TABLE 1 Goodness-of-Fit Indices for Measurement and Structural Models
Model
χ
2
df
χ
2
/df
GFI
AGFI
NFI
Std.
RMSR
Measurement model
107.12
71
1.51
.93
.88
.91
.052
Structural model
108.51
72
1.50
.93
.88
.91
.050
Note. GFI
= goodness-of-fit index; AGFI = adjusted goodness-of-fit index; NFI = normed fit index; Std.
RMSR
= standardized root mean square residual.
within the recommended levels of 1.0 to 2.0 (Hair et al., 1998), indicat-
ing that the model fit is acceptable. In addition to the normed chi-square,
other fit indices (GFI
= .93; AGFI = .88; NFI = .91) fell around the desired
level of .90, revealing that the model is representative of the observed data
(Bentler & Bonett, 1980; Hair et al., 1998). Lastly, the standardized RMSR
(.05) suggested that the magnitude of the differences between the actual
and predicted covariance matrices are relatively small (Brown & Chdeck,
1993).
The overall chi-square for the structural model was 108.51 with 72 df
(p
< .0055). Table 1 shows no significant difference between the structural
model and the measurement model (chi-square difference
= 1.4, df = 1).
Because the measurement model allows all latent constructs to covary freely,
a comparison of the conceptual model to the measurement model is one
indication of adequate model fit. A lack of significant difference between
the two models implied that the data supported the theory. Other fit values
for the structural model were almost identical to those of the measurement
model (Normed chi-square
= 1.51; GFI = .93; AGFI = .88; NFI = .91;
standardized RMSR
= .05), satisfying the acceptable fit criteria mentioned
earlier.
Another method of evaluating the model fit is to examine the mod-
ification indices (chi-square reduction computed for each nonestimated
relationship). The modification indices suggested that the proposed model
fit could be improved by freeing additional correlations among measure-
ment errors. However, because those relationships could not be justified
theoretically, no changes were made to the model (Joreskog, 1993).
Parameter Estimates
The significance of the parameter estimates was judged using t values. The
critical t values are 1.96 for the 0.05 significance level and 2.58 for the 0.01
significance level. Table 2 presents the summary statistics of the measure-
ment model with LISREL estimates (factor loadings) and Table 3 presents
the path coefficients for the structural portion of the proposed model. An
examination of Table 2 reveals that each relationship between the latent
variables and their respective indicators are large, and all are statistically
significant (t
> 2.58, p < .01). All latent variables displayed acceptable
630
H. J. Kim
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