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Example 25
Now that the Structural weights model fits the data, it can be asked whether the
Structural intercepts model fits significantly worse. Assuming the Structural weights
model to be correct:
The Structural intercepts model does fit significantly worse than the Structural weights
model. When the intercept in the equation for predicting post_verbal is required to be
constant across groups, the chi-square statistic increases by 51.12 while degrees of
freedom increases by only 1. That is, the intercept for the experimental group differs
significantly from the intercept for the control group. The intercept for the
experimental group is estimated to be 3.627.
Recalling that the intercept for the control group was fixed at 0, it is estimated that the
treatment increases post_verbal scores by 3.63 with pre_verbal held constant.
The results obtained in the present example are identical to the results of Example
16. The Structural weights model is the same as Model D in Example 16. The
Structural intercepts model is the same as Model E in Example 16.
Model NPAR CMIN DF P CMIN/DF
Measurement intercepts 24 2.797 4 0.59 0.699
Structural weights 23 3.976 5 0.55 0.795
Structural intercepts 22 55.094 6 0.00 9.182
Structural means 21 63.792 7 0.00 9.113
Structural covariances 20 69.494 8 0.00 8.687
Structural residuals 19 83.194 9 0.00 9.244
Measurement residuals 14 93.197 14 0.00 6.657
Saturated model 28 0.000 0
Independence model 16 682.638 12 0.00 56.887
Model DF CMIN P
NFI
Delta-1
IFI
Delta-2
RFI
rho-1
TLI
rho2
Structural intercepts 1 51.118 0.000 0.075 0.075 0.147 0.150
Structural means 2 59.816 0.000 0.088 0.088 0.146 0.149
Structural covariances 3 65.518 0.000 0.096 0.097 0.139 0.141
Structural residuals 4 79.218 0.000 0.116 0.117 0.149 0.151
Measurement residuals 9 89.221 0.000 0.131 0.132 0.103 0.105
Estimate S.E. C.R. P Label
post_verbal 3.627 0.478 7.591 <0.001 j1_2
pre_syn 18.619 0.594 31.355 <0.001 i1_1
pre_opp 19.910 0.541 36.781 <0.001 i2_1
post_syn 20.383 0.535 38.066 <0.001 i3_1
post_opp 21.204 0.531 39.908 <0.001 i4_1