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
------------------------------------------------------------------------------


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.

• Thank you very much for your post, subra. I tried to stick closely to your instructions and accomplished the comand ". margins, dydx(ExpDel)" in stata. You find the output in my original post. Do I Need to run this command over all my categorical (and now binary) variables I'd like to rank and then just need to compare the value dy/dx? The higher the more influence on my dependent variable? Thank you very much! Aug 26 '15 at 9:51
• @ Lukas:Yes, you are correct. In Stata, for discrete data, the 'margins' actually calculates the effect of a discrete change of the co-variate. Therefore, you only have to compare the dy/dx (from margins) for all the categories (now binary). The higher the value the more influence. Aug 26 '15 at 20:25
• @ subra: Thanks for clarifiying. The above mentioned procedure leads to the same ranking as if I would just rank the respective logit coefficients. I am still not sure about why I may refer to the marginal effects for ranking purposes and not to the logit coefficients. Do you have a source you could recommend for further readings? Furthermore, I am not sure why I should use the above mentioned stata command and not add, e.g., "atmeans" in order to use the means of the other variables for comparison purposes. Thank you very much. Aug 27 '15 at 8:16
• @ Lucas: Yes, you are rite. If you only wanted to rank the predictors, then logit coefficients should be sufficient. I am not clear with your second part of the question. if you are asking why we have to evaluate the marginal effects, please check the following post: stats.stackexchange.com/questions/167811/… Aug 27 '15 at 15:06

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...

• No that would only provide marginal association measures. May 15 '16 at 18:52

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.