Stepwise model selection using Generalized Akaike Information Criterion

Question

I run a series of models using gamlss stepGAIC() model selection. The problem that I have is that in gamlss, stepGAIC() uses AIC values to select the variables in the model. Since my sample size is considered small I probably need to use the AICc values to select the best model. I don’t know if I would be able to create models using AIC and select from those models the best based on AICc.

Answer 1

In general, you can't select "the best" model using stepwise regression. All statistics produced through stepwise model building have a nested chain of invisible/unstated "conditional on excluding X" or "conditional on including X" statements built into them with the result that:

• p-values are biased
• variances are biased
• parameter estimates are biased
• F statistics are biased
• false predictors are likely to be included
• true predictors are likely to be excluded

So, while you could use AIC as a stepwise model building, the consequences of doing so are unreliable and likely invalid model inferences.

Answer 2

AICc is given as:

$AICc = AIC + \frac{2k(k + 1)}{n - k + 1}$

where n is the sample size and k is the number of parameters being estimated. You could just create the multiple models you are interested in, then manually calculate the AICc.