This is a hacky question. What I'm hoping for is answers that identify and explain the problems and possible solutions.
I'm dealing with some code that is already in production that uses a logistic regression model. The existing model was trained by treating the response variable as a boolean.
What I would like to try is modeling the same training data with a continuous response variable from -1 to 1 (conceptually the same response variable, just stop pretending it's boolean, which it isn't). I would train various linear regression models and try to evaluate whether or not there is any improvement over the existing logistic regression model.
My questions are:
- Can I simply plug into the existing production logistic regression by substituting the linear regression coefficients and intercept? I'm wondering if the logit function will just be applied to the new linear regression equation, and the result will be a valid 0 or 1 classification.
- How should I compare the results of the new linear regression to the old logistic regression? If the answer to my first question is affirmative, then I can just evaluate the precision and recall of the two "classification" models. Otherwise, I suppose I could run the linear regression model separately and then apply a threshold to its continuous response variable, and then treat that as a classification.
- Is it reasonable to expect an improvement with this methodology?