[R-sig-ME] [R] Problem specifying Gamma distribution in lme4/glmer

[Ben Bolker]

  [Moving this to r-sig-mixed-models ]

David Winsemius wrote:
> On Mar 21, 2010, at 5:16 PM, Ben Bolker wrote:
> 
>> Dieter Menne <dieter.menne <at> menne-biomed.de> writes:
>>
>>> Ben Bolker wrote:
>>>> 3. zero-inflated data may not be particularly well-represented
>>>> by a Gamma distribution: if you actually have a significant number
>>>> of exactly-zero values, you may want to analyze your data in two
>>>> stages, first as a presence-absence problem and then as a  
>>>> conditional
>>>> density (i.e., what is the distribution of the non-zero values)?
>>> [...] Do you know of a example where this was done (independent
>>> of lmer)?  [...]
>>  Nothing springs to mind, but it seems sensible.
> 
> I thought this was what hurdle and ZIF models were supposed to handle  
> gracefully?

  hurdle/zero-inflated/zero-altered models are typically developed in
the context of discrete (count) data, where the base model has some
non-zero probability of recording a zero and has to be altered to
account for the presence of extra (or missing) zeros.  In this case
(continuous data) the gamma distribution has an infinitesimal
probability of producing an exact zero, so it's actually easier to deal
with the data as a mixture of zeros (with probability p) and
Gamma-distributed values (with shape and scale or rate parameters
specified).  If it's OK to model the mixture process and the conditional
density separately this is actually easier than a hurdle or ZIF model.

  Another possibility, which I've heard of but not ever looked at
carefully, would be to use Tweedie distributions with 1<p<2:

http://en.wikipedia.org/wiki/Tweedie_distributions
http://cran.r-project.org/web/packages/tweedie/index.html

  Incorporating random effects could be tricky, though: a mean-variance
relationship is given for Tweedie distributions (V = phi*mu^p), so
conceivably the fitting could be done as a two-dimensional search over
the GLMM fits obtained for fixed values of (phi,p).  (Yikes.)

  Ben



-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / people.biology.ufl.edu/bolker
GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc