[R-sig-ME] significance test of random and fixed effects in (quasi) poisson GLMM

Mon Mar 15 13:40:32 CET 2010

I guess the overdispersion parameter is equivalent to the sigma (within-group residual variance), which can be retrieved simply typing 'model$sigma' where 'model' is a glmmPQL object. I ran some analysis with alternatives models based on GAM and the estimate is coherent with the overdispersion parameter returned by them. Just remember that the phi (overdispersion parameter) is equal to sigma^2.
The estimates from glmmPQL seem coherent both in my analysis on real data and from simulations.

As already reported, glmmPQL always estimates a sigma (overdispersion) both with family 'poisson' or 'quasipoisson'. I think this is a problem related to the iterative calls to 'lme' for simple linear mixed models, where the sigma is not a fixed parameter as in Poisson models.

Regards,

Antonio Gasparrini
Public and Environmental Health Research Unit (PEHRU)
London School of Hygiene & Tropical Medicine
Keppel Street, London WC1E 7HT, UK
Office: 0044 (0)20 79272406 - Mobile: 0044 (0)79 64925523

>>> r-sig-mixed-models-request at r-project.org> 15/03/2010 11:00 >> ( mailto:r-sig-mixed-models-request at r-project.org> )

Message: 1
Date: Mon, 15 Mar 2010 10:44:24 +0100
From: Vincent Kint <Vincent.Kint at ees.kuleuven.be>
To: "r-sig-mixed-models at r-project.org"
<r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] significance test of random and fixed effects
in(quasi) poisson GLMM
Message-ID:
<562EA47F252E594B826D3B440E0B34A21288E58045 at ICTS-S-EXC2-CA.luna.kuleuven.be>

Content-Type: text/plain; charset="Windows-1252"

Dear Antonio and list members,

Thanks for the reply. The problem with quasi GLMM in lme4 seems to have been reported several times. As you suggested, I tried with glmmPQL, but I don't find how to retreive the overdispersion factor (it is not in the summary). Also, I don't see any difference using poisson or quasipoisson. Does that mean that this method is correcting for overdispersion in both cases?

Further suggestions on how to test fixed and radom factors in GLMMs are still welcome.

Regards,
Vincent

________________________________________
From: Antonio.Gasparrini at lshtm.ac.uk [Antonio.Gasparrini at lshtm.ac.uk] 
Sent: 13 March 2010 14:09
To: r-sig-mixed-models at r-project.org 
Cc: Vincent Kint
Subject: Re: significance test of random and fixed effects in (quasi)    poisson GLMM

Dear Vincent,

some time ago I posted a question on Poisson GLMM for overdispersed
data, including a simple simulation in order to compare the reliability
of glmmPQL and glmer.
See
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q1/003289.html 

While glmmPQL returns the correct estimates, glmer largely
overestimated the sigma (corresponding to the overdispersion), producing
an inflated within-group residual variance.
This odd behaviour seems to be confirmed by your analysis.

As pointed out in the response I had to my question, the quasi-Poisson
is not a distribution and the results are not grounded on an appropriate
statistical theory. Anyway, as in your case, the quasipoisson family is
currently used and I would expect the command to return (approximate)
correct results.

My suggestion is to repeat the analysis with glmmPQL, even if this
doesn't solve your problem to run a test. To my knowledge, the
approximation used by the penalized quasi-likelihood method is
reasonable for Poisson data and a moderate number of counts (McCulloch &
Searle say with mean count of 7 or higher). Interestingly, the command
always estimates the sigma (not fixed to 1 as in Poisson) even with the
simple poisson family.

I hope this helps

Antonio Gasparrini
Public and Environmental Health Research Unit (PEHRU)
London School of Hygiene & Tropical Medicine
Keppel Street, London WC1E 7HT, UK
Office: 0044 (0)20 79272406 - Mobile: 0044 (0)79 64925523

------------------------------

Message: 3
Date: Fri, 12 Mar 2010 15:46:23 +0100
From: Vincent Kint <Vincent.Kint at ees.kuleuven.be>
To: "r-sig-mixed-models at r-project.org"
<r-sig-mixed-models at r-project.org>
Subject: [R-sig-ME] significance test of random and fixed effects in
(quasi) poisson GLMM
Message-ID:
<562EA47F252E594B826D3B440E0B34A21288E5803C at ICTS-S-EXC2-CA.luna.kuleuven.be>

Content-Type: text/plain

Dear list members,

I am new to this list, and new to generalised mixed modelling.

My aim is to develop a model for tree branchiness (number of branches
per tree, with trees measured in different plots) with both tree and
plot-level predictors. My choice was for a generalised model using the
poisson family, since I have count data. And for a mixed approach since
I have a nested design.

I built a first model using the lme4 package (see below). My question
is: is there an approximate test for the significance of the random
effect? From previous posts on this list, I understand that such a test
is not always reliable, and good alternatives are not implemented yet.
But from my perspective of an applied modeller, even an approximate test
(or even a rule of thumb) would be helpful in making a decision. Indeed,
if the random effect turns out to be likely not significant, I could do
with a more simple GLM.

In a second step I tried to correct for overdispersion by running the
same model as a quasi GLMM. The output is also given below. Here I have
the same question as before, but now also concerning the fixed effects.
Additionally, I wonder whether I may have made a mistake in implementing
this model, since I get a result where nearly all the variation is
attributed to the error term, and (at a first glance) the random effect
and all the fixed predictors seem to be irrelevant.

I attach the output of both models below.
Thanks for all suggestions on how to proceed.
Vincent

#1. The GLMM model
> form1<-formula(response ~ TreeHeight + DBH + TreeAge + Vplot + mF +
mL + (1 | plots))
> M.glmm<-lmer(form1, data=data, family=poisson)
> summary(M.glmm)
Generalized linear mixed model fit by the Laplace approximation
Formula: form1
   Data: data
AIC  BIC logLik deviance
976 1008   -480      960
Random effects:
Groups Name        Variance Std.Dev.
plots  (Intercept) 0.044913 0.21193
Number of obs: 399, groups: plots, 30

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)
(Intercept)  6.0090427  1.4143768   4.249 2.15e-05 ***
TreeHeight  -0.0398146  0.0125816  -3.165 0.001553 **
DBH          0.0032600  0.0006599   4.940 7.80e-07 ***
TreeAge     -0.1193541  0.0242996  -4.912 9.03e-07 ***
Vplot       -0.0060713  0.0016115  -3.768 0.000165 ***
mF          -0.4838699  0.1672462  -2.893 0.003814 **
mL           0.4878563  0.1731139   2.818 0.004831 **
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.?
0.1 ? ? 1

#2. The same GLMM model with overdispersion
> M.glmm.q<-lmer(form1, data=data, family=quasipoisson)
> summary(M.glmm.q)
Generalized linear mixed model fit by the Laplace approximation
Formula: form1
   Data: data
AIC  BIC logLik deviance
978 1014   -480      960
Random effects:
Groups   Name        Variance Std.Dev.
plots    (Intercept)  1.6478  1.2837
Residual             36.6894  6.0572
Number of obs: 399, groups: plots, 30

Fixed effects:
             Estimate Std. Error t value
(Intercept)  6.009043   8.567129   0.701
TreeHeight  -0.039815   0.076209  -0.522
DBH          0.003260   0.003997   0.816
TreeAge     -0.119354   0.147187  -0.811
Vplot       -0.006071   0.009761  -0.622
mF          -0.483870   1.013039  -0.478
mL           0.487856   1.048581   0.465

_____________________________________
dr. ir. V. KINT
Forest Ecology and Management
Division Forest, Nature and Landscape
K.U.Leuven
Celestijnenlaan 200E - B-3001 Leuven
Tel.: +32 16 32 97 69
Fax:  +32 16 32 97 60
vincent.kint at ees.kuleuven.be 

www.kuleuven.be/forecoman<http://www.kuleuven.be/forecoman>

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