Controlling for categorical variables when generating logistic regression elasticity curve

Question

Assume we have a multiple logistic regression model with 3 continuous independent variables (x1,x2,x3).

I understand that if we want to create an elasticity curve for a continuous variable of interest (let's say x1) in a multiple logistic regression model, first we need to control for all the other continuous variables (x2 and x3) by averaging them and using the averages in the logistic regression equation to generate the predicted probabilities (y^) over a range of expected values for the variable of interest, x1. (see Miller, Marketing Data Science, ch.2 fig 2.4)

My question is what if we have a binary variable and a categorical variable in the model. How do we control for them? I would assume that we have to create a separate curve for each combination of the 2 categorical variables.

Any guidance would be much appreciated.

Answer 1

Let X2 be gender (0 = male, 1 = female), and X3 be height. Assume the mean of X2 is 0.37 and mean of X3 is 5.5001 ft. it is difficult to explain the elasticity curve based on the means X2 and X3, because we do not have a person with gender = 0.37. So under this situation, the separate elasticity curve for male and female should be generated.

For the continuous variable, we do not need to insist on its mean. We can select the value that more meaningful in practice. In the example above, I prefer to set height at 5.5 ft, instead of mean of the height 5.5001 ft.

For the categorical variable, you can just pick up several of them that you are interesting in, instead of all of them, if this variable has many unique values.