Yes, I think you are defintely right. And your results seem a more consistent with the mcmcglmm results reported by Jarrod Hadfield.
 
 
Sincerely,
 

Frédéric Gosselin 
Ingénieur-Chercheur 
Cemagref 
Domaine des Barres 
45 290 Nogent-sur-Vernisson 
FRANCE 

Tel: 02-38-95-03-58 
Fax: 02-38-95-03-59 

<http://www.cemagref.fr/les-contacts/les-pages-personnelles-professionnelles/gosselin-frederic>

 


________________________________

	De : aidan.m.keane@gmail.com [mailto:aidan.m.keane@gmail.com] De la part de Aidan Keane
	Envoyé : mercredi 10 novembre 2010 11:12
	À : Jarrod Hadfield
	Cc : Gosselin Frederic; r-sig-mixed-models@r-project.org; tiflo@csli.stanford.edu
	Objet : Re: [R-sig-ME] quasi-binomial family in lme4
	
	
	Is that just to do with the way the nesting has been specified?  If I fit

	gm3 <- lmer(incidence ~ period + (1 | herd/Id), family = poisson, data = cbppbis)

	or, safer,

	gm4 <- lmer(incidence ~ period + (1 | herd) + (1 | herd:Id), family = poisson, data = cbppbis)

	the herd:Id and Id estimates are not the same as one another (and identical for both specifications):

	> summary(gm3)
	Generalized linear mixed model fit by the Laplace approximation 
	Formula: incidence ~ period + (1 | herd/Id) 
	   Data: cbppbis 
	   AIC   BIC logLik deviance
	 102.2 114.4 -45.11    90.21
	Random effects:
	 Groups  Name        Variance   Std.Dev.  
	 Id:herd (Intercept) 5.9309e-01 7.7012e-01
	 herd    (Intercept) 9.4425e-16 3.0729e-08
	Number of obs: 56, groups: Id:herd, 56; herd, 15

	Fixed effects:
	            Estimate Std. Error z value Pr(>|z|)    
	(Intercept)   1.1129     0.2477   4.492 7.04e-06 ***
	period2      -1.1969     0.4185  -2.860 0.004233 ** 
	period3      -1.4223     0.4381  -3.246 0.001169 ** 
	period4      -2.0049     0.5292  -3.788 0.000152 ***
	---
	Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

	Correlation of Fixed Effects:
	        (Intr) perid2 perid3
	period2 -0.592              
	period3 -0.565  0.335       
	period4 -0.468  0.277  0.265
	> 

	> summary(gm4)
	Generalized linear mixed model fit by the Laplace approximation 
	Formula: incidence ~ period + (1 | herd) + (1 | herd:Id) 
	   Data: cbppbis 
	   AIC   BIC logLik deviance
	 102.2 114.4 -45.11    90.21
	Random effects:
	 Groups  Name        Variance   Std.Dev.  
	 herd:Id (Intercept) 5.9309e-01 7.7012e-01
	 herd    (Intercept) 9.4425e-16 3.0729e-08
	Number of obs: 56, groups: herd:Id, 56; herd, 15

	Fixed effects:
	            Estimate Std. Error z value Pr(>|z|)    
	(Intercept)   1.1129     0.2477   4.492 7.04e-06 ***
	period2      -1.1969     0.4185  -2.860 0.004233 ** 
	period3      -1.4223     0.4381  -3.246 0.001169 ** 
	period4      -2.0049     0.5292  -3.788 0.000152 ***
	---
	Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

	Correlation of Fixed Effects:
	        (Intr) perid2 perid3
	period2 -0.592              
	period3 -0.565  0.335       
	period4 -0.468  0.277  0.265
	> 

	Cheers,

	Aidan.



	On 10 November 2010 09:53, Jarrod Hadfield <j.hadfield@ed.ac.uk> wrote:
	

		Hi,
		
		It seems worrying to me that the Herd:Id estimate and the Id estimate are exactly the same. I get a (slightly) different estimate with version 0.999375-35 on Linux, but again the estimates are identical. MCMCglmm fitting the same model gives a very different answer.
		
		Cheers,
		
		Jarrod
		
		
		
		

			summary(gm2)
			

		Generalized linear mixed model fit by the Laplace approximation 

		Formula: incidence ~ period + (1 | Id/herd)
		  Data: cbpp
		
		  AIC   BIC logLik deviance
		 102.2 114.4 -45.11    90.21
		Random effects:
		 Groups  Name        Variance Std.Dev.
		
		 herd:Id (Intercept) 0.29654  0.54456
		 Id      (Intercept) 0.29654  0.54456 

		Number of obs: 56, groups: herd:Id, 56; Id, 56
		
		
		Fixed effects:
		           Estimate Std. Error z value Pr(>|z|)
		
		(Intercept)   1.1129     0.2477   4.492 7.04e-06 ***
		period2      -1.1969     0.4185  -2.860 0.004233 **
		period3      -1.4223     0.4381  -3.246 0.001169 **
		period4      -2.0049     0.5292  -3.788 0.000152 *** 

		---
		Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
		
		Correlation of Fixed Effects:
		       (Intr) perid2 perid3
		period2 -0.592
		period3 -0.565  0.335
		
		period4 -0.468  0.277  0.265
		
		Using a parameter expanded prior in order to improve mixing as the herd variance approaches zero:
		
		prior<-list(R=list(V=1, nu=0), G=list(G1=list(V=1, nu=1, alpha.mu=0, alpha.V=1000)))
		
		mcmc2<-MCMCglmm(incidence~period, random=~herd, family="poisson", data=cbpp)
		
		

			summary(mcmc2)
			


		 Iterations = 12991
		 Thinning interval  = 3001
		 Sample size  = 1000
		
		 DIC: 175.9590
		
		 G-structure:  ~herd
		
		    post.mean  l-95% CI u-95% CI eff.samp
		herd   0.01433 1.067e-16   0.0713    61.58
		
		 R-structure:  ~units
		
		     post.mean l-95% CI u-95% CI eff.samp
		units    0.7347   0.1564    1.421    222.9
		
		 Location effects: incidence ~ period
		
		           post.mean l-95% CI u-95% CI eff.samp  pMCMC
		(Intercept)    1.0749   0.4584   1.5987    844.5  0.002 **
		period2       -1.2054  -2.0862  -0.3556    771.8  0.004 **
		period3       -1.4568  -2.4362  -0.4839    674.8  0.004 **
		period4       -2.0584  -3.1851  -0.9430    446.5 <0.001 *** 

		---
		Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
		
		
		
		Quoting Gosselin Frederic <frederic.gosselin@cemagref.fr>:
		
		

			Dear Colleague,
			
			good question:
			
			the commands are under R2.5.1:
			************************************************************************
			library(lme4)
			cbppbis<-cbind.data.frame(cbpp,Id=as.factor(1:dim(cbpp)[1]))
			gm1 <- lmer(incidence ~ period + (1 | herd), family = quasipoisson, data = cbpp)
			summary(gm1)
			
			gm2 <- lmer(incidence ~ period + (1 | Id/herd), family = poisson, data = cbppbis)
			summary(gm2)
			**************************************************************************
			(fope it is declared in the good order for the random effects in gm2)
			
			The results do show a slight discrepancy between both methods:
			
			*************************************************************************
			

				summary(gm1)
				

			Generalized linear mixed model fit using Laplace
			Formula: incidence ~ period + (1 | herd)
			  Data: cbpp
			 Family: quasipoisson(log link)
			  AIC   BIC logLik deviance
			 112.2 122.3 -51.11    102.2
			Random effects:
			 Groups   Name        Variance Std.Dev.
			 herd     (Intercept) 0.35085  0.59233
			 Residual             1.40470  1.18520
			number of obs: 56, groups: herd, 15
			
			Fixed effects:
			           Estimate Std. Error t value
			(Intercept)   1.2812     0.2200   5.824
			period2      -1.1240     0.3315  -3.391
			period3      -1.3203     0.3579  -3.689
			period4      -1.9477     0.4808  -4.051
			
			Correlation of Fixed Effects:
			       (Intr) perid2 perid3
			period2 -0.339
			period3 -0.314  0.219
			period4 -0.233  0.163  0.151
			
			
			
			
			

				summary(gm2)
				

			Generalized linear mixed model fit using Laplace
			Formula: incidence ~ period + (1 | Id/herd)
			  Data: cbppbis
			 Family: poisson(log link)
			  AIC   BIC logLik deviance
			 102.2 114.4 -45.11    90.21
			Random effects:
			 Groups  Name        Variance Std.Dev.
			 herd:Id (Intercept) 0.29608  0.54413
			 Id      (Intercept) 0.29608  0.54413
			number of obs: 56, groups: herd:Id, 56; Id, 56
			
			Estimated scale (compare to  1 )  0.9249959
			
			Fixed effects:
			           Estimate Std. Error z value Pr(>|z|)
			(Intercept)   1.1149     0.2476   4.503 6.69e-06 ***
			period2      -1.2013     0.4184  -2.871 0.004089 **
			period3      -1.4224     0.4378  -3.249 0.001159 **
			period4      -2.0089     0.5294  -3.795 0.000148 ***
			---
			Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
			
			Correlation of Fixed Effects:
			       (Intr) perid2 perid3
			period2 -0.592
			period3 -0.565  0.335
			period4 -0.468  0.277  0.264
			************************************************************************
			
			The estimates and the standard errors are not exactly the same - which might not be unlogical given that the relationship between variance and mean is not the same in both models. They however are not very far one from the other.
			
			Of course, this needs further investigation.
			
			I remember of a paper that motivated the use of the quasi-poisson method based on empirical relationships between the residual variance and the mean:
			
			Ver Hoef J.M. et Boveng P.L., 2007, Quasi-poisson vs. negative binomial regression: How should we model overdispersed count data?, Ecology, 88, 11, p. 2766-2772.
			
			Sincerely,
			
			Frédéric
			
			-----Message d'origine-----
			De : John Maindonald [mailto:john.maindonald@anu.edu.au]
			Envoyé : mercredi 10 novembre 2010 09:51
			À : Gosselin Frederic
			Cc : r-sig-mixed-models@r-project.org; tiflo@csli.stanford.edu
			Objet : Re: [R-sig-ME] quasi-binomial family in lme4
			
			I wonder if you have compared the results that you quote with the result you get with observation level random effects in a poisson model.
			
			As I see it, use of observation level random effects should, unless there is evidence that a multiplicative effect on the scale of the response is a better fit, replace use of the quasi- models in glm() as well as in generalised linear mixed models.
			
			John Maindonald             email: john.maindonald@anu.edu.au
			phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
			Centre for Mathematics & Its Applications, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200.
			http://www.maths.anu.edu.au/~johnm
			
			On 10/11/2010, at 6:39 PM, Gosselin Frederic wrote:
			
			

				Hi Florian,
				
				a different perpsective on the quasi-likelihood debate - that comes out sporadically on this list:
				
				(i) I globally agree with the previous repliers that a fully
				probabilistic solution looks better - at least aesthetically - than a
				quasi-likelihood;
				
				(ii) however, as I have already mentioned on the list (cf. below), earlier versions of lme4 give much more sensible results than the latest versions:
				http://markmail.org/message/s4abxhhdacqjkunm
				
				This is why in the following papers:
				Elek Z., Dauffy-Richard & Gosselin F., 2010, Carabid species responses to hybrid poplar plantation in floodplains in France, Forest Ecology and Management, 260, 9, p. 1446-1455.
				
				and
				
				Vuidot A., Paillet Y., Archaux F. & Gosselin F. (In Press) Influence of tree characteristics and forest management on tree microhabitats in France, Biological Conservation.
				
				we used version the R version 2.5.1 and the associated lme4 version (here with quasi-poisson, not quasi-bionomial).
				
				Hope this helps.
				
				Sincerely,
				
				Frédéric Gosselin
				Engineer & Researcher (PhD) in Forest Ecology Cemagref Domaine des
				Barres F-45290 Nogent sur Vernisson France
				
				http://www.cemagref.fr/les-contacts/les-pages-personnelles-professionn
				elles/gosselin-frederic/english-short-scientific-cv
				
				
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