Can I drop a variable from a logistic regression, score on the other variables and then add back in for a different model? (See Body) So what I have is a logistic regression equation with the first variable having a large (not overly so) coefficient ie.
ln(p/1-p) = C + B1V1 + B2V2 + B3V3 + B4V4 +B5*V5
Because this coefficient is so large there is a need to remove this as part of a strategy but we could also try to adjust the power of this variable in the above model. I’ve considered ridge regression but I think the following method is much simpler and quicker if it indeed works.
My question is can I have the following model with B1*V1 removed:
ln(p/1-p) = C + B2V2 + B3V3 + B4V4 +B5V5
Then convert to a score base on pdo and base score and use this score to go into a new model with the previous first variable ie.
ln(p/1-p) = C + B1.1*(Score calculated from first model) + B1*V1
And would this result in the same model? I am thinking it would not because the iterative process would have less coefficients to optimise and the score from the previous model would be much more predictive than the variable we dropped and used in the second model.

In most cases, having a variable with a very large $\beta$ in the logistic model, even with $\beta=\infty$, does not cause a problem.  It still leads to the right probability estimate.  Of course we don't really believe the probability to be 1.0, and penalized maximum likelihood estimation will lead to a more reasonable probability.  But if you flip a coin 10 times and get 10 heads the maximum likelihood estimate of P(heads) is 1.0, leading to a log odds of $\infty$.
Large $\beta$ is not a reason to remove a variable from the model.  Only worry about this if you get probability estimates that don't make any sense.
