[R-sig-ME] GLMM for Combined experiments and overdispersed data

[Juan Pablo Edwards Molina]

I am analyzing data from 3 field experiments (farms=3) for a citrus flower
disease: response variable is binomial because the flower can only be
diseased or healthy.

I have particular interest in comparing 5 fungicide spraying systems
(trt=5).

Each farm had 4 blocks (bk=4) including 2 trees as subsamples (tree=2) in
which I assessed 100 flowers each one. This is a quick look of the data:

farm      trt      bk    tree   dis   tot     <fctr>   <fctr>  <fctr>
<fctr> <int> <int>
iaras      cal      1      1     0    100
iaras      cal      1      2     1    100
iaras      cal      2      1     1    100
iaras      cal      2      2     3    100
iaras      cal      3      1     0    100
iaras      cal      3      2     5    100...

The model I considered was:

resp <- with(df, cbind(dis, tot-dis))

m1 = glmer(resp ~ trt + (1|farm/bk) , family = binomial, data=df)

I tested the overdispersion with the overdisp_fun() from GLMM page
<http://glmm.wikidot.com/faq>

        chisq         ratio             p          logp
 4.191645e+02  3.742540e+00  4.804126e-37 -8.362617e+01

As ratio (residual dev/residual df) > 1, and the p-value < 0.05, I
considered to add the observation level random effect (link
<http://r.789695.n4.nabble.com/Question-on-overdispersion-td3049898.html>)
to deal with the overdispersion.

farm      trt      bk    tree   dis   tot tree_id    <fctr>   <fctr>
<fctr> <fctr> <int> <int> <fctr>
iaras      cal      1      1     0    100    1
iaras      cal      1      2     1    100    2
iaras      cal      2      1     1    100    3...

so now was added a random effect for each row (tree_id) to the model, but I
am not sure of how to include it. This is my approach:

m2 = glmer(resp ~ trt + (1|farm/bk) + (1|tree_id), family = binomial, data=df)

I also wonder if farm should be a fixed effect, since it has only 3
levels...

m3 = glmer(resp ~ trt * farm + (1|farm:bk) + (1|tree_id), family =
binomial, data=df)

I really appreciate your suggestions about my model specifications...



*Juan​ Edwards- - - - - - - - - - - - - - - - - - - - - - - -# PhD student
- ESALQ-USP/Brazil*

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