[R] What is my replication unit? Lmer for binary longitudinal data with blocks and two treaments.

[hpdutra]

First I would like to say thank you for taking the time to read it.Here is my
problem.

I am running a lmer analysis for binary longitudinal (repeated measures) 
data.
Basically, I  manipulated fruits and vegetation to two levels each(present
and absent) and I am trying to access how these factors affect mice foraging
behavior. The design consist of  12 plots, divided in 3 blocks.  So each
block has 4 plots assigned to one of the following treatments. 
Fruit intact and Vegetation intact 
Fruit intact and Vegetation removed
Fruit removed and Vegetation intact 
Fruit removed and Vegetation removed

Within each plot I had 16 track plates. Track plates were checked monthly
for presence or absence of paw prints. I am trying to fit lmer model
track~fruit*vegetation*time*block in which fruit vegetation time are fixed
effects and time is repeated measures and block is a random effect here is
my code.

> model<-lmer(track~veget*fruit*time*(time|plate)*(1|block),family=binomial)
> summary(model)
Generalized linear mixed model fit by the Laplace approximation 
Formula: track ~ veget * fruit * time * (time | plate) * (1 | block) 
   AIC   BIC logLik deviance
 933.9 994.5 -454.9    909.9
Random effects:
 Groups Name        Variance    Std.Dev. Corr   
 plate  (Intercept)  0.226747   0.47618         
             time        0.054497   0.23345  -1.000 
 block  (Intercept)  0.615283 0.78440         
Number of obs: 1152, groups: plate, 192; block, 3

Fixed effects:
                                            Estimate Std.    Error         z
value           Pr(>|z|)   
(Intercept)                                -1.68645    0.58718       -2.8721       
0.00408 **
vegetremoved                            -1.39291    0.57742       -2.4123       
0.01585 * 
fruitremoved                               -0.54486    0.53765       -1.0134       
0.31086   
time                                          -0.02091    0.10118      
-0.2067        0.83626   
vegetremoved:fruitremoved            0.75130    0.86342        0.8701       
0.38422   
vegetremoved:time                       0.38229    0.14695        2.6014       
0.00928 **
fruitremoved:time                         0.17012    0.14227        1.1958       
0.23178   
vegetremoved:fruitremoved:time    -0.47526    0.22134       -2.1473       
0.03177 * 
---

OK, the method that I am using is Laplace and someone has pointed out that
this is more accurate than PQL. I am still confused about the structure of
the model though. I want time to be a fixed effects but I also want it to be
repeated measures giving that I sample the same plates multiple times, this
way I have time appearing twice in my model, is this correct?
The variable plate is the identity of each of the 192 plates. But I am not
sure if this is the correct approach, because this approach establishes that
the plates are the replication unit and I wonder if I should use the plot as
the replication unit? But if I do that then I change the approach from a
binary data (the plate had a paw print or not) to continuos variable in
which I would count the number of plates in plot that had paw print. I am
not sure which is the best approach?
Am I in the right track?
Thanks
Humberto

PS: I would like to say that posted kind of the similar post before but
addressing different questions. I deleted the previous post to avoid
confusion 
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