Is it mandatory to have a comparison group (one "tau" is coded as -1 and it does not have its own column)? If it is mandatory, can you explain why?
I am trying to represent the model Y=Xb+e in matrices. I have an X matrix that is a 24x3 matrix and includes a column called "mu" that only has 1, a column called tau1 and a column called tau2, tau 3 do not have a column, instead, tau3 is represented by -1 at the end of columns tau1 and tau2. I also have a b matrix that is a 3x1 matrix, that includes "mu", tau1 and tau 2. My question is: can I include in my X matrix a column for tau3 and replace the -1 for zeros(24x4)?, also, can I include the tau3 in my beta matrix (4x1)?