Logistic regression with multicategory categorical explanatory variables I'd like to perform logistic regression with some categorical explanatory variables with more categories than just binary 0/1. Is this possible and why?
I am inclined to think that this would give just the wrong result because of the geometric intuition, however most opinions online say that explanatory variables can be discrete/categorical (although I don't see any mentions of more categories). For 0/1 this is fine because the distances between 0 and 1 is easy.
If I have even 3 categories 0/1/2, it's unclear if 1-0 is the same as 2-1.
One thought I had is to do a sort of one-vs-all thing for the explanatory variables. So if I had one parameter that can on 3 categories A/B/C I remake this into 3 separate parameters:   A: 0/1
B: 0/1
C: 0/1

Where 0 is not belonging to the letter class and 1 is belonging to the letter class.
Background: My dependent variable should be binary. I really wanted to use logistic regression because of the probability interpretation. If you can recommend another method that can output a probability estimate (instead of only classification) that takes in categorical explanatory variables, that would also be helpful.  
A: The comments from @Scortchi and @Penguin_Knight essentially say it all. Any generalized linear model can handle categorical predictors, and several options exist to accommodate different styles of comparison. Dummy coding is probably simplest, and would only require you to drop one of your binary parameters corresponding to your choice of a reference group. Scortchi's link to the UCLA Statistical Consulting Group's R Library: Contrast Coding Systems for categorical variables page covers this and many other coding options nicely with r code included.
Sorry I don't have more to add; it seems you already understand the method, and I don't know of any other methods to recommend for your specific purpose, nor do I see the problem with the geometric intuition...Feel free to expand on that though.
