Re: [R] lme: null deviance, deviance due to the random effects, residual deviance
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). McCullagh Nelder (1989) would be the authorative reference, but the 1982 first edition manages to use 'deviance' in three separate senses on one page. In particular, what you are describing is the unscaled residual deviance. 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 contrastscoefficients [5] varFix sigmaapVarlogLik [9] numIter groups call method [13] fitted residualsfixDFfamily 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, [EMAIL PROTECTED] 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, UKFax: +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.html
Re: [R] lme: null deviance, deviance due to the random effects, residual deviance
Dear Prof. Ripley: comments in line Prof Brian Ripley wrote: On Mon, 1 May 2006, Spencer Graves wrote: snip McCullagh Nelder (1989) would be the authorative reference, but the 1982 first edition manages to use 'deviance' in three separate senses on one page. In particular, what you are describing is the unscaled residual deviance. Thanks: I'll review this carefully. Best Wishes, spencer graves __ 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.html
Re: [R] lme: null deviance, deviance due to the random effects, residual deviance
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. 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. 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 contrastscoefficients [5] varFix sigmaapVarlogLik [9] numIter groups call method [13] fitted residualsfixDFfamily 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 __ 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.html __ 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.html
Re: [R] lme: null deviance, deviance due to the random effects, residual deviance
I often want to know what proportion of the variation is being
contributed by different levels of random effects.
When the random effects are only intercepts, with no slopes, then you
can compute the intra-class correlation, which is the proportion of
the variation explained by the different levels of random effects,
using components from the output of VarCorr. I wrote a function that
extracts the components and computes them for such models:
varianceDetails - function(model) {
if (class(model) != lme)
stop(Input must be an lme!)
dimension - floor(dim(VarCorr(model))[1])/2
j - c(1:dimension) * 2
if (length(j) == 1)
j - 1
i - c(j, dim(VarCorr(model))[1])
variances - as.numeric(VarCorr(model)[i, 1])
mse - sum(variances)
icc - rep(0, length(j))
for (k in 1:length(j)) icc[k] - as.numeric(VarCorr(model)[j[k],
1])/mse
rmse - sqrt(mse)
list(icc = icc, rmse = rmse)
}
e.g.
require(nlme)
fm1 - lme(distance ~ age, data = Orthodont)
varianceDetails(fm1)
(Any feedback on that function is welcomed!)
This function uses the ReML estimates of the variance components (if
the fiting method is ReML!). When the random effects have slopes then
the problem is more tricky, as the proportion of variance explained
will depend on the predictor variables (see Goldstein et al. at
http://www.mlwin.com/team/materials/pvmm.pdf
). As a loose rule of thumb, I tend to take a method-of-moments type
of estimate of the standard deviation of the residuals at each level,
and compare those.
Thus,
sd(Orthodont$distance)
sd(residuals(fm1, level=0, type=response))
sd(residuals(fm1, level=1, type=response))
You can compute an ad-hoc icc from those components, if you are
comfortable averaging across the random effects. They will not be the
same as those from varianceDetails, above, because they're not based
on the ReML estimates of the variance components.
I suspect that fitting more complex random effects structures will
render these estimates invalid. I welcome any further comments on
these ideas.
Cheers
Andrew
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 contrastscoefficients
[5] varFix sigmaapVarlogLik
[9] numIter groups call method
[13] fitted residualsfixDFfamily
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
__
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--
Andrew Robinson
Department of Mathematics and StatisticsTel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599
Email: [EMAIL PROTECTED] http://www.ms.unimelb.edu.au
__
Re: [R] lme: null deviance, deviance due to the random effects, residual deviance
Andrew and Spencer, Thanks for your answers. I was feeling that moving from variance and least-square estimates to deviance and MLE or REML was the reason why I could not find easy equivalent estimates for the proportion of variation of a given effect to the total. Thus this was not a trivial issue... I will try and understand Andrew's function which will be helpful to make the things clearer in my mind. Your advice both are useful and drive people on the good track. All the best, Patrick Spencer Graves a écrit : 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. 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. 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 contrastscoefficients [5] varFix sigmaapVarlogLik [9] numIter groups call method [13] fitted residualsfixDFfamily 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 __ 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.html __ 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.html
[R] lme: null deviance, deviance due to the random effects, residual deviance
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 contrastscoefficients [5] varFix sigmaapVarlogLik [9] numIter groups call method [13] fitted residualsfixDFfamily 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 __ 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.html
