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Appendix C
CFI
The comparative fit index (CFI; Bentler, 1990) is given by
where , d, and NCP are the discrepancy, the degrees of freedom, and the
noncentrality parameter estimate for the model being evaluated, and , , and
are the discrepancy, the degrees of freedom, and the noncentrality parameter
estimate for the baseline model.
The CFI is identical to McDonald and Marsh’s (1990) relative noncentrality index
(RNI)
except that the CFI is truncated to fall in the range from 0 to 1. CFI values close to 1
indicate a very good fit.
Note: Use the \cfi text macro to display the value of the comparative fit index in the
output path diagram.
Parsimony Adjusted Measures
James, et al. (1982) suggested multiplying the NFI by a parsimony index so as to take
into account the number of degrees of freedom for testing both the model being
evaluated and the baseline model. Mulaik, et al. (1989) suggested applying the same
adjustment to the GFI. Amos also applies a parsimony adjustment to the CFI.
See also “PGFI” on p. 615.
()
()
b
bb
dC
dC
NCP
NCP
1
0,
ˆ
max
0,
ˆ
max
1CFI −=
−
−
−=
C
ˆ
C
ˆ
b
d
b
NCP
b
bb
dC
dC
−
−
−=
ˆ
ˆ
1RNI