exists between the two groups), Multi-group Structural Equation Modeling
(MSEM) was applied. When the theory underlying the model indicates that
a moderating relationship among predictors may vary by specific population
subgroups, such as the two diabetes groups, MSEM is preferable. A
single
χ
2
goodness-of-fit statistic evaluates a set of complex models—one for
each group. To validate the usual assumptions that groups are equivalent,
sub-samples are required to have identical estimates for all parameters (i.e.
a “fully constrained” model). Differences among the groups can be evaluated
for their appropriateness by “freeing” special parameters or allowing
the groups to vary.
The theoretical model is separately applied to each subgroup and then the
invariance analyses are conducted. Before the invariance models can be
estimated, it must be established that the model without any invariances (i.e.
a model that is different in each group) is “acceptable”. This model can be
used as a basis of assessment of more constrained models. The constraints
are placed in a sequence of nested models. To compare the models, the
χ
2
difference test and the Tucker-Lewis index can be used to test the equality
constraints (Marsh, Hau, & Wen, 2004; Kenny, 2005). If the difference
between the
χ
2
-statistics is not statistically significant then the statistical
evidence points toward no cross-group differences between the constrained
parameters (precondition for testing Research Objective 2). If the
χ
2
difference
is statistically significant, then the evidence of cross-group inequality
exists. The Tucker-Lewis Index estimates the models for the groups separately
and sums the
χ
2
s and the degrees of freedom. Differences in the TLI
up to .05 are considered trivial in practical terms. For the test of significant
paths and significant differences across the subgroups,
p
≤
.10 was used
because unidirectional hypotheses were stated.
To complete
Research Objective 3
(i.e. determine the explained variance and
compare the strength of regression paths of the SCT constructs in predicting
PA for both diabetes type models; our main study objective), the factor
interrelation equivalence model was examined to determine if there were
significantly different regression paths for the two diabetes groups. This was
done in order to examine the regression paths unconstrained for each of the
two diabetes groups, and to examine the explained variance of goals and
behavior for each group. The analyses were conducted to test a longitudinal
model (baseline social-cognitive measures and the 6-month PA measure).
SEM was performed using AMOS 4.01 employing the AMOS Graphics.
To test whether the path coefficients were significantly different, we
employed AMOS Pairwise Parameter Comparison. We employed the Full
Information-Maximum Likelihood Model (FIML) to impute and examine
the effects of the 6-month study dropouts; however, an almost identical
pattern was revealed between the imputed and non-imputed models. Thus
imputed models are not reported in this paper.