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@ees.kuleuven.be

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

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