[R] Question about BIC of two different regression models? how should we compare two regression models?

[Patrick Breheny]

On 09/02/2011 11:26 AM, Prof Brian Ripley wrote:
>> This is wrong.  Hypothesis tests rely on nested models; information criteria
>> do not.
>
> Actually, this is off-topic on this list. But blanket statements are
> often themselves untrue: there are hypothesis tests of non-nested
> models (most famously due to Cox, 1961), and Akaike explicitly
> considered only nested models in his paper introducing AIC.
> Certainly criteria such as AIC and BIC (in the sense of Schwarz: there
> are several criteria of that name) can be used with non-nested models
> but are much sharper tools for nested models.

Good point; my remark was only meant to refer to the simple case of 
logistic regression in the original post, and certainly should not be 
construed as a blanket statement applying to all possible hypothesis 
tests of all possible models.

-- 
Patrick Breheny
Assistant Professor
Department of Biostatistics
Department of Statistics
University of Kentucky