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Appendix
E
Using Fit Measures to Rank Models
In general, it is hard to pick a fit measure because there are so many from which to
choose. The choice gets easier when the purpose of the fit measure is to compare
models to each other rather than to judge the merit of models by an absolute standard.
For example, it turns out that it does not matter whether you use RMSEA, RFI, or TLI
when rank ordering a collection of models. Each of those three measures depends on
and d only through , and each depends monotonically on . Thus, each
measure gives the same rank ordering of models. For this reason, the specification
search procedure reports only RMSEA.
The following fit measures depend on and d only through , and they depend
monotonically on . The specification search procedure reports only CFI as
representative of them all.
C
ˆ
C
ˆ
d⁄
C
ˆ
d⁄
RMSEA
C
ˆ
d–
nd
-------------
1
n
---
C
ˆ
d
---- 1–
⎝⎠
⎛⎞
==
RFI
ρ
1
1
C
ˆ
d⁄
C
ˆ
b
d
b
⁄
------------------–==
TLI
ρ
2
C
ˆ
b
d
b
------
C
ˆ
d
----–
C
ˆ
b
d
b
------ 1–
----------------==
C
ˆ
C
ˆ
d–
C
ˆ
d–