ClimMobTools (version 1.4)

randomize: Set an experimental incomplete block design

Description

Generate an incomplete block A-optional design. The function is optimized for incomplete blocks of three, but it will also work with comparisons of any other number of options. The design strives for approximate A optimality, this means that it is robust to missing observations. It also strives for balance for positions of each option. Options are equally divided between first, second, third, etc. position. The strategy is to create a "pool" of combinations that does not repeat combinations and is A-optimal. Then this pool is ordered to make subsets of consecutive combinations also relatively balanced and A-optimal

Usage

randomize(
  npackages,
  itemnames,
  ncomp = 3,
  availability = NULL,
  props = NULL,
  ...
)

Value

A dataframe with the randomized design

Arguments

npackages

an integer for the number of incomplete blocks to be generated

itemnames

a character for the name of items tested in the experiment

ncomp

an integer for the number of items to be assigned to each incomplete block

availability

optional, a vector with integers indicating the number of plots available for each itemnames

props

optional, a numeric vector with the desired proportions for each itemnames

...

additional arguments passed to methods

Author

Jacob van Etten

References

Bailey and Cameron (2004). Combinations of optimal designs. https://webspace.maths.qmul.ac.uk/l.h.soicher/designtheory.org/library/preprints/optimal.pdf

Examples

ncomp = 3
npackages = 20
itemnames = c("apple","banana","grape","mango", "orange")
availability = c(5, 8, 50, 50, 50)

randomize(ncomp = ncomp,
          npackages = npackages,
          itemnames = itemnames)

randomize(ncomp = ncomp,
          npackages = npackages,
          itemnames = itemnames,
          availability = availability)

if (FALSE) { # interactive()
# run diagnostics to certify that randomization is balanced
# the number of interactions should have the lower sd as possible
# this verification may not work well when technologies are 
# tested in different proportions
design = randomize(ncomp = ncomp,
                   npackages = npackages,
                   itemnames = itemnames)

design$best = "A"

design$worst = "C"

# number of times each item is tested in the 
# trial design
ntest = table(unlist(design[,c(1:3)]))

ntest

# put into the PlackettLuce structure to check 
# number of interactions between items 
r = gosset::rank_tricot(design, c(1:3), c(4:5))

bn = gosset::set_binomialfreq(r)

bn$interactions = bn$win1 + bn$win2

bn = bn[,c(1,2,5)]

bn
}