I am using fractional response regression for dependent variable that can take values anywhere between 0 and 1, inclusive, in the same spirit as the Papke/Wooldridge. My setup looks like:
E(y|X) = G(XB) = 1 / (1 + exp(XB))
0 <= y <= 1.
Now, when the predictions, y_hat, are made, it looks like the predicted values range from (0,1), and not [0,1] because the function G above is specified as the logistic function.
Is this right?
It was not clear in the Papke/Wooldridge paper because the references were made to the unit interval. I am not sure if the unit interval means (0,1) or [0,1] for the range of the predicted values.
The paper I am referring to is
ECONOMETRIC METHODS FOR FRACTIONAL RESPONSE VARIABLES WITH AN APPLICATION TO 401 (K) PLAN PARTICIPATION RATES
LESLIE E. PAPKE AND JEFFREY M. WOOLDRIDGE
JOURNAL OF APPLIED ECONOMETRICS, VOL. 11, 619-632 (1996)
In the processing editing my initial question, I found the answer to my question in p.612 of the paper, which was
This ensures that the predicted values of y lie in the interval (0,1).