In a comment on another question, clarification was asked if the topic under discussion was "count proportions" or "continuous proportions", and a followup indicated that the difference was critical information (to the topic of logistic/binomial vs. beta regression).
What is the distinction between the two, and where does the distinction matter? What are important things to keep in mind when working with "count proportions" versus when working with "continuous proportions"?
Best Answer
Perhaps an example would help. Suppose you observe a number of people and count how many of them are women. The resulting proportion is what is called a count proportion and takes on values between zero and one but only $n+1$ of them where $n$ is the total number you observed. Suppose you buy a sausage from your local supermarket and observe on the label that it is 80% pork that is an example of a continuous proportion and could take on any value between 0 and 100.
The distinction in modelling is that in the first case it is meaningful to predict the probability of a random person being a woman (logistic regression) but in the second case that is not a sensible question and something else (often beta regression) would be preferred.