Following the loose cross-validation, a baseline multi-group SEM analysis was
performed using the two split sample groups. This procedure estimates both
groups at the same time and calculates a set of overall model fit statistics based
on the estimates for both groups. This is apparent when we look at the degrees
of freedom for the baseline multi-group model where, in this example, there are
196 degrees of freedom which is exactly double the 98 degrees of freedom for the
original Model 5b. The fit statistics for the baseline multi-group model indicate a
satisfactory fit (this is a necessary pre-requisite for continuing the multi-group
analysis in SEM) and are as follows:
χ^2 = 210.523, d.f. = 196, sig = 0.227; RMSEA = 0.019; CFI = 0.993; SRMR =
0.0704; and Hoelter’s CN = 232The baseline model is also referred to as the unconstrained model, differentiating
it from the subsequent models in which the factor loadings, structural coefficients
and factor covariances are successively constrained to evaluate inter-group
equivalence. Table 7 - 33 describes the model fit statistics for the baseline and
successively constrained models.
Because each of the models demonstrates good overall fit, it is possible to move
on to the next stage of cross-sample validation where the successively
constrained models are compared and assessed using chi square difference tests.
Constrained Model 1 (CM1) is compared to the baseline model, Constrained Model
2 (CM2) is compared with CM1 and finally CM3 is compared with CM2.
Model specifications χ^2 d.f. p RMSEA CFI
Unconstrained (baseline) 210.523 196 .227 0.019 0.993
Factor loadings
constrained (CM1) 221.447^207 .234^ 0.018^
0.993
Structural Coefficients
constrained (CM2)
230.863 212 .178 0.021 0.990
Structural Covariances
constrained (CM3) 234 .591^215 .171^ 0.021^ 0.990^
Table 7-33 Model fit for the baseline and constrained models
The difference in the model chi-square value between successive models is
calculated by subtracting the smaller chi-square value of the less constrained
model from the larger chi-square of the more constrained model. The difference