[R-sig-eco] Continuous distribution for zero or positive values (inGLM or GLMM)

[Fred Takahashi]

Ben and Ruben, thank you very much  for the suggestions. I started the
“homework” and I had the impression that I can forget to find a GLMM
implementation with Tweedie distribution (in a preliminar GLM, this
distribution produced a very decent fit...). However the two-part
analysis looks a good option. About the transformation of continous
data to discret (to fit a poisson distribution), wouldn't include some
subjectivity in the analysis (once the "size of container" of the
Ruben example need to be choosed)?

Regards
Fred


2011/5/19 Rubén Roa <rroa at azti.es>:
> This is a well known modeling issue and several approaches are available.
>
> We have tried the Delta approach with good results. This is essentially a binomial glm for the presence-absence representation of the data, and conditional on the Bernoulli variable being 1, a regular continuous distribution such as Gamma glm for the positive values. Option 3) in Ben Bolker's list.
>
> See
>
> Aitchison, J. 1955. On the distribution of a positive random variable having a discrete
> probability mass at the origin. Journal of American Statistical Association 50, 901-908
>
> Pennington, M. 1983. Efficient estimators of abundance, for fish and plankton surveys.
> Biometrics 39, 281-286
>
> Another option is to transform your continuous response into counts. For example, if you have 0.745 kg of grass from one plot, how many stahdard 100 ml containers can you fill in a standardized manner with that? That's a count. Now if you turn your grass biomass into counts and if you are lucky (not excessive number of zeroes) then maybe a Poisson glm will be good. And the Poisson does not bug you with nuisance parameters ...
>
> We tried several things like that, and also the Tweedie distribution (number 4) in Ben Bolker's list) in this paper:
>
> Tascheri, R., Saavedra-Nievas, J.C., Roa-Ureta, R. 2010. Statistical models to standardize
> catch rates in the multi-species trawl fishery for Patagonian grenadier (Macruronus magellanicus)
> off Southern Chile. Fisheries Research 105: 200–214
>
> Adding a constant to the zeroes is just not right (see p. 324 of the below quoted article for an authoritative sentence on this matter):
>
> Venables, W.N., Dichmont, C.M. 20004. GLMs, GAMs and GLMMs: an overview of theory for
> applications in fisheries research. Fisheries Research 70: 319–337.
>
> HTH
>
> Rubén
>
> ____________________________________________________________________________________
>
> Dr. Rubén Roa-Ureta
> AZTI - Tecnalia / Marine Research Unit
> Txatxarramendi Ugartea z/g
> 48395 Sukarrieta (Bizkaia)
> SPAIN
>
>
>