[R] Logistic regression with factorial effect

[Billy.Requena]

Hello,

I’d like to evaluate the temporal effect on the relationship between a
continuous variable (e.g. size) and the probability of mate success.
Initially I was trying to do a logistic regression model incorporating the
temporal effect, but I don’t know if that is the best option. I simulated
some data and that’s the problem:


rep(c("Jan","Feb","Mar","Apr","May"), each=20) -> month
as.factor(month)

rep(LETTERS[seq(1:20)], 5) -> ind

rep(sort(rnorm(20, 5.5, 0.2)), 5) -> size
size

c(c(rep(0,12), rep(1,8)), c(rep(0,12), rep(1,8)),
	c(rep(c(0,1), 10)),
	c(rep(1,8), rep(0,12)),
	c(rep(1,8), rep(0,12))) -> success1
success1

With the object ‘success1’, only the highest values of size are successful
at the two first months, but only the lowest values of size are successful
at the two last months. So, the overall effect of size on the successful
probability should not exist, but if we consider the interaction between
size and time, we should be able to see that effect.


glm(success1 ~ size, family=binomial) -> test1.1
glmer(success1 ~ size + (1|ind), family=binomial) -> test2.1
glmer(success1 ~ size + month + (1|ind), family=binomial) -> test3.1
glmer(success1 ~ size : month + (1|ind), family=binomial) -> test4.1


However, the expected result is not observed in the output of all these
models. Using a model selection approach and comparing the AIC values of all
models, it seems that ‘test1.1’ model is the most likely. All the deviances
are almost at the same level and the differences in AIC values are due for
the new parameters added.

Given the data was simulated to generate differences between models and
model ‘test4.1’ is supposed to be the best one, I’m probably doing something
wrong.
Has anyone faced this kind of problem? Or has anyone any idea how to solve
that?

Thanks and Regards 
Gustavo Requena 
PhD student - Laboratory of Arthropod Behavior and Evolution 
Universidade de São Paulo 
http://ecologia.ib.usp.br/opilio/gustavo.html

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