OK, I will try to detail my question:
1) I know deviance in WinBUGS=-2log(likelihood)=-2logL (cf: http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/dicpage.shtml#q1).
2) When running my models with WinBUGS, I'm able to obtain the deviance for each model:
Null model=> mean deviance=4012.59
First model with covariate => mean deviance=-198.78
Second model with covariate + effect.one => mean deviance=-497.17
3) With a frequentist approach, I know there is a deviance based R-square (Cameron et al 1996, Journal of Business and Economic Statistics) to give an estimation of the pourcentage of explained variability :
R2D=(logLmodel-logLnull)/(logLsaturated-logLnull).
4) Using WinBUGS, I would like to compute an index close to the R-square to give an estimation of the explained variability for each covariate/factors.
I thought I need the deviance of the saturated model but I can't manage to obtain it with WinBUGS.
Is my problem clearer?
Would you have any practical suggestion?
Thanks a lot for your help.
Regards,
Ghislain Vieilledent.
-----Message d'origine-----
De : David Lunn [mailto:[log in to unmask]]
Envoyé : jeudi 4 octobre 2007 13:13
À : Vieilledent Ghislain
Objet : Re: Deviance for a saturated model ?
Perhaps you are confusing the posterior mean deviance given by BUGS with
the *minimum* deviance given by a more classical technique?
Vieilledent Ghislain wrote:
>
> Dear WinBUGS users,
>
>
>
> I wonder *how parameterizing a WinBUG model to obtain the deviance for
> a saturated model.*
>
>
>
> I tried this for a model with a Gompertz function as mean:
>
>
>
> (Note: Number of observations=N)
>
>
>
> # MODEL 014: Gompertz model.
>
>
>
> model {
>
>
>
> for (n in 1 : N) {
>
> mu[n] <-log(K[n])-(log(K[n]/1.3)*exp(-r*x[n])) # Expression of
> the mean
>
> Y[n] ~ dnorm(mu[n],tau) # Y [n] : Response variable
>
> K[n]<-exp(a[n])
>
> a[n]~dnorm(0,1.0E-6)
>
> }
>
>
>
> r<-0.6
>
> tau<-1
>
>
>
> }
>
>
>
> With such a model I have as many parameters as observations but it
> gives me a positive deviance (5767) much more superior to the best
> model I was able to calibrate before (deviance=-661.90) ?
>
>
>
> Would you have any suggestion?
>
> Thanks for your help.
>
>
>
> Regards,
>
>
>
> Ghislain Vieilledent.
>
>
>
--
Dave Lunn
MRC Biostatistics Unit,
Institute of Public Health,
University Forvie Site,
Robinson Way,
Cambridge CB2 0SR
+44 (0)1223 330394
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