Hello, I'm hoping someone can point me in a new direction with this
particular issue...

I have count data for many species across 20-30 years.  I know that many
species are declining, probably in association with habitat destruction, and
I have been using binomial regression to model the declines
(e.g. glm(cbind(presence,visits-presence)~years,binomial).  I have also used
the glm.binomial.disp function for overdispersion.  So far so good, but
here's the issue: not all species decline in the same way...

Some go down steadily over the years, while others will be holding steady
and then suddenly start on a decline.  There are other patterns, but those
two are dominant and I would like to be able to say that different species
have these different dynamics.  But how do I quantify those different
curves?  I have played with fitting quadratic and cubic terms within the
binomial
regression (e.g.
glm(cbind(presence,visits-presence)~years+I(years^2),binomial)),
and then comparing models with AIC to think about the better fit of the
model with the quadratic.  That kinda makes sense for some species, but it's
far from satisfying... In the case I described (a species holding steady for
2 decades and then going into a steady decrease for another 10), what it
really looks like is two different lines, one flat and one precipitous.

Is there a way to ask if a given relationship is better fit by two lines
than one?  any other hints on how to describe these kinds of dynamics?

thanks!
Matt


-- 
Matthew L Forister
Assistant Professor
Department of Biology / MS 314
1664 N. Virginia St.
University of Nevada, Reno
Reno, Nevada 89557
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