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606
Appendix C
See also “ECVI” on p. 607.
Note: Use the \aic text macro to display the value of the Akaike information criterion
in the output path diagram.
BCC
The Browne-Cudeck (1989) criterion is given by
where if the
Emulisrel6 command has been used, or if it
has not.
BCC imposes a slightly greater penalty for model complexity than does AIC. BCC
is the only measure in this section that was developed specifically for analysis of
moment structures. Browne and Cudeck provided some empirical evidence suggesting
that BCC may be superior to more generally applicable measures. Arbuckle (in
preparation) gives an alternative justification for BCC and derives the above formula
for multiple groups.
See also “MECVI” on p. 608.
Note: Use the \bcc text macro to display the value of the Browne-Cudeck criterion in
the output path diagram.
BIC
The Bayes information criterion (Schwarz, 1978; Raftery, 1993) is given by the
formula
In comparison to the AIC, BCC, and CAIC, the BIC assigns a greater penalty to model
complexity and, therefore, has a greater tendency to pick parsimonious models. The
BIC is reported only for the case of a single group where means and intercepts are not
explicit model parameters.
()
() ()
()
() ()
() ()
()
∑
∑
=
=
+
−−
+
+=
G
g
gg
G
g
gg
gg
g
pp
pN
pp
b
qC
1
1
3
2
3
2
ˆ
BCC
b
g()
N
g()
1–=
b
g()
n
N
g()
N
---------
=
BIC C
ˆ
qN
1()
()ln+=