Ranking of categorical variables in logistic regression I am doing some research using logistic regression. 10 variables influence the dependent variable. One of the aforementioned is categorical (e.g., express delivery, standard delivery, etc.). Now I want to rank those categories based on the "strength" of their effect on the dependent variable. 
They are all significant (small p-value), but I think I can't just use the value of the odds for ranking purposes. I somehow need to figure out, if each category is also significantly different from the other categories. Is this correct?
I read about the possibility of centering the variable. Is this really an option? I do not want the rest of my model to be affected.

Stata output in order to support my comment to @subra's post:
Average marginal effects                          Number of obs   =     124773
Model VCE    : OIM

Expression   : Pr(return), predict()
dy/dx w.r.t. : ExpDel

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ExpDel |   .1054605   .0147972     7.36   0.000     .0798584    .1378626
------------------------------------------------------------------------------

 A: Since you are interested in ranking the categories, you may want to re-code the categorical variables into a number of separate binary variables. 
Example: Create a binary variable for express delivery- which would take the value 1 for express delivery cases and 0 otherwise. Similarly, a binary variable for standard delivery.
For each of these recoded binary variables you can calculate the marginal effects as indicated below:

Let me explain a bit on the above equation: lets say d is the re-coded binary variable for express delivery
  is the probability of event evaluated at mean when d=1
 is the probability of event evaluated at mean when d=0
Once you calculate the marginal effects for all the categories (re-coded binary variables) you can rank them.
A: You could fit the logistic regression model using only 1 variable at the time and examine the adjusted R2.
The one explaining most of the variance should have more impact on the model... 
I am just guessing, not sure that it is a rigorous solution...
A: This is a common question with a multitude of answers. The simplest is to use standardized features; the absolute value of coefficients that come back can then loosely be interpreted as 'higher' = 'more influence' on the log(odds). For the most part, using standard scores should not affect your overall results (ROC curve should be the same; confusion matrix should be the same assuming you choose a comparable decision threshold).  I usually compute the regression both ways; once using raw scores (to get the prediction equation I will use) and a second time using standardized scores to see which are largest.
As for categorical predictors, I assume (but have not checked) that the same holds true when using normalized predictors.
If you haven't already, you should also consider using regularization: Lasso/ridge/elastic net. This will help weak, irrelevant or redundant features to drop out, leaving you with a more parsimonious model.
