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 Stefanie Hinkle posted on Wednesday, August 10, 2011 - 11:21 am
Hi.

I was wondering what formula mplus uses to calculate AIC. The text book that I have indicates that AIC is calcualted as model chi-square minus 2*df.

This seems very different from the AIC that I get from the Mplus output which is ~30,000.

Can you please explain the difference?
 Bengt O. Muthen posted on Wednesday, August 10, 2011 - 12:23 pm
Mplus defines AIC as in Akaike (1987),

AIC = -2logL + 2*r,

where r is the number of free parameters. A definition in terms of chi-square also exists and gives the same results as discussed in connection with BIC below.

Bengt O. Muthen posted on Tuesday, August 31, 2010 - 2:36 pm
Comparing models using the formula "chi2-df (ln(N))" is the same as using the Mplus BIC = -2logL + p*ln(N), where p is the number of parameters. Note that
chi2 = -2(logL_a - logL_b),
where a is a model nested within b. In the usual SEM case b is the totally unrestricted
model called H1. Note also that
df = p_b - p_a,
where p is the number of parameters.
So when you look at the difference between the BIC of two models using the formula
chi2-df (ln(N)) there is a canceling out of the terms -2logL_b and of the terms p_b*ln(N).
This means that BIC differences are the same for both formulas.
 Bengt O. Muthen posted on Wednesday, August 10, 2011 - 12:27 pm
P.S.

Akaike's 1987 Psychometrika article also explains the relationship between the two expressions of the AIC (see page 321).
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