(iv) face validity – also known as content validity (Hair et al. 2006: 136), this is
the correspondence between the observed variables and the construct that is
intended to be measured by the latent factor.
The four sub-sections below describe the procedures that have been used to
assess these four aspects of construct validity: following this, Section 7.2.6
provides details of the procedures used to assess model fit. The measurement
model for Model 1 is then tested against these criteria (Section 7.2.7) following
which Section 7.2.8 to 7.2.10 describe the subsequent modifications to the
measurement model for Model 1.
Convergent validity
Factor loadings To proceed with the analysis, all of the indicators’ factor
loadings should be statistically significant (Hair et al., 2006: 777; Byrne, 2010:
68). Hair et al. (p. 796) note, however, that statistical significance alone does not
indicate that a particular item is contributing to the model adequately. They
suggest (2006: 777, 795) that factor loadings should preferably be above 0.7 and
at least 0.5. The rationale for these figures is that:
(i) the square of the standardised loading - known as the squared multiple
correlation (SMC) (Kline 2005-177), or commonality estimate (Schumaker and
Lomax 2004: 170) - represents how much of the item’s variance is accounted for
by the latent construct; and
(ii) therefore, a factor loading of 0.71, when squared, describes a situation where
0.5 (0.71*0.71) of the item variance is accounted for by the factor.
Hair et al. (2006: 796) write that low loading items are “candidates for deletion”
and suggest that the associated standardised residual covariances and
modification indices^11 are consulted to further evaluate the performance of these
11
The standardised residual covariance matrix provides information about the levels
of unmeasured (residual, or error) covariance between specific indicator variables.
That is, covariance not accounted for by the model. The modification indices estimate
the extent to which model fit would improve if the path between two indicator
variables’ error variances is freed (i.e. a connecting path between them is created).
There should be a good theoretical rationale for linking error variances in this way
(Kline 2005: 318).