Logistic/Probit Regression if the response variable is not a probability

I am working on a model which involves predicting a ratio between 0 and 1 using a number of variables. The ratio in question cannot be thought of as a probability. I am wondering if a logistic regression or profit regression is appropriate.

For example: $Y \sim a_0 + a_1 X_1 + a_2 X_2 +... + error$, where $Y \in [0, 1]$ and Y is not a probability.