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Re: negative values of Mallows Cp

To: mtexeira@agro.uba.ar
Subject: Re: negative values of Mallows Cp
From: Prof Brian Ripley <ripley@stats.ox.ac.uk>
Date: Wed, 17 Aug 2005 05:58:41 +0100 (BST)
Cc: "'s-news@lists.biostat.wustl.edu'" <s-news@lists.biostat.wustl.edu>
In-reply-to: <1124188147.4301bff35a561@webmail3.agro.uba.ar>
References: <1124188147.4301bff35a561@webmail3.agro.uba.ar>
On Tue, 16 Aug 2005 mtexeira@agro.uba.ar wrote:

It makes sense to obtain negative values of Mallows Cp when running
leaps function ?

Yes.  Mallows' C_p is usually (but not always) defined as

        RSS/sigma^2 + 2p - n

and the expected value of the first term is n-p, so the expected value is p. Thus an unusually good fit will result in negative values, for example if the data actually fitted the model exactly the value would be 2p-n and that would be negative for p < n/2.

The comments in the help file are consistent with this definition.

--
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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