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Hi. I was wondering what formula mplus uses to calculate AIC. The text book that I have indicates that AIC is calcualted as model chisquare 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? 


Mplus defines AIC as in Akaike (1987), AIC = 2logL + 2*r, where r is the number of free parameters. A definition in terms of chisquare 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 "chi2df (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 chi2df (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. 


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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