AICc adjusted or corrected Akaike information criterion

[JP Montagne]

Does STATA calculate AICc, and how do I do it? I am comparing models run with meqrlogit for one question, and glm for another. I have compared AIC between models with estat ic, however I would like to use AICc. Is there an option to do that in STATA?

Thank you.

[Julia Jones]

Hello Statalisters,

I am using Stata IC 16 to estimate a discrete choice model using the user written command mixlogit. I would like to evaluate different distributions of the random parameters (eg normal, lognormal, triangular, uniform) using the AIC, BIC and CAIC (same as AICc) criterion. I have found instructions for generating the AIC and BIC criterion using the estat command, but I have not found instructions for generating the CAIC criterion, which is also referred to as Bozdogan's Criterion, Consistent or Corrected AIC.

Arne Risa Hole examines the CAIC criterion to select the preferred number of classes for a latent class model in his 2013 guide, "Mixed Logit Modeling in Stata: An Overview". This overview does not provide guidance on how to generate CAIC for mixed logit models, as I would like to do. Like JP, I've searched everywhere for code or instructions, but still haven't had success.

Here is Dr. Hole's code for reference:

forvalues c = 2/10{
quietly lclogit y price contract local wknown tod seasonal, ///

id(pid) group(gid) nclass(`c')
matrix b = e(b)
matrix ic = nullmat(ic) \ `e(nclasses)', `e(ll)', ///
`=colsof(b)', `e(aic)', `e(caic)', `e(bic)'

}

matrix colnames ic = "Classes" "LLF" "Nparam" "AIC" "CAIC" "BIC"

matlist ic, name(columns)

Any feedback would be greatly appreciated!

Best,

Julia Jones
Department of Natural Resources & the Environment
University of New Hampshire

[Jackson Monroe]

Hurvich and Tsai write,

Thus, AICc is the sum of AIC and an additional nonstochastic penalty term, 2(m + 1)(m +2)/(n - m -2).

So it seems like taking the log-likelihood from the output, multiplying by -2, then adding the number of parameters * 2, then adding the term given above should leave you with CAIC. Note that Hurvich and Tsai give m + 1 as the total number of parameters including an intercept, etc.

[Julia Jones]

Hi Jackson,

Thank you for your response and for the clarification on AICc! I am curious about calculating Bozdogan's Criterion CAIC, which is slightly different. CAIC has a stronger penalty than the AIC for overparametrized models - which also sets it apart from Hurvich and Tsai's AICc criterion. On another note - it appears that AICc varies directly with AIC. I would be adding the same value to each of my AIC estimates. In terms of deciding between models, this criterion doesn't seem to help me any more than AIC. Let me know what you think.