Dear all,

I have the following dataset with results from an experiment with individual 
bats that performed two tasks related to prey capture under different 
conditions:

X variables:
indiv - 5 individual bats used in the experiment; all of which performed both 
tasks
task - 2 tasks that each individual bat had to perform
dist - 5 repeated measures of individual bats at 5 different distances from the 
object

all x variables I treat as categorical factors with levels

Y - I have 8 dependent variables related to the structure of ultrasound calls 
emitted by bats when performing each task. I know I can use them together in 
the same model with the function “cbind()” but each variable behaves a bit 
differently. Thus, I guess it would be better to build 8 separate models. 

I believe "indiv" should be a random effect in the model; "dist" and "task" 
should be fixed effects.

I´d like to use the “glmer” (lme4) function to test two hypotheses:

Main hypothesis:
There are differences in Y measurements between tasks, which are related also 
to distance from the object.

Secondary hypothesis:
Differences in Y measurements between tasks do not depend on the individual.


I guess the simplest model for an AIC model selection would be:
print(Model.01<-glmer(y~task*dist+(1|indiv))
 - so any model that provides more details should have a lower (better)  AIC 
score.
I’m not sure if I’m coding the model correctly, so my hypothesis would be 
properly tested. 

1- Literature suggests to get rid of the pseudo-replication: my repeated 
measures (“dist”) seem to behave like longitudinal data (as it is basically a 
time series). This way, "indiv" would be nested in "dist". Furthermore, "dist" 
levels have different variance, so it would be good to group the data and 
somehow tell the model, that it should ignore differences in variance.
(1|dist:indiv) or (dist|indiv)?
I am still wondering if the “weights=” argument would apply here?

2- “dist” is nested in “task”, as for both tasks I have the same distances 
measured.
According to the description of the package “lme4”, I should write:
print(Model.02<-glmer(y~task*dist+(1|indiv)+(1|task:dist))

3- according to the text -book “The R book” I understand that I should do the 
following (as mentioned for the ratliver treatment-dataset):
rename factor levels to unique labels:
taskdist<-task:dist
taskdistindiv<-task:dist:indiv
print(Model.03<-glmer(y~task+(1|taskdist)+(1|taskdistindiv)))

Or, pooling 1 and 3 together myself I would end up with:
print(Model.04<-glmer(y~dist*task+(1|indiv)+(1|task:dist)+(1|dist:indiv))

I doubt that all of them actually describe correctly what I want the model to 
answer...

I did not find any directly related comment in the R help.

Thank you for your attention and for any help you may provide.

--

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