How to implement a mixed model using betareg function in R?

I have a dataset comprised of proportions that measure “activity level” of individual tadpoles, therefore making the values bound between 0 and 1. This data was collected by counting the number of times the individual moved within a certain time interval (1 for movement, 0 for no movement), and then averaged to create one value per individual. My main fixed effect would be “density level”.

The issue I am facing is that I have a factor variable, “pond” that I would like to include as a random effect – I do not care about differences between ponds, but would like to account for them statistically. One important point about the ponds is that I only have 3 of them, and I understand it is ideal to have more factor levels (5+) when dealing with random effects.

If it is possible to do, I would like some advice on how to implement a mixed model using betareg() or betamix() in R. I have read the R help files, but I usually find them difficult to understand (what each argument parameter really means in the context of my own data AND what the output values mean in ecological terms) and so I tend to work better via examples.

On a related note, I was wondering if I can instead use a glm() under a binomial family, and logit link, to accomplish accounting for random effects with this kind of data.

Answer

The current capabilities of betareg do not include random/mixed effects. In betareg() you can only include fixed effect, e.g., for your three-level pond variable. The betamix() function implements a finite mixture beta regression, not a mixed effects beta regression.

In your case, I would first try to see what effect a fixed pond factor effect has. This “costs” you two degrees of freedom while a random effect would be slightly cheaper with only one additional degree of freedom. But I would be surprised if the two approaches lead to very different qualitative insights.

Finally, while glm() does not support beta regression, but in the mgcv package there is the betar() family that can be used with the gam() function.

Attribution
Source : Link , Question Author : Kat Y , Answer Author : Achim Zeileis

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