I'm attempting a multiple regression model where the predicted variable is runoff ratio - the ratio of watershed discharge to the precipitation input. This should generally be bounded [0,1], however, due to measurement error some values > 1 occur.
Originally, I modeled this with the predicted variable un-transformed, but logistic regression has been suggested to me, I also have heard Beta regression suggested. I'm not sure how to proceed, and if these transformations are appropriate to my data:
My questions are: 1) Is a logistic regression appropriate for these data? and 2) If I were to proceed with logistic regression, would I need to convert the runoff ratios to proportions, or would I apply the logit to the values as they are?
Sorry if these are obtuse questions - I'm new to logit and most of the information I have found is for binary response variables.
Edited for suggested additions: As a simple version: I am modeling runoff ratio (rr) as an effect of precipitation (pcp) and antecedent water table position (ant):
rr ~ pcp + ant
rr is a continuous variable. I am not interested in the probability of specific values, rather I'm interested in the values themselves - both to assess the significance of the predictors and as a predictive model.
Conceptually, I was fine modeling it un-transformed. However, a simple linear regression allows predicted values outside of the physical range of [0,1]. As mentioned above, measurement error does lead to values >1, which I'll eventually have to deal with.