Bioequivalence and Bioavailability Forum • The optional tolerance argument

The optional tolerance argument [Design Issues]

posted by ElMaestro – Denmark, 2019-12-23 15:37 (1757 d 15:36 ago) – Posting: # 21021
Views: 6,725

Hi Hötzi,

❝ ❝ ❝ For observation 8 we have -3.608225e-16, I think,

❝ ❝ I think, is around the "effective zero" for fits in R at default settings on 64- and 32-bit systems.

❝

❝ Yes, it is. ;-)

❝

x <- -3.608225e-16

❝ zero <- .Machine$double.eps

❝ all.equal(x, zero)

❝ [1] TRUE

❝ zero

❝ [1] 2.220446e-16

This comparison in your context is just a test if the difference is less than about 10^-8since there is an implied tolerance argument for all.equal, the square root of .Machine$double.eps

Effective zero residuals will be somewhat better than 10^-8 in practice. They will depend on the approach used to find the solution; in lm I believe the approach is via a qr decomposition of the model matrix, and R by defualt has a tol argument in that function of 10^-7 which lm may be leaning on.

Here's an example of a perfect fit, therefore having effective zero residuals:

a=c(rep(1,5), rep(2,5), rep(3,5))

b=c(rep("A",5), rep("B",5), rep("C",5))

M=lm(a~0+b)

resid(M)

It may actually not be the best example since the dependents are all representable inernally in R's (and computer's) binary.

Perhaps this makes a better point:

a=c(rep(pi,5), rep(sin(1.5+pi),5), rep(log(pi),5))

b=c(rep("A",5), rep("B",5), rep("C",5))

M=lm(a~0+b)

resid(M)

—
Pass or fail!
ElMaestro

Complete thread:

Should those subjects have only one period data be included in BE analysis? ssussu 2019-12-06 10:58 [Design Issues]
- No way! But... Beholder 2019-12-06 12:36
  - No way! But... ElMaestro 2019-12-06 13:14
    - No way! But... Helmut 2019-12-06 14:47
      - No way! But... PharmCat 2019-12-06 23:46
        
        No way! But... wienui 2019-12-07 04:01
        
        EMA guideline: no way...: mittyri 2019-12-07 20:58
        
        EMA guideline: no way...: wienui 2019-12-09 05:25
        
        Slightly off topic, but related :-) ElMaestro 2019-12-08 01:31
        
        Slightly off topic, but related :-) Shuanghe 2019-12-09 12:00
        Slightly off topic, but related :-) PharmCat 2019-12-09 15:13
        
        Slightly off topic, but related :-) ElMaestro 2019-12-21 15:02
        
        Slightly off topic, but related :-) PharmCat 2019-12-22 01:12
        2.220446e-16 ≈ 0 Helmut 2019-12-22 10:37
        
        The optional tolerance argumentElMaestro 2019-12-23 14:37
        2.220446e-16 ≈ 0 PharmCat 2019-12-24 14:18
        
        Sum of residuals ~ ε Helmut 2019-12-24 14:54
        
        Sum of residuals ~ ε ElMaestro 2019-12-24 15:10
        
        Wrong terminology Helmut 2019-12-28 13:55
        
        Sum of residuals ~ ε PharmCat 2019-12-24 18:40