Fitting in a Model a beta distribution with within-subject variable involved: formula requested

Question

The distribution of my dependent variable called st follows the Beta distribution (visible through the command descdist). Now I have to create my model. The only problem is that my experimental design is a 3x2, where I have an IV called temp, a factor with 3 levels measured within participants (the same participants at different time), and an IV called cond, a factor with 2 levels measured as a between-participants effect (two different groups). I want to see both main effects and interaction effects. So far I have applied the betareg() formula for beta distribution after fitting the distribution with fitdist(). The only problem is that I don't know how in the betareg() formula I can indicate that my temp variable is within while my cond variable is between subjects. Can you help me out?

I tried to apply this formula:

MSTb=betareg(scaledst~temp*cond, data=ds.cy)

and then the ANOVA

Anova(MSTB)

It gives me a result but I think it doesn't considered the repeated measure situation.

Applying this formula instead doesn't work:

MSTb=betareg(scaledst~temp*cond+(1|id), data=ds.cy)

Where "id" is the Code of the participants to filter. It gives me this error: Error in

`contrasts<-`(`*tmp*`, value = contr.funs[1 + isOF[nn]]) : 
  the contrast can be applied only to factors variable with 2 or more levels 
In addition: Warning message:
In Ops.factor(1, id) : ‘|’ not meaningful for factors 

neither this one:

betareg(scaledst~temp*cond+(1+temp|id), data=ds.cy)

Error in `contrasts<-`(`*tmp*`, value = contr.funs[1 + isOF[nn]]) : 
  contrasts can be applied only to factors with 2 or more levels
In addition: Warning messages:
1: In Ops.factor(1, temp) : ‘+’ not meaningful for factors
2: In Ops.factor(1 + temp, id) : ‘|’ not meaningful for factors

Answer 1

betareg doesn't handle mixed models/random effects, so its formula processor is getting confused. You could try glmmTMB:

library(glmmTMB)
MSTb <- glmmTMB(scaledst~temp*cond+(1|id), data=ds.cy, family = beta_family)

Since temp is a within-subjects variable, and you have more than two levels (so the within-subject variation won't be confounded with the residual variation), you could try

scaledst~temp*cond+(temp|id)

to account for among-subject variation in the effect of temperature.

I believe the GLMMadaptive and brms packages also handle mixed models with Beta-distributed responses (although the Mixed Models task view is less clear on this than it might be ...)

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PS it doesn't really make sense to use descdist and fitdist to characterize the marginal (overall) distribution of your response; you need to evaluate whether the conditional distribution of the data follows some particular assumed distribution sufficiently well ...