Yes, but.... [🇷 for BE/BA]

posted by ElMaestro  – Denmark, 2024-02-23 18:41 (56 d 16:40 ago) – Posting: # 23878
Views: 648

Hi Mittyri,

❝ I have nothing to add to this: that's a price for identifiability. The only solution I see besides you already gave is to turn off the contrasts as shown there:

f <- sample(gl(3, 4, labels = letters[1:3]))

❝ # [1] c a a b b a c b c b a c

❝ #Levels: a b c

❝ g <- sample(gl(3, 4, labels = LETTERS[1:3]))

❝ # [1] A B A B C B C A C C A B

❝ #Levels: A B C

❝ X0 <- model.matrix(~ f + g, contrasts.arg = list(

❝                    f = contr.treatment(n = 3, contrasts = FALSE),
❝                    g = contr.treatment(n = 3, contrasts = FALSE)))

Nice, but are you aware that this model matrix is also not full rank, but rank-deficient? A cardinal question was how to get the (or a) full rank matrix.
The rank of your X0 is 5 but there are 7 columns. Seems you went to the opposite extreme of full rank, i.e. one column for every level of factors, plus intercept. Deficiency here = 2 redundant columns.
Anyways, I guess I will just live with it and do my stuff in a dumb but necessary fashion. Keep me posted if you find a nifty way of generating a full rank matrix model, please.:-)

Pass or fail!

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