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Table 3. Goodness-of-fit indices for the measurement model
χ
2
df
p-value
NFI
NNFI
CFI
GFI
AGFI
RMR
Group
Total
249.98
137
.0001
.94
.97
.97
.93
.90
.03
Male
201.63
137
.0001
.93
.97
.98
.91
.88
.03
Female
202.78
137
.0002
.88
.95
.96
.86
.81
.03
procedure proposed by Anderson and Gerbing
(1988). The first step involves developing an ef-
fective measurement model with confirmatory
factor analysis, while the second step analyzes
the structural model. Both SAS and AMOS are
adopted as the tools for analyzing the data for
reconfirmation.
MI (modification index) is the index for refer-
ence used to select indicator variables (Jöreskog
& Sorbom, 1986). Through repeated filtering,
some indicator variables have been removed. The
indicators retained in each model (total group,
male group, and female group) are identical. Ev-
ery construct in the final measurement models is
measured, using at least two indicator variables
as in Table 2. The overall goodness-of-fit indices
shown in Table 3 (chi-square/d.f. smaller than 2.0;
RMR smaller than 0.05; CFI, NNFI, CFI, GFI, and
AGFI greater than 0.9 except four values slightly
lower than 0.9) indicate that the fits of the three
models are all satisfactory.
Reliability can reflect the internal consistency
of the indicators measuring a given factor. As
shown in Table 2, reliabilities for all constructs
exceed 0.7 for all three models, satisfying the
general requirement of reliability for research
instruments.
validity can be assessed by reviewing the t tests
for the factor loadings (Hatcher, 1994). Here, for
all three models, all factor loadings for indicators
measuring the same construct are statistically
significant, showing that all indicators effectively
measure their corresponding construct (Anderson
& Gerbing, 1988). Hence, this supports conver-
gent validity.
Discriminant validity is achieved, if the cor-
relations between different constructs, measured
with their respective indicators, are relatively
weak. The chi-square difference test can be used to
assess the discriminant validity of two constructs
by calculating the difference of the chi-square
statistics for the constrained and unconstrained
measurement models (Hatcher, 1994). The unique
and critical advantage of the chi-square difference
test is that it allows for simultaneous pair-wise
comparisons (based on the Bonferroni method)
for the constructs. The constrained model is
identical to the unconstrained model, in which
all constructs are allowed to covary, except that
the correlation between the two constructs of
interest is fixed at 1.
Discriminant validity is demonstrated, if the
chi-square difference (with 1 df) is significant,
meaning that the model in which the two con-
structs are viewed as distinct (but correlated)
factors is superior. Since we need to test the
discriminant validity for every pair of five con-
structs, we should control the experiment-wise
error rate (the overall significance level). By using
the Bonferroni method under the overall 0.05 and
0.01 levels, the critical values of the chi-square
Convergent validity and
discriminant validity
Convergent validity is achieved, if different indi-
cators used to measure the same construct obtain
strongly correlated scores. In SEM, convergent
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