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Measures of Fit
Note: Use the \bic text macro to display the value of the Bayes information criterion in
the output path diagram.
CAIC
Bozdogan’s (1987) CAIC (consistent AIC) is given by the formula
CAIC assigns a greater penalty to model complexity than either AIC or BCC but not as
great a penalty as does BIC. CAIC is reported only for the case of a single group where
means and intercepts are not explicit model parameters.
Note: Use the \caic text macro to display the value of the consistent AIC statistic in the
output path diagram.
ECVI
Except for a constant scale factor, ECVI is the same as AIC.
The columns labeled LO 90 and HI 90 give the lower limit and upper limit of a 90%
confidence interval on the population ECVI:
See also “AIC” on p. 605.
Note: Use the \ecvi text macro to display the value of the expected cross-validation
index in the output path diagram, \ecvilo to display its lower 90% confidence estimate,
and \ecvihi for its upper 90% confidence estimate.
()
(
)
1ln
ˆ
CAIC
1
++= NqC
()
n
q
F
n
2
ˆ
AIC
1
ECVI +==
n
qd
L
2
90 LO
+
+
=
δ
n
qd
U
2
90 HI
+
+
=
δ