## The optional tolerance argument [Design Issues]

Hi Hötzi,

This comparison in your context is just a test if the difference is less than about 10

Effective zero residuals will be somewhat better than 10

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

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:

❝ ❝ ❝ 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

^{-8 }since 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

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

- EMA guideline: no way...: mittyri 2019-12-07 20:58
- 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

- Sum of residuals ~ ε ElMaestro 2019-12-24 15:10

- Sum of residuals ~ ε Helmut 2019-12-24 14:54

- Slightly off topic, but related :-) ElMaestro 2019-12-21 15:02

- No way! But... wienui 2019-12-07 04:01

- No way! But... PharmCat 2019-12-06 23:46

- No way! But... Helmut 2019-12-06 14:47

- No way! But... ElMaestro 2019-12-06 13:14

- No way! But... Beholder 2019-12-06 12:36