I'm working on a health care outcome regression model using the deviation contrast scheme described on the UCLA SAS help page here for a collection of dichotomous predictor variables measuring medical diagnoses. Everyone in my analysis dataset has one primary diagnosis. Deviation contrast coding would compare each diagnosis category with the other categories. However, as illustrated in the example with the hsb2.sas7bdat dataset using the race variable, one category (White) is still left out of the regression model.
My question: Is there a way to code deviation contrasts comparing each level to the grand mean with no reference category while avoiding one variable level being a linear combination of the others?