I appreciate some help with deciding whether I should (and how to) construct a zero-and-one-inflated beta regression model. I want to use R to test the hypothesis that there is a
age interaction effect on
investment can be none (i.e. 0), half (i.e. 0.5) or all (i.e. 1). This makes
investment non-binomial, and, strictly speaking, inappropriate for a GLMM with
family = binomial. It looks like I should use
gamlss() to run a beta regression with
family = BEINF.
condition is a factor with 3 levels.
age is a continuous variable.
There is another fixed effect
sex, and a random effect
the mu.formula of a
gamlss beta regression should look like this:
investment ~ condition * age + sex + re(random = ~1 | groupID)
I have three questions:
Since my goal is hypothesis testing other than model selection, shall I just use something like
drop1to test the effect of each predictor?
If the answer to #1 is yes, how should I specify sigma.formula, nu.formula and tau.formula? (I am aware of the function
stepGAICAll.Afor selecting the best model, but that's kind of a forward model selection and my goal isn't model selection anyway).
Let's forget beta regression for the moment. How justified I am if I just go ahead and use a binomial GLMM via
lme4? The two reasons for this include:
investment has only three possible values (0, 0.5 and 1), it's clearly not a binary response, but it's not far from it. It doesn't look like a true frequency either. Even if I stick with zero-and-one-inflated beta regression, I have a hard time understanding what the mu.formula means? Does it mean the probability of
investment equals 0.5?
(2) a quote from this paper (Warton & Hui 2011 Ecology pp9):
For non-binomial proportions, there was never any theoretical reason to use the arcsine transform in the first place, and we instead suggest using the logit transform.
Thank you very much for your comments and suggestions in advance!