[R-sig-eco] Multivariate quasi-bionomial analysis of proportion data?

[Bob O'Hara]

On 08/02/15 12:27, Amanda Greer wrote:
> Hi All,
>
> I am trying to best analyse a set of foraging ecology data with >10
> behaviour categories (DVs) and 3 levels of IV (season, sex, age). The time
> which an animal spent engaged in a behaviour was recorded and then divided
> by the total time spent in sight of the observer, so my data are
> proportional. As is typical, not all animals engaged in all behaviours and
> there are a large number of zeros in my dataset which is severely
> over-dispersed. I had initially analysed all the data using the glm
> function (family = quasibinomial, followed by anova. The intention was then
> to use the false discovery rate alpha to account for the large number of
> analyses. However, it was pointed out to me that a multivariate approach
> might be better so I have been trying to figure out (a) if it's possible to
> run a quasi-binomial multivariate analysis of proportion data  (b) how to
> go about it.
>
> In the R Documentation quasi-binomial family function page (
> http://artax.karlin.mff.cuni.cz/r-help/library/VGAM/html/quasibinomialff.html
> ) it is stated that if multivariate response = TRUE the response matrix
> should be binary. This seems a pretty straightforward indictment of my idea
> to run this analysis on my proportion data, but I am wondering why - is
> this just not possible, or is there a particular package that could help?
> If anyone could provide me with an answer or some much needed guidance on
> this topic I would be very grateful.
Ignoring the zeroes problem for the moment, I think (quasi-)binomial 
distributions are a distraction: binomials are based on counts of things 
(see Petr Keil's post: http://www.petrkeil.com/?p=603). If you're 
looking at proportions of times, then it might be better to think in 
terms of gamma distributions, which lead to a beta distribution for the 
proportion of times spent doing one thing, and a Dirichlet distribution 
if you have several items (as you do here).

Once you have to worry about the zeroes, you need to do something more, 
for example see this paper:
<http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12122/abstract>

Bob

> Thanks,
>
> Amanda
>
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>
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-- 

Bob O'Hara

Biodiversity and Climate Research Centre
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