From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Tue 02 May 2006 - 18:21:28 EST

Date: Tue 02 May 2006 - 18:21:28 EST

On Mon, 1 May 2006, Spencer Graves wrote:

> As far as I know, the term "deviance" has no standard definition. A

*> good, fairly common definition (I think) is that the deviance is "up to
**> [an additive] constant, minus twice the maximised log-likelihood. Where
**> sensible, the constant is chosen so that a saturated model has deviance
**> zero." ("http://finzi.psych.upenn.edu/R/library/gnm/html/gnm.html".)
**> Because of this "constant", the "the proportion of deviance 'explained'
**> by the model" in not a well defined concept. I found this definition
**> using RSiteSearch("deviance define"). However, even this definition is
**> not used consistently; it's not even used for 'deviance.lm', which I
**> discovered using methods("deviance") and methods("logLik") followed by
**> 'getAnywhere("deviance.lm"), etc.
*

It _is_ used by deviance.lm. In that case the saturated model has infinite log-likelihood, so it would not be sensible to choose an infinite constant and if you did the result for the saturated model would be NaN (= Inf - Inf).

> This is not a "trivial and stupid question". Instead, it's connected

*> to subtle issues in statistical methods, and this reply may contribute
**> more obfuscation than enlightenment. If you describe some more specific
**> application where you might want to use something like this and what you
**> are trying to achieve, you might get a more useful reply.
*

He may be looking for extensions/analogues of R^2, of which there exist several.

> hope this helps,

*> spencer graves
**>
**> Patrick Giraudoux wrote:
**>
**>> A maybe trivial and stupid question:
**>>
**>> In the case of a lm or glm fit, it is quite informative (to me) to have
**>> a look to the null deviance and the residual deviance of a model. This
**>> is generally provided in the print method or the summary, eg:
**>>
**>> Null Deviance: 658.8
**>> Residual Deviance: 507.3
**>>
**>> and (a bit simpled minded) I like to think that the proportion of
**>> deviance 'explained' by the model is (658.8-507.3)/658.8 = 23%
**>>
**>> In the case of lme models, is it possible and reasonable to try and get the:
**>> - null deviance
**>> - the total deviance due to the the random effect(s)
**>> - the residual deviance?
**>>
**>> With the idea that Null deviance = Fixed effects + Random Effects +
**>> Residuals
**>>
**>> If yes how to do it ? A lme object provides the following:
**>>
**>> > names(glm6)
**>> [1] "modelStruct" "dims" "contrasts" "coefficients"
**>> [5] "varFix" "sigma" "apVar" "logLik"
**>> [9] "numIter" "groups" "call" "method"
**>> [13] "fitted" "residuals" "fixDF" "family"
**>>
**>> so no $null.deviance and $deviance elements as in glm objects...
**>>
**>> I tried to find out an answer on R-help & Pineihro & Bates (2000).
**>> Partial success only:
**>>
**>> - null deviance: Response: possibly yes: see
**>> http://tolstoy.newcastle.edu.au/R/help/05/12/17796.html (Spencer
**>> Graves). The (null?) deviance is -2*logLik(mylme), but a personnal trial
**>> with some glm objects did not led to the same numbers that the one given
**>> by the print.glm method...
**>>
**>> - the deviance due to the the random effect(s). I was supposing that the
**>> coefficients given by ranef(mylme) may be an entry... but beyond this, I
**>> guess those coefficients must be weighed in some way... which is a far
**>> beyond my capacities in this matter...
**>>
**>> - residual deviance. I was supposing that it may be
**>> sum(residuals(mylme)^2). With some doubts as far as I feel that I am
**>> thinking sum of squares estimation in the context of likelihood and
**>> deviance estimations... So most likely irrelevant. Moreover, in the
**>> case I was exploring, this quantity is much larger than the null
**>> deviance computed as above...
**>>
**>> Any hint appreciated,
**>>
**>> Patrick Giraudoux
*

-- 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 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Tue May 02 18:26:05 2006

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