Constraints for Dummy Variable

Definition

When using Dummy Variable, the design matrix $X=[1,2,D_1,\dots ,D_c]$ where $c$ is the number of groups, is not a full rank. The problem can be solved by assigning some constraints.

Sum-to-Zero Constraint

Sum-to-zero constraint uses row-wise demeaned dummy variables. $\sum _{i=1}^c{D}_j=0$

With sum-to-zero constraint, each coefficient indicates discrepancy from overall mean, and the intercept term indicates overall mean.

Corner-Point Constraint

Corner-point constraint omit a base group from the model. $X=[1,D_2,D_3,\dots ,D_c]$

With corner-point constraint, each coefficient indicates discrepancy from base group, and the intercept term indicates mean of base group.