# Regression and contrast codings with multiple categorical variables

In regression with multiple explanatory categorical variables, how should I model the problem to compare the effects of the categorical variables with each other?

Most contrast coding schemes (e.g. also on Wikipedia) seem to be designed (or at least, that's how they are described) to compare the effects of different levels within a given categorical variable (e.g. German vs British nationality). But what if I want to compare contributions between categorical variables?

For example, say that we want to estimate the contribution of two explanatory categorical variables (dress size and color) to a single dependent variable (dress price). How can I design my coding to measure interpretable contributions of size and color to price?

• Thanks. I am still missing some level of detail on how to do this. Assuming that you have P(N-1) dummies (i.e. using one level per variable as a reference level), after fitting, how do I estimate the contribution of a full variable? – Amelio Vazquez-Reina Apr 6 '15 at 17:41