Statistics of model comparison

[Caio Lucidius Naberezny Azevedo]

Hi all,

Which are the formulas used to calculate AIC, BIC, SABIC, AICc and DIC?

In addition, when using prior information for item parameters, is it possible to ask mirt to provide only the loglikelihoo instead of the logposterior?

Thanks a lot,

Best,

Caio

[Caio Lucidius Naberezny Azevedo]

To complement my question. I am aware about the general formulas I am not sure, however, how mirt calculate those statistics.

[Phil Chalmers]

Hi Caio,

Where are you hung up exactly? If you now the formula, then it should be clear how mirt computes these (they are just a combination of log-likelihood, #of parameters, and sample size).

Phil

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[Caio Lucidius Naberezny Azevedo]

Hi Phill,

Sorry if I was not clear. My question was toward that, sometimes, these formulas can differ (even slightly) from package to package (either by the signal of likelihood and/or by the penalty term). Concerning the statistics, from the EM frequentist approach, I supposed that they are:

AIC = -2loglik + 2p

BIC = -2loglik + p log(n)

AICc = AIC + 2p(p+1)/(n-p-1)

SABIC = -2loglik + p log((n+2)/24)

where n is the number of sujects and p is the number of parameters to be estimatted. Concering DIC, I usually consider it within an MCMC context so, I am not sure the exactly way to calcule it using only the punctual estimates provided by the EM bayesian approach.

Many thanks,

Caio

Phil

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[Phil Chalmers]

Hi Caio,

Fair enough, I've noticed similar trends in other software as well. The formula you've provided look to be what mirt uses. For DIC, the form is that of what is found in AIC, but with the log-posterior instead of the log-likelihood. HTH. 

Phil

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[Caio Lucidius Naberezny Azevedo]

Hi Phil,

Thank you very much. Understood.

All the best,

Caio