I want to fit a logistic regression model where predictor variables have different weights. Can I achieve this by not normalizing the variables?
For example let's say I have two predictor variables A and B. If the range of A is [0,10] and the range of B is [0,20] will my model give twice as much importance to B compared to A? If not, what is the solution?
If you want to give $B$ twice of the weight of $A$, then you may consider to estimate the following model $$ \log\left(\frac{p}{1 - p} \right) = \beta_0 + \beta_1(A+2B)\quad (1) $$ Or alternatively, you can estimate $$ \log\left(\frac{p}{1 - p} \right) = \beta_0 + \beta_1A+\beta_2B, \quad (2) $$ and then to check the hypothesis $H_0: \beta_2 = 2\beta_1$ by comparing model $(1)$ with $(2)$ using the Deviance residuals.