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

Prof Brian Ripley ripley at stats.ox.ac.uk
Fri Sep 2 17:26:06 CEST 2011

On Fri, 2 Sep 2011, Patrick Breheny wrote:

> On 09/02/2011 08:48 AM, John Sorkin wrote:
>> I believe when using BIC one needs to compare nested models
> 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.

> -- 
> Patrick Breheny
> Assistant Professor
> Department of Biostatistics
> Department of Statistics
> University of Kentucky
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Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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