Linear regression models do not assume independence of the coefficients and thus dummy coding is often the only coding that is taught in this context. It captures all of the coefficients, but it complicates matters when the model assumes independence of the coefficients such as in ANOVA. On the other hand, a set of contrasts for a categorical variable with k levels is a set of k-1 functionally independent linear combinations of the factor level means that are also independent of the sum of the dummy variables. This is because the dummy variables add to one and are not functionally independent of the model’s intercept. In fact, the dummy coding is not technically a contrast coding. There are, however, different coding methods that amount to different sets of linear hypotheses. This dummy coding is called Treatment coding in R parlance, and we will follow this convention. That is, each test statistic for these variables amounts to testing whether the mean for that level is statistically significantly different from the mean of the base category. This amounts to a linear hypothesis on the level means. This document is based on this excellent resource from UCLA.Ī categorical variable of K categories, or levels, usually enters a regression as a sequence of K-1 dummy variables.

Ordinal encoding in r