”
RMSEA values are below 0.10 for most acceptable models (Hair
et al. 2009).
- NFI (Normed Fit Index) – the NFI is a ratio of the difference in
the χ2 value for the fitted model and a null model divided by the
χ2 value for the null model. It ranges between 0 and 1; a model
with perfect fit would produce an NFI of 1 (Hair et al. 2009).
- CFI (Comparative Fit Index) – the CFI is an incremental fit in-
dex that is an improved version of the normed fit index (NFI).
The CFI is normed so the values range between 0 and 1, with
higher values indicating better fit (Hair et al. 2009).
The ultimate goal of any of these fit indexes is to assist the researcher
in discriminating between acceptably and unacceptably specified models
(Hair et al. 2009). Academic journals are replete with SEM results citing
a 0.90 value on key indexes, such as the TFI, CFI, NFI and GFI, as indi-
cating an acceptable model (Hair et al. 2009). Hoyle and Panter (1995) sug-
gest that 0.90 stands as the agreed-upon cutoff for overall fit indexes (in
our case, pertaining to the NFI, NNFI and CFI). In general, 0.90 is the
“magic number” for good-fitting models (Hair et al. 2009). In addition,
Hair et al. (2009) stressed that more complex models with larger samples
should not be held to the same strict standards; thus, when samples are
large and the model contains a large number of measured variables and
parameter estimates, cutoff values of 0.95 on key goodness-of-fit measures
are unrealistic.
too large, but the researcher should carefully scrutinize any stan-
dardized residual exceeding |4.0| (below -4.0 or above 4.0) (Hair
et al. 2006) With regard to the SRMR values, Hu and Bentler
(1999 in Murovec et al. 2012) suggest that SRMR values of less
than 0.08 indicate an acceptable fit.
- RMSEA (Root Mean Square Error of Approximation) – another
measure that attempts to correct for the tendency of the χ2 go-
odness-of-fit test statistic to reject models with large samples or a
large number of observed variables. It differs from the RMSR in
that it has a known distribution. Thus, it better represents how
well a model fits a population, not just a sample used for estima-
tion. Lower RMSEA values indicate better fit; typically, “good”
RMSEA values are below 0.10 for most acceptable models (Hair
et al. 2009).
- NFI (Normed Fit Index) – the NFI is a ratio of the difference in
the χ2 value for the fitted model and a null model divided by the
χ2 value for the null model. It ranges between 0 and 1; a model
with perfect fit would produce an NFI of 1 (Hair et al. 2009).
- CFI (Comparative Fit Index) – the CFI is an incremental fit in-
dex that is an improved version of the normed fit index (NFI).
The CFI is normed so the values range between 0 and 1, with
higher values indicating better fit (Hair et al. 2009).
The ultimate goal of any of these fit indexes is to assist the researcher
in discriminating between acceptably and unacceptably specified models
(Hair et al. 2009). Academic journals are replete with SEM results citing
a 0.90 value on key indexes, such as the TFI, CFI, NFI and GFI, as indi-
cating an acceptable model (Hair et al. 2009). Hoyle and Panter (1995) sug-
gest that 0.90 stands as the agreed-upon cutoff for overall fit indexes (in
our case, pertaining to the NFI, NNFI and CFI). In general, 0.90 is the
“magic number” for good-fitting models (Hair et al. 2009). In addition,
Hair et al. (2009) stressed that more complex models with larger samples
should not be held to the same strict standards; thus, when samples are
large and the model contains a large number of measured variables and
parameter estimates, cutoff values of 0.95 on key goodness-of-fit measures
are unrealistic.
