[R-sig-ME] decimal data with nested random effects

[Ben Bolker]

Claire Brittain <cabrittain at ...> writes:

> I have some decimal data (a diversity index) with nested random effects
> (sites within years).
> 
> There are a lot of zeros in the diversity index (19 out of 61 data points).
> 
> I would like to investigate the effects of two variables (one continuous,
> one categorical) on the diversity index.
> 
> I am more familiar with modeling count data and would set up a mixed model
> with Poisson error and a subject level random variable for overdispersion
> (there is one data point per site, per year so in the model below the random
> effects are at the subject level).
> 
> model1<-lmer(DiversityIndex~categorical_variable*continuous_variable+(1|Year
> /Site),family=poisson)
> 
> However I get the error that the poisson distribution is for integers only -
> although if I look at the summary of the model the output still looks
> sensible. Can I use the poisson distribution on non-integer data?

  It's dicey.  You _could_ make the argument that you're just trying
to get the mean-variance relationship right (although in that case
you would probably be better off using lme with a varPower() variance
structure ...)

> The diversity index cannot be transformed to normal and I need to keep the
> nested random effects in the model so I am not sure what error distribution
> I should be using for non integer, non normal data with nested random
> effects?
> 
> Any suggestions as to the type of model/family I should be using would be
> much appreciated.

  It's pretty tough.  Tweedie distributions are possible (and there is
a cplm package that implements mixed models with Tweedie distributions),
but with a non-huge data set I might be tempted just to use something
simple (e.g. linear models) and do some kind of resampling solution
(bootstrapping, permutation test, etc.) to get confidence intervals/p
values -- the hard part being that you have to be careful with
resampling when you have blocking in your data.