[R] lme: null deviance, deviance due to the random effects, residual deviance

[Patrick Giraudoux]

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"         "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
>>
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