in degrees of freedom between the two models is then used in combination with
the difference in chi-square value to calculate a chi-square probability value.
A non-significant (p ≥ 0.05) chi square p value signals equivalence of parameter
estimates across groups. The logic of this test is that:
the chi square value for the less-constrained model indicates the closeness of
fit of the sample covariance matrices for both groups compared to the model
implied covariance matrix
the more-constrained model then imposes a situation of no difference between
groups for the parameters that are constrained (fixed to zero) for both groups
where the change in chi square value is small enough to be non-statistically
significant, this indicates that the differences between groups for those
parameters in the less-constrained model were close to zero and, as a
consequence, we can conclude that those parameters are statistically
equivalent across the groups.
Table 7 - 34 shows that for each model iteration, the chi square difference p value
is ≥ 0.05. This finding shows that Model 5b demonstrates full metric invariance
(Hair et al. 2006: 825). Put another way, this means that it can be can concluded
that the factor loadings, structural path coefficients and structural covariances are
statistically equivalent across the random split-sample groups. This finding
indicates that the Model 5b is likely to cross-validate in an independent sample.
Assuming the unconstrained model to be correct:
Δ χ^2 Δ d.f. p
Factor loadings constrained (CM1) 10.923 11 0.450
Structural Coefficients constrained (CM2) 20.339 16 0.205
Structural Covariances constrained (CM3) 24.067 19 0.194
Assuming Model CM1 to be correct:
Structural Coefficients constrained (CM2) 9.416 5 0.094
Structural Covariances constrained (CM3) 13.144 8 0.107
Assuming Model CM2 to be correct:
Structural Covariances constrained (CM3) 3.728 3 0.292
Table 7-34 Chi-square difference tests for Model 5b validation
There was one noteworthy difference between the estimates for the two groups in
the unconstrained model. Specifically, three structural path coefficients were
found to be non-statistically significant. These were for the paths ML→JP (p =
0.111) and EPA→JP (p = 0.121) in Group 1 and in Group 2 ML→EPA (p = 0.062).