selecting which ones to employ presents something of challenge for researchers
(Kline 2005: 133-134). Kline goes on to describe how:
Because a single index reflects only a particular aspect of model fit, a
favorable value of that index does not by itself indicate good fit. This
is also why model fit is usually assessed based in part on the values of
more than one index. That is, there is no single “magic index” that
provides a gold standard for all models.
(Kline 2005: 134)Hooper et al. (2008: 56) reviewed the findings of Boomsma (2000) Hayduk et al.
(2007) and Hu and Bentler (1999) and came to the same conclusions as Kline
(2005: 134) in recommending that researchers use a combination of:
(i) the model chi-square (including its degrees of freedom and associated p
value);
(ii) the root mean square error of approximation (RMSEA; Steiger 1990)
(including its related 90 per cent confidence interval);
(iii) the Bentler comparative fit index (CFI; Bentler 1990); and
(iv) the standardised root mean square residual (SRMR).
In addition to these four fit indices recommended by Kline (2005), Hooper et al.
(2008: 56) suggest that researchers also utilise one of the parsimony fit indices
such as the PNFI for model comparisons.
Before describing each of the selected fit indices in greater detail, the three broad
categories of fit indices are introduced.
Absolute fit indices provide a direct measure of the accuracy with which the
researcher’s hypothesised model reproduces the observed data. These fit indices
are based on comparisons between the sample covariance matrix and the model-
implied covariance matrix.
Incremental (comparative) fit indices are model comparison fit indices. That is,
they assess the extent to which a hypothesised model fits in comparison with a
baseline model (also referred to as an independence or null model). The null
model assumes that none of the observed variables are correlated. Because there
are no correlations between any of the observed variables, no data reduction
(identification of common factors) can occur. The adequacy of fit of the