# [R-sig-ME] Could the random effect at the level of each observation be a trap?

Billy billy.requena at gmail.com
Mon Dec 13 20:50:42 CET 2010

```Hi Drew!

Thanks for the reply, but I think I wasn't clear enough before. As I
have sampled males throughout one year, some individuals were sampled
in more than one month, but several individuals were sampled just once
(as a successful or as unsuccessful). Therefore, differently from your
example, I don't have the same individuals recaptured in all 12
months, just changing their breeding success status. I think that's
the reason to the overdispersion I mentioned before. It means the most
of my data are about unsuccessful individuals (more than half of the
sample size fall into the unsuccessful category) and I wanna
investigated if some specific characteristics of the successful males
are responsible to that success in achieving mates.

Billy

On Mon, Dec 13, 2010 at 1:39 PM, Drew Tyre <atyre2 at unl.edu> wrote:
> This question of overdispersion in binomial models is near and dear to
> my heart - so I tried to make an example to see if I can replicate the
> type of situation you're describing Billy (code below). I guess I
> don't understand the data you have, because as long as each male is
> either successful or unsuccessful (once), you will never observe
> overdispersion, at least not the way I understand it?
>
> setseed(32493)
> x = rnorm(100)
> z = rnorm(100)
> maleID = sample(1:40,size=100,replace=TRUE)
> n.male = length(unique(maleID))
> sigmaMale = 1
> sigmaResid = 0.2
> Maleeffect = rnorm(40,sd=sigmaMale)
> Resideffect = rnorm(100,sd=sigmaResid)
> beta = c(0,2,1,0.54) # effect of x, z, and x*z
>
> logodds.y = cbind(1,x,z,x*z) %*% beta + Maleeffect[maleID] + Resideffect
>
> y = rbinom(100,1,1/(1+exp(-logodds.y)))
>
> df = data.frame(x=x,z=z,maleID=maleID,y=y)
>
> glm(y~x*z,data=df,family=binomial) # OK, seems to work
>
> library(lme4)
>
> models = list(y~x*z + (1|maleID),
>        y~x+z + (1|maleID),
>        y~x + (1|maleID),
>        y~z + (1|maleID),
>        y~1 + (1|maleID))
>
> fits = lapply(models,function(ff)glmer(ff,family=binomial,data=df))
>
> sapply(fits,function(fm)summary(fm)@AICtab) # model 2 is best,
>
> # ok try this residual idea
> resid <- as.factor(1:dim(df)[1])
>
> models = list(y~x*z + (1|maleID)+(1|resid),
>        y~x+z + (1|maleID)+(1|resid),
>        y~x + (1|maleID)+(1|resid),
>        y~z + (1|maleID)+(1|resid),
>        y~1 + (1|maleID)+(1|resid))
>
> fits = lapply(models,function(ff)glmer(ff,family=binomial,data=df))
>
> # lots of warnings, otherwise results unaffected - estimated variance
> of resid very small
>
>
> On Mon, Dec 13, 2010 at 11:33 AM, Billy <billy.requena at gmail.com> wrote:
>> Hi Ben,
>>
>> In fact, I've tried the additive random effect of MaleID and resid,
>> but I got the same problem: quantitatively and qualitatively
>> differences. Models considering Male ID + resid showed smaller
>> deviances than models that only considered MaleID AND among models
>> considering MaleID + resid, the best model was the one which consider
>> no effect of any explanatory variable, while among models considering
>> only MaleID as random variable, the best model was the one considering
>> effect of the interaction between 2 explanatory variables.
>> I still have doubts about the usage of this "resid" variable, mainly
>> because the interpretation of the results is completely different. Is
>> the decrease of the whole deviance enough justification to use that
>> and interpret only the results obtained among models considering
>> MaleID + resid?
>>
>> Thanks again for you all,
>>
>> Billy
>>
>> On Sat, Dec 11, 2010 at 12:27 PM, Ben Bolker <bbolker at gmail.com> wrote:
>>> On 10-12-10 09:39 PM, Billy wrote:
>>>> Hi all!
>>>>
>>>> I'm a relatively newbie ecologist student getting adventures at the
>>>> mixed models world and facing some trouble to interpret random
>>>> effects. I hope someone could help me.
>>>> Quickly, I'm constructing different models using glmer() to discover
>>>> which factors could influence females' reproductive decisions. I have
>>>> sampled several males and classified them as successful or
>>>> unsuccessful.  Therefore, I'm modelling logistic regressions with more
>>>> than one fixed variable and random variables.
>>>> I have sampled individuals monthly and, sometimes, the same individual
>>>> (MaleID) was sampled more than once, in different status. Then, I used
>>>> "MaleID" as a random variable.
>>>> Well, I built a bunch of models considering only MaleID as the random
>>>> variable as:
>>>>
>>>> m1 <- glmer(y ~ 1 + (1|MaleID), family=binomial)
>>>> m2 <- glmer(y ~ x + (1|MaleID), family=binomial)
>>>> m3 <- glmer(y ~ z + (1|MaleID), family=binomial)
>>>>
>>>>
>>>> Moreover, in several posts here I've read about count data show high
>>>> overdispersion, even using family=binomial for the error. One
>>>> recurrent solution suggested is create a vector to each observation
>>>> as:
>>>>
>>>> resid <- as.factor(1:dim(data)[1])
>>>>
>>>> Then, I built models considering this random variable too, trying to
>>>> understand that, as following
>>>>
>>>> m4 <- glmer(y ~ 1 + (1|resid), family=binomial)
>>>> m5 <- glmer(y ~ x + (1|resid), family=binomial)
>>>> m6 <- glmer(y ~ w + (1|resid), family=binomial)
>>>>
>>>> and
>>>>
>>>> m7 <- glmer(y ~ 1 + (1|MaleID:resid ), family=binomial)
>>>> m8 <- glmer(y ~ x + (1|MaleID:resid ), family=binomial)
>>>> m9 <- glmer(y ~ z + (1|MaleID:resid ), family=binomial)
>>>>
>>>> Using a model selection approach and looking for the deviance and the
>>>> AIC values, I observed that the correspondent models from the second
>>>> block (m4, m5 and m6 in the example above) and the third block (m7, m8
>>>> and m9) showed the same values. Is that due to the "resid" random
>>>> effect?
>>>>
>>>
>>>   I think you want
>>>
>>>  ~ [fixed predictor(s)] + (1|MaleID)+(1|resid)
>>>
>>> ?
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>>
>>
>> --
>> Gustavo Requena
>> PhD student - Laboratory of Arthropod Behavior and Evolution
>> Departamento de Ecologia - IBUSP
>> Rua do Matão - Travessa 14 no 321 Cidade Universitária, São Paulo - SP, Brasil
>> CEP 05508-900
>> Phone number: 55 11 3091-7488
>>
>> http://ecologia.ib.usp.br/opilio/gustavo.html
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
>
>
> --
> Drew Tyre
>
> School of Natural Resources
> 416 Hardin Hall, East Campus
> 3310 Holdrege Street
> Lincoln, NE 68583-0974
>
> phone: +1 402 472 4054
> fax: +1 402 472 2946
> email: atyre2 at unl.edu
> http://snr.unl.edu/tyre
> http://aminpractice.blogspot.com
> http://www.flickr.com/photos/atiretoo
>

--
Gustavo Requena
PhD student - Laboratory of Arthropod Behavior and Evolution