# Stepwise model selection using Generalized Akaike Information Criterion

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.

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.

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.

• Thank you for your response. I already did that but my dilemma is that if I should use AICc for selecting the variables in my models rather than the default AIC used in the stepGAIC function in GAMLSS. – user36467 Dec 23 '13 at 14:07