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Appendix C
The GFI is given by
where is the minimum value of the discrepancy function defined in Appendix B and
is obtained by evaluating F with , g = 1, 2,...,G. An exception has to be
made for maximum likelihood estimation, since (D2) in Appendix B is not defined for
. For the purpose of computing GFI in the case of maximum likelihood
estimation, in Appendix B is calculated as
with , where is the maximum likelihood estimate of . GFI is
always less than or equal to 1. GFI = 1 indicates a perfect fit.
Note: Use the \gfi text macro to display the value of the goodness-of-fit index in the
output path diagram.
AGFI
The AGFI (adjusted goodness-of-fit index) takes into account the degrees of freedom
available for testing the model. It is given by
where
The AGFI is bounded above by 1, which indicates a perfect fit. It is not, however,
bounded below by 0, as the GFI is.
Note: Use the \agfi text macro to display the value of the adjusted GFI in the output
path diagram.
b
F
F
ˆ
ˆ
1GFI −=
F
ˆ
F
b
ˆ
Σ
g()
0=
Σ
g()
0=
f Σ
g()
S
g()
;()
() ()
()
() () ()
()
2
2
1
tr
⎥
⎦
⎤
⎢
⎣
⎡
Σ−=Σ
−
ggggg
f SKS;
1
K
g()
Σ
g()
γ
ˆ
ML
()=
γ
ˆ
ML
γ
()
d
d
b
GFI11AGFI −−=
()
∑
=
=
G
g
g
b
pd
1
*