[R-sig-eco] glm for ratio [0,1] data

[Marcelino de la Cruz]

Hi,
Venables and Ripley, commenting on the use of glm with binomial family
(MASS book, page 190):
"If  the response is a numeric vector it is assumed to hold the data in
a ratio form, y[i] = s[i]/a[i], in which case tha a[i]s must be given as
a vector of weights using the weights argument".
So, if your ratio comes from e.g. estimating cover as s[i] cells occupied
from a total of a[i] cells in a sampling grid, you still can use the
binomial glm.

I recal that another possible aproch could be betaregression (see package
betareg).

Cheers,

Marcelino

Con fecha 31/8/2009, "Peter Solymos" <solymos at ualberta.ca> escribió:

>Hi Bálint,
>
>Here are my two cents.
>
>By using LM with transformed data (which transformation can also be
>logit, loglog, cloglog, probit) you loose the Binomial error
>structure, because you won't follow the trial/success experiment
>scheme. But percent cover is not that kind of [0,1] data where this
>sampling is assumed, I think that's why you have asked :)
>
>If your data is an estimate of a hidden response, than there must be
>ways to account for this, but I can only recall an example where e.g.
>Y is Poisson, but you observe it as ordinal (0, few, many). So you can
>establish cutoff values to get ordinal response from you percent
>cover, and use a hierarchical model in BUGS/JAGS (see WinBUGS manual
>for an example).
>
>Cheers,
>
>Peter
>
>
>On Mon, Aug 31, 2009 at 6:24 AM, Bálint Czúcz<czucz at botanika.hu> wrote:
>> Dear List,
>>
>> does anyone know a good way to perform GLM on ratio data (i.e. data
>> between 0 and 1)? Binomial GLM is quite straightforward to use if you
>> have integer numbers for successes/failures. But how to proceed if you
>> only have the ratio? This can occur in a multitude of ways, e.g the
>> response variable is the estimated cover of a species, percentage of
>> canopy lost, etc.
>>
>> One solution I know about is to try to transform such responses to
>> normal with the arcsine-squarroot transformation, and use lm on the
>> transformed response -- e.g. Crawley (2007, The R Book, p. 570.)
>> explicitely suggests this strategy.
>>
>> But I would still be interested if there is a glm approach that could
>> be used with the untransformed data. After hours spent with searching
>> for literature on such a glm, I couldn't find any. Do you know of
>> some?
>>
>> I would also be interested what happens if I just proceed with a
>> binomial glm with the response being between [0,1] and weights left to
>> 1. I know glm() will throw a warning -- but it also produces an
>> output. Can this output contain some valid, interpretable results, or
>> is it completely bullshit because of the violation of the assumptions?
>>
>> Thank you!
>> Bálint
>>
>>
>> --
>> Bálint Czúcz
>> Institute of Ecology and Botany of the Hungarian Academy of Sciences
>> H-2163 Vácrátót, Alkotmány u. 2-4. HUNGARY
>> Tel: +36 28 360122/137 Â +36 70 7034692
>> magyar nyelvű blog: http://atermeszettorvenye.blogspot.com/
>>
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>>
>>
>
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