Bioequivalence and Bioavailability Forum

Yes, but.... [🇷 for BE/BA]

posted by ElMaestro  – Denmark, 2024-02-23 23:15 (455 d 00:02 ago) – Posting: # 23880
Views: 3,219
(edited on 2024-02-24 00:00)

Hi Mittyri,

❝ may be I misunderstood your

❝

❝ ❝ is not full rank. Neither is does it contain a column for every level of every factor.

❝ The solution you proposed with qr() does not give a column for every level of every factor

❝ > (MakeFullRank(model.matrix(~ f + g)))


❝    Q       

❝ 1  1 0 0 1 0

❝ 2  1 0 1 1 0

❝ 3  1 1 0 0 1

❝ 4  1 0 1 1 0

❝ 5  1 0 0 0 0

❝ 6  1 0 0 0 1

❝ 7  1 0 1 0 0

❝ 8  1 1 0 0 0

❝ 9  1 0 1 1 0

❝ 10 1 1 0 0 0

❝ 11 1 0 0 0 1

❝ 12 1 1 0 0 1

A full rank model matrix means there are not more columns than the rank. Then X^tX becomes invertible.
A model matrix with a column for every level of every factor (plus intercept) is not the same. Rather that's redundancy. X^tX now becomes trouble
My function creates a full rank model matrix.

Complete thread:

• lm and the model matrix ElMaestro 2024-02-19 09:51 
  • the model matrix and the contrasts mittyri 2024-02-22 20:21
    • Yes, but.... ElMaestro 2024-02-23 17:41
      • Yes, but.... mittyri 2024-02-23 19:39
        • Yes, but....ElMaestro 2024-02-23 22:15