6.3 Data assumptions and software
Regarding data assumptions for SEM. Section 6.6.1 (below) describes in detail
how the choice of maximum likelihood (ML) estimation is driven by the
requirement to use a model estimation technique that provides diagnostic
information for the iterative development of models (in particular, the estimation
of modification indices to guide model modifications). The ML estimation method
assumes that data are continuous; because, however, a large proportion of
psychometric data are collected using attitudinal (Likert-type) scales that
generate ordinal-level data, a number of studies have been undertaken to
evaluate the performance of ML estimation techniques when applied using such
ordinal scaled data. Byrne (2001: 83; 2010: 148) cites a number of such studies
(Muthén and Kaplan 1985; Babakus et al. 1987; Bentler and Chou 1987; Atkinson
1988; West et al. 1995) which have demonstrated that where ordinal data
approximate a normal distribution and variables use four or more data points then
continuous methods (such as ML estimation) ‘...can be used with little need for
concern’ (Byrne 2001: 83, and see also Raykov and Marcolides 2006: 31 for a
similar assessment).
Regarding issues of distributional normality, both skewness and kurtosis can
influence the model fit diagnostics and parameter estimates in SEM analyses.
Byrne (2010: 330) and West et al. (1995: 56-57) note that it is not uncommon
for psychometric data being used in SEM analyses to depart from the normal
distribution. This is because responses to scaled data can often cluster around
one two scale points, thus creating deviations from normal kurtosis and possibly
also deviations from normal skewness.
In relation to model fit, West et al. (1995: 59) note that significant multivariate
non-normality can impact on model χ^2 (chi-square) values by biasing χ^2 upward,
resulting in the rejection of too many models that should have good fit (i.e. with
model χ^2 p>0.05). For model development this situation can give rise to models
being simplified (indicator variables being removed) beyond the point where good
fit might have been achieved.
In relation to parameter estimates, Byrne (2010: 103; 148-149) describes the
influence of skewness and kurtosis in some detail. Briefly, skewness typically has
an impact on the measurement of means while kurtosis has an influence on the
measurement of variances and covariances. Because the latter (variances and