# Using continuous dependent variable which is already a probability (0,1) to predict probabilities (0,1)

I am building a model to predict probabilities based on the scores given by a logistic regression. I have tried cv.glmnet but it doesn't give the probability score, instead it gives scores lying in (-0.06,0.289).

Please suggest a modeling technique that would predict probabilities which uses probabilities from another model as a DV.

Note: I used the same input for glm.fit function and it gives predicted probabilities ranging from 0 to 1 even when the dv is supposed to be binary when the family is assigned as binomial(). I believe the result is error prone as it is not designed to do it. It would be helpful if someone can explain this anomaly.

• You can use glm() with a quasibinomial family! – kjetil b halvorsen Oct 17 '16 at 10:00
• Can you clarify why you think that glm.fit is erring when it gives you probabilities in [0,1]? What values were you expecting? – mdewey Oct 17 '16 at 12:42

What predict() function is giving you is the linear value for the regression (called $\hat{f}(X)$) ; that is:
$\hat{f}(X) = \hat{\beta}_0 + \sum\limits_{i=1}^n \hat{\beta}_i X_i$.
So, to obtain the predicted probabilities (called $\hat{\pi}(X)$), you should use this transformation:
$\displaystyle\frac{e^{\hat{f}(X)}}{1 + e^{\hat{f}(X)}} = \displaystyle\frac{\hat{\beta}_0 + \sum\limits_{i=1}^n \hat{\beta}_i X_i}{1 + \hat{\beta}_0 + \sum\limits_{i=1}^n \hat{\beta}_i X_i}$.