[R-sig-ME] quasi-binomial family in lme4

[Gosselin Frederic]

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 at anu.edu.au] 
Envoyé : mercredi 10 novembre 2010 09:51
À : Gosselin Frederic
Cc : r-sig-mixed-models at r-project.org; tiflo at 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 at 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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