7.2.3 Measurement model estimation
Following the discussion in Section 6.3, the measurement model (and the
subsequent structural model) is estimated using the Maximum Likelihood (ML)
estimation method.
As described in Sections 6.3 and 6.6.2, and reported in Appendix II, none of the
measured variables for this research violated the bounds of 2 for univariate
skewness, or 7 for univariate kurtosis noted by Curran et al. (1996: 26). As with
all of the structural equation models in this research, multivariate normality is
assessed for the optimal measurement and structural regression model
specifications. Details of multivariate normality for the data used to estimate
Model 1 are described in Sections 7.2.10 (measurement model) and 7.3
(structural regression model) and are fully reported along with the corresponding
bootstrapped estimates in Appendix IV.
7.2.4 Measurement model testing
Procedures for assessment of model fit fall into two broad categories: (a)
assessments of construct validity (how well the indicators variables measure the
constructs they are intended to); and (b) overall assessments of model fit. Model
fit reflects the extent to which the relationships proposed in the theoretical model
can actually be observed in the collected data and is measured using a
combination of individual fit indices.
It is not uncommon for the initially specified model to fit the data rather poorly
(see e.g. Kline 2005: 185) – the assessment of model fit being made according to
a number of fit indices (see Section 7.2.6 below). Typically, then, following an
assessment of unsatisfactory model fit, the measurement model is respecified by
examining various measures of construct validity (Section 7.2.5 below).
Identifying poorly performing indicator variables allows these variables to be
removed from the model. As these poorly performing indicators are removed, it
is usual to see improvements in both construct validity and overall model fit. It
is, of course, important that researchers carefully report model modifications and
that any changes made are done so with consideration for, and reference to, the
theoretical implications of these changes (Boomsma 2000: 475).