[R] lmer or glm with family=binomial : probability variable

[lorenz.gygax at art.admin.ch]

> We are dealing with a variable (BA) which indicates the overlap
> between small mammal home ranges. It varies between 0 and 1 and it
> can be interpreted as "the probability of two home ranges to
> overlap", therefore we would have modelled it with the binomial
> family, also supported by  the distribution of the variable itself.  
> However, lmer or glm require the data to be presented as successes
> vs failures. In our case, this is not possible as BA is calculated
> by GIS on raster maps; in other words, BA expressess p (probability
> of success), but it is not possible to know from how many
> cases/attempts p came from. 

These models internally use the logit link. You could potentially transform your response variable accordingly and fit a model based on the assumption of normally distributed variables (of course, you have to check whether the corresponding assumptions were met e.g. by conducting an analysis of the residuals).

the logit link is: log (P/(1-P))

Regards, Lorenz Gygax
- 
Swiss Federal Veterinary Office
Centre for proper housing of ruminants and pigs
Agroscope Reckenholz-Tänikon Research Station ART