[R] Overdispersion using repeated measures lmer

[Christine Griffiths]

Dear All

I am trying to do a repeated measures analysis using lmer and have a number 
of issues. I have non-orthogonal, unbalanced data.  Count data was obtained 
over 10 months for three treatments, which were arranged into 6 blocks. 
Treatment is not nested in Block but crossed, as I originally designed an 
orthogonal, balanced experiment but subsequently lost a treatment from 2 
blocks. My fixed effects are treatment and Month, and my random effects are 
Block which was repeated sampled.  My model is:

Model<-lmer(Count~Treatment*Month+(Month|Block),data=dataset,family=poisson(link=sqrt))

Is this the only way in which I can specify my random effects? I.e. can I 
specify them as: (1|Block)+(1|Month)?

When I run this model, I do not get any residuals in the error term or 
estimated scale parameters and so do not know how to check if I have 
overdispersion. Below is the output I obtained.

Generalized linear mixed model fit by the Laplace approximation
Formula: Count ~ Treatment * Month + (Month | Block)
   Data: dataset
   AIC   BIC logLik deviance
 310.9 338.5 -146.4    292.9
Random effects:
 Groups Name        Variance   Std.Dev. Corr
 Block  (Intercept) 0.06882396 0.262343
        Month       0.00011693 0.010813 1.000
Number of obs: 160, groups: Block, 6

Fixed effects:
                          Estimate Std. Error z value Pr(>|z|)
(Intercept)               1.624030   0.175827   9.237  < 2e-16 ***
Treatment2.Radiata        0.150957   0.207435   0.728 0.466777
Treatment3.Aldabra       -0.005458   0.207435  -0.026 0.979009
Month                    -0.079955   0.022903  -3.491 0.000481 ***
Treatment2.Radiata:Month  0.048868   0.033340   1.466 0.142717
Treatment3.Aldabra:Month  0.077697   0.033340   2.330 0.019781 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Trt2.R Trt3.A Month  T2.R:M
Trtmnt2.Rdt -0.533
Trtmnt3.Ald -0.533  0.450
Month       -0.572  0.585  0.585
Trtmnt2.R:M  0.474 -0.882 -0.402 -0.661
Trtmnt3.A:M  0.474 -0.402 -0.882 -0.661  0.454


Any advice on how to account for overdispersion would be much appreciated.

Many thanks in advance
Christine

----------------------
Christine Griffiths
School of Biological Sciences
University of Bristol
Woodland Road
Bristol BS8 1UG
Tel: 0117 9287593
Fax 0117 925 7374
Christine.Griffiths at bristol.ac.uk
http://www.bio.bris.ac.uk/research/mammal/tortoises.html