Bioequivalence and Bioavailability Forum

So we had a dataset, we got X constructed so that it was full rank and we didn't waste any time on meaningless babble about subjects nested in sequence. The number of columns of X is the rank, which is the number of rows in b, which is the number of constants we have freedom to determine. We're doing this by minimising ete. The story ends here, submit, get approval, celebrate.

Almost. I often do not fit with the intercept, and then I specify Treatment as the first factor. This means we do not have an interceept column in X, and the first two columns will be the two treatment columns. This is very handy, because then the first two estimates or constants in b are the treatment effects: One for Test and one for Reference.
So we just extract these to estimates from the b-vector and use them directly for the construction of the confidence interval. Note that the residual sum of squares is not affected by this. It doesn't matter which factors you specify first or whether you want an intercept. If you have one way or another Period, Subject, Sequence, Treatment in your model, then regardless of the permutation of the order of them the mean squared error is unaffected.