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Measures of Fit
where and d are the discrepancy and the degrees of freedom for the model being
evaluated, and and are the discrepancy and the degrees of freedom for the
baseline model.
The RFI is obtained from the NFI by substituting F / d for F. RFI values close to 1
indicate a very good fit.
Note: Use the \rfi text macro to display the relative fit index value in the output path
diagram.
IFI
Bollen’s (1989b) incremental fit index (IFI) is given by:
where and d are the discrepancy and the degrees of freedom for the model being
evaluated, and and are the discrepancy and the degrees of freedom for the
baseline model. IFI values close to 1 indicate a very good fit.
Note: Use the \ifi text macro to display the incremental fit index value in the output path
diagram.
TLI
The Tucker-Lewis coefficient (ρ
2
in the notation of Bollen, 1989b) was discussed by
Bentler and Bonett (1980) in the context of analysis of moment structures and is also
known as the Bentler-Bonett non-normed fit index (NNFI).
The typical range for TLI lies between 0 and 1, but it is not limited to that range. TLI
values close to 1 indicate a very good fit.
Note: Use the \tli text macro to display the value of the Tucker-Lewis index in the
output path diagram.
C
ˆ
C
ˆ
b
d
b
dC
CC
b
b
−
−
=Δ=
ˆ
ˆˆ
IFI
2
C
ˆ
C
ˆ
b
d
b
1
TLI
ˆ
ˆ
ˆ
2
−
−
==
b
b
b
b
d
C
d
C
d
C
ρ