covariance) are central to SEM analysis, problems with kurtosis are generally
regarded as being of greater importance.
Raykov and Marcolides (2006: 29) suggest that researchers first check univariate
normality and then multivariate normality. Curran et al. (1996) examined the
issue of distributional non-normality when estimating CFA models and found that
univariate skewness values of less than 2 and univariate kurtosis values of less
than 7 are acceptable (i.e. had no impact on parameter estimates and model fit
statistics). Those authors were, however, unable to determine at what point
multivariate non-normality becomes a problem. More recently, Bentler (2005,
cited in Byrne 2010: 104) has suggested that when Mardia’s coefficient for
multivariate non-normality (Mardia 1970) is greater than 5, then a departure from
multivariate normality is indicated. Elsewhere, Raykov and Marcolides (2006: 30)
and Hair et al. (2006: 743) have both cited a number of empirical studies
demonstrating that ML estimation is robust in the face of minor deviations from
normality.
For this research, none of the measured variables depart (or even approach
departing) from Curran et al.’s (1996: 26) bounds of 2 for univariate skewness or
7 for univariate kurtosis (Appendix II reports the univariate skewness and
kurtosis estimates for all of the observed variables). Accordingly, following the
arguments detailed by Byrne (2001: 83 and 2010: 148), ML estimation methods
are employed for this research.
Multivariate normality is measured using AMOS’s critical ratio (C.R) for
multivariate kurtosis which is equivalent to Mardia’s (1970) normalised estimate
of multivariate kurtosis (Byrne 2010: 104). Where an optimal model specification
demonstrates a multivariate kurtosis C.R. value greater than 5, the model is re-
estimated (following the procedure described by Byrne 2010: 329-352) using
AMOS’s bootstrap procedure for estimating models with multivariate non-normal
data. The bootstrap estimation procedure generates confidence intervals for each
estimated parameter allowing these to be checked for robustness to multivariate
non-normality as required. The relevant estimates for multivariate normality and
associated bootstrapped parameter estimates are reported in Appendix IV.
Structural equation modelling is undertaken using the IBM AMOS Version 18
software for SEM analysis and the data screening and other analyses are
undertaken using IBM SPSS Statistics Version 18.