AIC and BIC formula for multiple logistic regression in survey data in Stata

Question

In the recent article, for fit models, we only use parameters: crude, adjusted odds ratio, and p-value. The model fit criterion other researchers usually used it is the likelihood ratio test, but another comment said that AIC and BIC are also acceptable.

My question is about the command of the Akaike information criterion (AIC) and Bayesian information criterion (BIC) issue for survey data.

Is there any command to count AIC and BIC in Stata for multiple logistic regression in survey data?

However, in one of reference show that "estat ic", for display information criteria both of AIC and BIC were not running for multiple logistic regression in survey data. (Williams, R. (2015). Analysing complex survey data: Some key issues to be aware of). Further, Stata does accept neither "estat" alone nor "estat ic" after "svy", and I could not find an "estat (svy)"command yet which would produce any of these statistics (respectively AIC/BIC for the ordered logit).

Also, I have find syntax and succeed executed the command to count AIC and BIC both in simple regression liner, and multiple regression liner for survey data even in simple logistic regression. However, the command is not running in multiple logistic regression for survey data which use (svy) syntax in Stata. Please advise.

Answer 1

The usual formulations of AIC and BIC don't work under survey sampling because the estimation isn't by maximum likelihood. For example, if you had the same data but from a population twice as big, the weights would be twice as big, and the $-2\log \hat L$ would be twice as big, but the penalty $2p$ or $p\log n$ would not be. The penalty needs modifying to take account of the weights and clustering (if there is clustering). That's different from AIC or BIC using precision weights, where you're still doing maximum likelihood estimation.

The theory for this has been worked out, but relatively recently, so it isn't implemented much. It's not in Stata.