hypothesised model is then established by measuring the improvement in model
fit (over the null model) brought about by the specification of multi-item
constructs which explain the inter-item correlations that do exist in the sample
data when these are analysed according to the hypothesised model.
Parsimony fit indices are used to determine the optimal model from a number of
competing models. The fit of each model is calculated relative to its complexity.
Parsimony fit measures improve as (i) model fit improves and (ii) model
complexity (number of estimated parameter paths) is reduced. The rationale for
parsimony fit indices is that, since more complex models are expected to fit the
data better, there should be some model fit measures that account for model
complexity. These indices are not appropriate for assessing the fit of a single
model, but are used to compare the fit of two or more models with varying levels
of complexity.
Model chi-square tests the hypothesis that the sample covariance matrix (i.e.
the covariance matrix derived from the collected data) is not significantly different
from the covariance matrix implied by the theoretical model. Because the
objective of SEM is to establish a model which concurs (closely) with empirical
observations, the researcher is seeking a non-significant (i.e. ≥0.05) p value from
the chi-square test. Model chi-square has come under criticism (see e.g:
Jöreskog 1969; Bentler and Bonett 1980), however, on the basis that the chi-
square is so sensitive to sample size that even good-fitting models can be
rejected when sample sizes exceed around 200 (Schumaker and Lomax 2004:
100). Nevertheless, chi-square offers a useful comparison measure for
hierarchical models evaluated with the same data and it is included in the formula
for many of the alternative fit measures. For these reasons it is usually included
in SEM model assessments (Kline 2005: 137).
RMSEA (root mean square error of approximation) was developed by (Steiger
and Lind 1980) and belongs within the family of absolute fit indexes. The
calculation of the RMSEA is based on a non-central chi-square distribution (as
opposed to the central chi-square distribution used in the model chi-square test).
In practical terms, this means that the RMSEA does not assume that the
researcher’s model fits the observed data perfectly. The RMSEA value provides
an indication of the degree of misspecification of the researcher’s model, with
lower values indicating better fit. Hair et al. (2006: 748) note that RMSEA values
of <0.10 are typically achieved for most acceptable models; elsewhere, Browne