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Appendix
G
Rescaling of AIC, BCC, and BIC
The fit measures, AIC, BCC, and BIC, are defined in Appendix C. Each measure is of
the form , where k takes on the same value for all models. Small values are
good, reflecting a combination of good fit to the data (small ) and parsimony
(small q). The measures are used for comparing models to each other and not for
judging the merit of a single model.
The specification search procedure in Amos provides three ways of rescaling these
measures, which were illustrated in Examples 22 and 23. This appendix provides
formulas for the rescaled fit measures.
In what follows, let , , and be the fit values for model i.
Zero-Based Rescaling
Because AIC, BCC, and BIC are used only for comparing models to each other, with
smaller values being better than larger values, there is no harm in adding a constant,
as in:
C
ˆ
kq+
C
ˆ
AIC
i()
BCC
i()
BIC
i()
AIC
0
i()
AIC
i()
min
i
AIC
i()
[]–=
BCC
0
i()
BCC
i()
min
i
BCC
i()
[]–=
BIC
0
i()
BIC
i()
min
i
BIC
i()
[]–=