GLMM for Combined experiments and overdispersed data

Dear Juan,

Use unique id's for random effects variables. So each bk should only be
present in one farm. And each tree_id should be present in only one bk. In
case each block has different treatments then each tree_id should be unique
to one combination of bk and trt.

Farm has too few levels to be a random effects. So either model is as a
fixed effect or drop it. In case you drop it, the information will be
picked up by bk. Note that trt + (1|farm) is less complex than trt * farm.

Assuming that you are not interested in the effect of a specific farm, you
could use sum, polynomial or helmert contrasts for the farms. Unlike the
default treatment contrast, these type of contrasts sum to zero. Thus the
effect of trt will be that for the average farm instead of the reference
farm.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2017-04-21 22:32 GMT+02:00 Juan Pablo Edwards Molina <
edwardsmolina at gmail.com>:

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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