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P. 143
Methodology 143
a priori model reproduces the sample data (Hu and Bentler 1995). Abso-
lute fit indexes are a direct measure of how well the model specified by the
researcher reproduces the observed data; they provide the most basic as-
sessment of how well a researcher’s theory fits the sample data (Hair et al.
2009). They do not explicitly compare the goodness-of-fit of a specified
model to any other model; rather, each model is evaluated independently
of other possible models (Hair et al. 2009). Absolute-fit measures (e.g., χ2
statistic, GFI, RMSR, SRMR, RMSEA etc.) only assess the overall good-
ness-of-fit for both the structural and measurement models collectively
and do not make any comparison to a specified null model (incremen-
tal fit measure) or adjust for the number of parameters in the estimated
model (parsimonious fit measure) (Hair et al. 2006). An incremental fit
index measures the proportionate improvement in fit by comparing a tar-
get model with a more restricted, nested baseline model (Hu and Bentler
1995). Incremental fit indexes differ from absolute fit indexes in that they
assess how well a specified model fits relative to some alternative baseline
model (Hair et al. 2009). The most common baseline model is referred
to as a null model, one that assumes all observed variables are uncorre-
lated (Hair et al. 2009). It implies that no data reduction could possibly
improve the model because it contains no multi-item factors, thus mak-
ing impossible any multi-item constructs or relationships between them
(Hair et al. 2009). Incremental fit indexes are: NFI, CFI, TLI, RNI (Hair
et al. 2009). Finally, the third group of indexes is designed specifically to
provide information about which model among a set of competing mod-
els is best, considering its fit relative to its complexity. A parsimony fit
measure (e.g. PR, PGFI, PNFI) is improved either by a better fit or by a
simpler model. In this case, a simpler model is one with fewer estimat-
ed parameter paths. Parsimony fit indexes are conceptually similar to the
notion of an adjusted R2 in the sense that they relate model fit to model
complexity. More complex models are expected to fit the data better. The
indexes are not useful in assessing the fit of a single model but are quite
useful in comparing the fit of two models when one is more complex that
the other (Hair et al. 2009).
There are three major problems involved in using fit indexes for eval-
uating goodness of fit: a) small sample bias, b) estimation effects and c)
effects of violation of normality and independence. The previously men-
tioned problems are a natural consequence of the fact that these index-
es typically are based on χ2 tests. As noted previously, these χ2 tests may
not perform adequately at all sample sizes; moreover, because the adequa-
cy of an χ2 statistic may depend on the particular assumptions it requires
a priori model reproduces the sample data (Hu and Bentler 1995). Abso-
lute fit indexes are a direct measure of how well the model specified by the
researcher reproduces the observed data; they provide the most basic as-
sessment of how well a researcher’s theory fits the sample data (Hair et al.
2009). They do not explicitly compare the goodness-of-fit of a specified
model to any other model; rather, each model is evaluated independently
of other possible models (Hair et al. 2009). Absolute-fit measures (e.g., χ2
statistic, GFI, RMSR, SRMR, RMSEA etc.) only assess the overall good-
ness-of-fit for both the structural and measurement models collectively
and do not make any comparison to a specified null model (incremen-
tal fit measure) or adjust for the number of parameters in the estimated
model (parsimonious fit measure) (Hair et al. 2006). An incremental fit
index measures the proportionate improvement in fit by comparing a tar-
get model with a more restricted, nested baseline model (Hu and Bentler
1995). Incremental fit indexes differ from absolute fit indexes in that they
assess how well a specified model fits relative to some alternative baseline
model (Hair et al. 2009). The most common baseline model is referred
to as a null model, one that assumes all observed variables are uncorre-
lated (Hair et al. 2009). It implies that no data reduction could possibly
improve the model because it contains no multi-item factors, thus mak-
ing impossible any multi-item constructs or relationships between them
(Hair et al. 2009). Incremental fit indexes are: NFI, CFI, TLI, RNI (Hair
et al. 2009). Finally, the third group of indexes is designed specifically to
provide information about which model among a set of competing mod-
els is best, considering its fit relative to its complexity. A parsimony fit
measure (e.g. PR, PGFI, PNFI) is improved either by a better fit or by a
simpler model. In this case, a simpler model is one with fewer estimat-
ed parameter paths. Parsimony fit indexes are conceptually similar to the
notion of an adjusted R2 in the sense that they relate model fit to model
complexity. More complex models are expected to fit the data better. The
indexes are not useful in assessing the fit of a single model but are quite
useful in comparing the fit of two models when one is more complex that
the other (Hair et al. 2009).
There are three major problems involved in using fit indexes for eval-
uating goodness of fit: a) small sample bias, b) estimation effects and c)
effects of violation of normality and independence. The previously men-
tioned problems are a natural consequence of the fact that these index-
es typically are based on χ2 tests. As noted previously, these χ2 tests may
not perform adequately at all sample sizes; moreover, because the adequa-
cy of an χ2 statistic may depend on the particular assumptions it requires
