Suppose I want to build a model to predict some kind of ratio or percentage. For example, let's say I want to predict the number of boys vs. girls who will attend a party, and features of the party I can use in the model are things like amount of advertising for the party, size of the venue, whether there will be any alcohol at the party, etc. (This is just a made-up example; the features aren't really important.)
My question is: what's the difference between predicting a ratio vs. a percentage, and how does my model change depending on which I choose? Is one better than the other? Is some other function better than either one? (I don't really care about the specific numbers of ratio vs. percentage; I just want to be able to identify which parties are more likely to be "boy parties" vs. "girl parties".) For example, I'm thinking:
- If I want to predict a percentage (say,
# boys / (# boys + # girls), then since my dependent feature is bounded between 0 and 1, I should probably use something like a logistic regression instead of a linear regression.
- If I want to predict a ratio (say,
# boys / # girls, or
# boys / (1 + # girls)to avoid dividing-by-zero errors), then my dependent feature is positive, so should I maybe apply some kind of (log?) transformation before using a linear regression? (Or some other model? What kind of regression models are used for positive, non-count data?)
- Is it better generally to predict (say) the percentage instead of the ratio, and if so, why?