>
> Dear Gavin Simpson,
> Thanks for your help and yes, I mean generalized linear model instead of
> general linear model. My first attempt analyzing my dataset was with the
> glm() function. Taking a closer look on my data both functions (glm() and
> mle2()) gave the same results. The glm() didn’t return warnings when I
> considered the categorical variable where one of the groups showed no case
> of predation. Again, the standard errors are extremely high, and I am
> interpreting such thing as analytical problem. Am I right?


This is likely due to a problem called *separation, *where some linear
combination of predictors results in perfect prediction of either outcome.
If this occurs, the standard glm analysis will always result in a huge
standard error for the predictor in question, since the "true" parameter in
this case, at least according to maximum likelihood, is infinitely large. In
your case, it means that glm is trying to assign a parameter of -inf to
the species a-b coefficient.

>
> The idea to include such variable among the tested models was to be
> consistent along my manuscript, where I defined, with biological arguments,
> the necessity of such categorization. However, given that one of the
> groups
> resulted in no case of predation, could be correct to run the analysis only
> with those groups where predation occurred?


I wouldn't throw out the groups where no predation occurred, especially
since that fact may be incredibly biologically relevant! Fortunately, you
can get around the separation problem by introducing some regularization, by
imposing a weak prior on the distribution of potential logistic regression
coefficients. This is well-described in the paper "A weakly informative
default prior distribution for logistic and other regression models" by
Andrew Gelman (2008), and he's implemented as the function bayesglm in the *
arm* package.
In your case, I'd start by trying just the basic bayesglm, using the default
parameters for the priors, since they're designed to be fairly conservative
and work over a wide range of different model situations. For your data, the
models you listed would look like:

m1 <- bayesglm(predation ~ 1, family = binomial)

m2 <- bayesglm(predation ~ size_difference, family = binomial)

m3 <- bayesglm(predation ~ size_difference*treatment, family = binomial)

m4 <- bayesglm(predation ~ size_difference*pairing, family = binomial)

m5 <- bayesglm(predation ~ size_difference*treatment:pairing, family =
binomial)

the *arm* package also provides the *display* function, which is a somewhat
more easily interpretable verision of summary.glm. Just use display(m1) to
see the output.

Eric


> I mean, I could verbally explain
> the analysis of only a subset of my data, since there is no biological
> meaning to infer about some effect of any variable over predation risk in a
> situation where predation did not occurs...
> Thanks again for your attention. Best wishes!
> Ernesto



-- 
Eric Pedersen
PhD. candidate
Biology department, McGill University
Guichard lab

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