[R-sig-ME] zero-inflation with mixed-effects, glmmADMB, and cloglog

[Ben Bolker]

Anne Bjorkman <annebj at ...> writes:


> 

 [snip]

> Do you (or anyone else from the list) have any advice for me about using
> the slope parameters from the mixed-effects models? My original email was
> probably far to long for anyone to read, so I will paraphrase my primary
> question here very briefly:
> 
> I am interested in change over time, so I would like to use slope
> parameters for a number of different species (abundance data for 154
> locations of 42 different species, measured in 5 equally-spaced years, the
> same locations are measured in each year, thus the need for a random effect
> of location).  I would like to model each species separately and use the
> slope parameter from each model as an estimate of the direction and
> magnitude of change over time for that species.  However, the distribution
> of the data for each species are quite different - some are highly
> zero-inflated, others are nearly normal.
> 
> My question is this: should I use the same model specifications for every
> species (e.g., use negative binomial/zero-inflated distributions even for
> those species that appear more normally distributed), or can I use the
> "best" model for each species (based on the distribution of the data for
> that species) and still compare the slope values to each other?  The
> important thing is that the slope values are comparable, because I am
> interested in how much each species has changed relative to the other
> species.
> I don't often see slope parameters from mixed models used in this way, so I
> am a little hesitant about the feasibility of what I'm trying to do. Any
> insight would be hugely appreciated.
> 
> Thanks very much!
> Anne
> 

  It depends a bit on what you mean by "compare". In any case you need
to make sure that the slope parameters are measuring the same thing --
so for example it would be a bad idea to compare (1) parameters
estimated using a model with a log link (e.g. negative binomial), so
that the parameter represented an exponential growth rate or
per-capita proportional change per year and parameters estimated on a
raw scale and (2) parameters estimated on the data or identity scale
(e.g. ordinary least-squares regression), so that the parameter
representing a linear rate of increase -- then you would be comparing
apples and oranges.  Similarly, if you have a model that incorporates
zero-inflation, you need to make sure that you're comparing a quantity
that reflects the change in the _mean_ density over time. On the
other hand if you use a zero-inflation model with a constant level of
zero-inflation over time, then the means at times t and t+1 will be
(1-p_z)*mu(t) and (1-p_z)*mu(t+1), so you should be able to disregard the
zero-inflation if you're comparing the proportional growth rate.
  At this level, just making sure that you know what your slope
parameter means, and that you are comparing comparable things, should
be sufficient.

  The next-level issue is doing _statistical_ comparisons among
species (i.e. species A is shrinking significantly faster than
species B).  Ideally you would do this by incorporating all of the
data in a single model and testing the significance of the
species*time interaction coefficients, but that would be hard
with your data.  It's a bit crude, but you could do _post hoc_
t-tests based on the estimated slope parameters and their
standard errors ...