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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). 

deana desa posted on Tuesday, June 16, 2015  2:01 pm



Hi Mplus, May I know how/where to find BIC and DIC values from a BSEM analysis or how can I calculate it from Mplus BSEM output? 

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