Is a beta regression appropriate for a skewed bounded continuous dependent variable when sample size is small? My data contain a bounded continuous variable (score between 0 and 10) representing the efficacy of a given method to control an invasive species. As there are more high scores than low ones, the variable is skewed to the left. My purpose is to identify which independent variables explain this dependent variable. In other words, I would like to know which variables affect the efficacy of the method.
According to some answers I found on CV (e.g. here), a model with a beta-distribution family could be used to model the relationship between my variables. However, considering that my dependent variable is fairly skewed and that I have a small sample size ($n$ = 98), I was wondering:

*

*If a model with a beta-distributed response would be the most appropriate option here? (Provided that I transform my DV so as to lie between 0 and 1, but with no 0 and no 1, right?)

*If there was a sort of rule of thumb regarding the minimum number of observations per predictor possibly included in this type of model?

 A: It seems that an ordinal model makes more conceptual sense. A cumulative logit is a standard as is an ordinal logit model (there are slight differences in approaches).
In Harrell's Regression Modeling Strategies, section 4.4 p. 73, the author presents a few considerations for sample size. He says that the number of variables in the model should take into consideration a limiting factor. $p$, the number of variables in the model should be less than $m/20$ where $m$ is the limiting factor.
Just for clarification, in the case of a continuous variable, $m$ is the total sample size, so with 100 in the sample, a model should have at most 5 parameters estimated. Remember that a categorical variable with 7 categories entails 7-1 parameters estimated.
For the case of an ordinal outcome, the sample limiting factor $m$ is given by:
$$
n - \frac{1}{n^2} \sum_{i=1}^{k} n_i^3
$$
where there are $k$ categories in your outcome and $n_i$ is the sample size of category $i=1,...,k$.
Here you have a good tutorial for ordinal response modeling in a Bayesian setting.
