[R] OT: (quasi-?) separation in a logistic GLM

[David Winsemius]

If you look at the distribution of those with analogs==TRUE versus the  
whole groups it is not surprising that the upper range of Dij's result  
in a very low probability estimate:

  plot(density(dat$Dij))
lines(density(dat[dat$analogs == TRUE, 2]))

Appears as though more than 25% of the predict(mod, type="response")  
elements will satisfy
all.equal(0, <predict>) which on my machine occurs when <predict> is  
(roughly)  below 1e-9


Best;

David Winsemius

On Dec 15, 2008, at 1:03 PM, Gavin Simpson wrote:

> Dear List,
>
> Apologies for this off-topic post but it is R-related in the sense  
> that
> I am trying to understand what R is telling me with the data to hand.
>
> ROC curves have recently been used to determine a dissimilarity
> threshold for identifying whether two samples are from the same "type"
> or not. Given the bashing that ROC curves get whenever anyone asks  
> about
> them on this list (and having implemented the ROC methodology in my
> analogue package) I wanted to try directly modelling the probability
> that two sites are analogues for one another for given dissimilarity
> using glm().
>
> The data I have then are a logical vector ('analogs') indicating  
> whether
> the two sites come from the same vegetation and a vector of the
> dissimilarity between the two sites ('Dij'). These are in a csv file
> currently in my university web space. Each 'row' in this file
> corresponds to single comparison between 2 sites.
>
> When I analyse these data using glm() I get the familiar "fitted
> probabilities numerically 0 or 1 occurred" warning. The data do not  
> look
> linearly separable when plotted (code for which is below). I have read
> Venables and Ripley's discussion of this in MASS4 and other sources  
> that
> discuss this warning and R (Faraway's Extending the Linear Model  
> with R
> and John Fox's new Applied Regression, Generalized Linear Models, and
> Related Methods, 2nd Ed) as well as some of the literature on Firth's
> bias reduction method. But I am still somewhat unsure what
> (quasi-)separation is and if this is the reason for the warnings in  
> this
> case.
>
> My question then is, is this a separation issue with my data, or is it
> quasi-separation that I have read a bit about whilst researching this
> problem? Or is this something completely different?
>
> Code to reproduce my problem with the actual data is given below. I'd
> appreciate any comments or thoughts on this.
>
> #### Begin code snippet  
> ################################################
>
> ## note data file is ~93Kb in size
> dat <- read.csv(url("http://www.homepages.ucl.ac.uk/~ucfagls/ 
> dat.csv"))
> head(dat)
> ## fit model --- produces warning
> mod <- glm(analogs ~ Dij, data = dat, family = binomial)
> ## plot the data
> plot(analogs ~ Dij, data = dat)
> fit.mod <- fitted(mod)
> ord <- with(dat, order(Dij))
> with(dat, lines(Dij[ord], fit.mod[ord], col = "red", lwd = 2))
>
> #### End code snippet  
> ##################################################
>
> Thanks in advance
>
> Gavin
> -- 
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> Dr. Gavin Simpson             [t] +44 (0)20 7679 0522
> ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
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