The n ext crackpot iteration [Two-Stage / GS Designs]

posted by Helmut Homepage – Vienna, Austria, 2017-08-20 02:20  – Posting: # 17717
Views: 23,443

Capt’n,

some remarks. More maybe tomorrow.

» The polynomial provides a fantastic approximation within our entire interval of interest.

Played around a little. Based on the AIC the 4th degree is the winner indeed.

» ##note: We might not want to write blah^3 etc if we optimize for speed, not sure.

Old wisdom. Here with my coefficients (total sample sizes [not N/seq], exact method for GRM 0.95, 80% power, CV 0.1–1.0).

library(microbenchmark)
a <- c(5.897943, -40.988390, 603.109578, -338.281351, 70.43138)
old.school <- function(a, CV) {
  x <- a[1] + a[2]*CV + a[3]*CV*CV + a[4]*CV*CV*CV + a[5]*CV*CV*CV*CV
  x + (2 - x %% 2)
}
lazy <- function(a, CV) {
  x <- a[1] + a[2]*CV + a[3]*CV^2 + a[4]*CV^3 + a[5]*CV^4
  x + (2 - x %% 2)
}
res <- microbenchmark(old.school(a, CV), lazy(a, CV), times=500L,
                      control=list("random", warmup=10))
boxplot(res, boxwex=0.25, las=1)
options(microbenchmark.unit="us")
print(res)


» ## perhaps ceil would be better?

I would round up to the next even (as above).

» You see, the sample size estimates are sort of almost perfect already. If you want to remove the very few 1's and -1's then just increase the polynomial degree above.

That doesn’t help. With CV <- seq(0.1, 1, 0.01) I got a match in 46/91 and +2 in 45/91. OK, conservative.

Cheers,
Helmut Schütz
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