Hi, 

Transforming the proportions and doing a linear regression is probably the best thing to do in this case. Some would recommend the arcsine transformation in this case, but a quick search of “arcsine logit proportion transform” gave this article that recommends the logic transformation
The arcsine is asinine: the analysis of proportions in ecology
DI Warton, FKC Hui - Ecology, 2011


Other comments relevant to the issue…
Multiplying by 100 to convert proportions to binomial is not statistically valid if there weren’t 100 independent trials. 
 
Breaking binomial data up into binary data and adding a random effect for the experimental unit (bird in this case) is adding unnecessary complexity (see Murtaugh 2007). It only makes sense to separate binomial data in this way if there is another covariate of interest at the level of the binary observations (a smaller observational unit). There’s no need to fool around with repeated measures / pseudoreplication issues when you only have one observation (successes and failures) per experimental unit.

To the best of my knowledge, you cannot interpret residuals from binary data. Pearson residuals of logistic/binomial regression can be approximately normal if the number of trials (n) is large and the number of successes and failures are greater than 5 for each group. Binary data only has n=1 trial per observation.

Cheers,
Mollie
------------------------
Mollie Brooks, PhD
Postdoctoral Researcher, Population Ecology Research Group http://www.popecol.org
Institute of Evolutionary Biology & Environmental Studies, University of Zürich



On 28 Nov 2013, at 7:29 AM, Chris Howden <chris@trickysolutions.com.au> wrote:

> Hi Marieline,
> 
> I would consider using the raw data so it is binary, and use a random
> intercept to account for the different sampling intensities for each bird.
> 
> 
> If U have summarised the data so it is 1 score for each bird which is a %
> I can’t see how U can account for repeated measures since U don’t have the
> correlation structure in your data.
> 
> It's also hard to tell if you will likely need to account for
> pseudoreplication caused by serial correlation i.e. repeated measure since
> I can’t see any indication of the fix rate. However if you plot the
> residuals this may help, that said residuals from logistic regressions can
> be hard to interpret so some type of lagged correlation plot would likely
> be better.
> 
> Chris Howden B.Sc. (Hons) GStat.
> Founding Partner
> Evidence Based Strategic Development, IP Commercialisation and Innovation,
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> 
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> -----Original Message-----
> From: r-sig-ecology-bounces@r-project.org
> [mailto:r-sig-ecology-bounces@r-project.org] On Behalf Of marieline gentes
> Sent: Thursday, 28 November 2013 8:30 AM
> To: r-sig-ecology@r-project.org; moi
> Subject: [R-sig-eco] Logistic regression with repeated measures ?
> 
> Dear list,
> 
> I am a bit new to logistic regressions. I am working with GPS data from
> GPS-tracked birds. My objective is to investigate whether various
> covariates influence the probabilty of visiting specific habitats. Each
> bird has visited many habitats during the course of its GPS tracking.
> 
> Here is a small sample of the data:
> 
> Bird.ID Year Sex body.index Recapt PrevWeek.Rain AgriYes AgriNo UrbanYes
> UrbanNo CAL 2010 M 21.99155 13-May-10 1.43 0 100 0 100 CAO 2011 F
> -19.91797 27-Apr-11 4.23 54 46 9 91 CFL 2010 F 25.61063 12-May-10 2.16 31
> 69 2 98 CFP 2010 M -30.65814 13-May-10 1.43 60 40 0 100
> 
> I understand that I have to use logistic regression, with a cbind code,
> because my response variable is not binary anymore (the response is a
> summary of the success vs failures).
> 
> Based on R tutorials, I am thinking about codes that would look like this:
> 
> Agri.RainSex = glm(cbind(AgriYes, AgriNo) ~ PrevWeekRain + Sex + Year +
> Year*Sex,family=binomial (logit), data=mydata) However, contrary to the
> examples I see online, my data are from individual birds, not from groups
> of birds. If I had been using the raw binary data, each bird would have
> 100 hundred lines (I converted the percentages into success/failures)(all
> my % are weighted the same - that is not a problem here). Am I supposed to
> take into account some kind of repeated measure in my model ?
> 
> Notes:
> For people who are thinking about overdispersed data: my data does not
> seem to be overdispersed. But I will inspect that after I am confident
> that my basic model is ok. So this question is about dealing with repeated
> measured, not about adding a random intercept for overdispersion.
> 
> For people who are working with habitat selection models: this is not the
> case here. We are not working on resource selection. We want to fit a
> simple logistic regression on this data as a part of data exploration.
> This ultimate goal is to link contaminant burden with the proportion of
> time spent in a given habitat.
> 
> Thank you for your advice,
> 
> Marie
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