Open issues [🇷 for BE/BA]

posted by PharmCat  – Russia, 2020-08-07 02:02 (907 d 06:42 ago) – Posting: # 21828
Views: 11,865

Hi ElMaestro!


❝ Gurka requires me to derive Xi, the design matrix for fixed effects of subject i.

❝ They mention that "Xi is a (ni × p) known, constant design matrix for the i' th subject

❝ with rank p"


I think it means rank of whole X, because after: "and β is a (p × 1) vector of unknown, constant population parameters". Xi is a part of X and have same count of columns, rank Xi can be lower. Here is no contradictions I think. If look at Xiuming Zhang, 2015* p is just length of β and rank should be the same. If not, we will have rank-deficient matrix.

And if look generally - it really doesn't matter because -(N-p)*log(2π)/2 is a constant and it can be excluded from optimization. If you want find AIC ets - this will matter.

And as I know some softaware using different N for calculation (some use all observations, some only statistically independent (m)), and some include second constant part: logdet(Σim(X'X))/2

So if you want find only θ, you can minimize REML without constants at all. And add constants when you need to have real value of REML or AIC, BIC, ets.

*A Tutorial on Restricted Maximum Likelihood Estimation in Linear Regression and Linear Mixed-Effects Model

Example N=3, n=9, p=6

X:
β1 β2 β3 β4 β5 β6

1  1  0  1  0  0
1  1  0  1  0  0
1  1  0  1  0  0
1  0  1  0  1  0
1  0  1  0  1  0
1  0  1  0  1  0
1  1  0  0  0  1
1  1  0  0  0  1
1  1  0  0  0  1

X1
β1 β2 β3 β4 β5 β6

1  1  0  1  0  0
1  1  0  1  0  0
1  1  0  1  0  0

X2
β1 β2 β3 β4 β5 β6

1  0  1  0  1  0
1  0  1  0  1  0
1  0  1  0  1  0

X3
β1 β2 β3 β4 β5 β6

1  1  0  0  0  1
1  1  0  0  0  1
1  1  0  0  0  1

Complete thread:

UA Flag
Activity
 Admin contact
22,477 posts in 4,708 threads, 1,603 registered users;
13 visitors (0 registered, 13 guests [including 5 identified bots]).
Forum time: 07:45 CET (Europe/Vienna)

The mediocre teacher tells.
The good teacher explains.
The superior teacher demonstrates.
The great teacher inspires.    William Arthur Ward

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5