R/contr.Power.R
contr.Power.RdA contrast function based on regular factorials for number of levels a prime or prime power
contr.Power(n, s = 2, contrasts = TRUE)integer or vector; either an integer number of levels of the factor for
which contrasts are created, which must be a a power of s; or a factor
whose number of levels is a power of s; or a vector of levels whose
number of elements is a power of s.
integer; prime or prime power
logical; must be TRUE
contr.Power yields a matrix of contrasts. It can be used in
function model.matrix or anywhere where factors with the number of
levels a power of $s$ are used with contrasts. The exponent for s
is determined from the number of levels.
The function is a generalization (with slowest first instead of fastest first)
of function contr.FrF2 from package DoE.base. It is in this
package because it needs Galois field functionality from package lhs
for non-prime s. Its purpose is (was) the calculation of the
stratification (or space-filling) pattern by Tian and Xu (2022), see also
Groemping (2022). The package now calculates the pattern with function
contr.TianXu.
Groemping (2022) Tian and Xu (2022)
## the same n can yield different contrasts for different s
contr.Power(16, 2)
#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
#> 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
#> 2 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1
#> 3 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1
#> 4 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1
#> 5 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1
#> 6 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1
#> 7 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1
#> 8 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1
#> 9 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1
#> 10 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1
#> 11 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1
#> 12 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1
#> 13 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1
#> 14 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1
#> 15 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1
#> 16 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1
contr.Power(16, 4)
#> 1 2 3 4 5 6 7 8 9
#> 1 -1.3416408 1 -0.4472136 -1.3416408 1 -0.4472136 -1.3416408 1 -0.4472136
#> 2 -1.3416408 1 -0.4472136 -0.4472136 -1 1.3416408 -0.4472136 -1 1.3416408
#> 3 -1.3416408 1 -0.4472136 0.4472136 -1 -1.3416408 0.4472136 -1 -1.3416408
#> 4 -1.3416408 1 -0.4472136 1.3416408 1 0.4472136 1.3416408 1 0.4472136
#> 5 -0.4472136 -1 1.3416408 -1.3416408 1 -0.4472136 -0.4472136 -1 1.3416408
#> 6 -0.4472136 -1 1.3416408 -0.4472136 -1 1.3416408 -1.3416408 1 -0.4472136
#> 7 -0.4472136 -1 1.3416408 0.4472136 -1 -1.3416408 1.3416408 1 0.4472136
#> 8 -0.4472136 -1 1.3416408 1.3416408 1 0.4472136 0.4472136 -1 -1.3416408
#> 9 0.4472136 -1 -1.3416408 -1.3416408 1 -0.4472136 0.4472136 -1 -1.3416408
#> 10 0.4472136 -1 -1.3416408 -0.4472136 -1 1.3416408 1.3416408 1 0.4472136
#> 11 0.4472136 -1 -1.3416408 0.4472136 -1 -1.3416408 -1.3416408 1 -0.4472136
#> 12 0.4472136 -1 -1.3416408 1.3416408 1 0.4472136 -0.4472136 -1 1.3416408
#> 13 1.3416408 1 0.4472136 -1.3416408 1 -0.4472136 1.3416408 1 0.4472136
#> 14 1.3416408 1 0.4472136 -0.4472136 -1 1.3416408 0.4472136 -1 -1.3416408
#> 15 1.3416408 1 0.4472136 0.4472136 -1 -1.3416408 -0.4472136 -1 1.3416408
#> 16 1.3416408 1 0.4472136 1.3416408 1 0.4472136 -1.3416408 1 -0.4472136
#> 10 11 12 13 14 15
#> 1 -1.3416408 1 -0.4472136 -1.3416408 1 -0.4472136
#> 2 0.4472136 -1 -1.3416408 1.3416408 1 0.4472136
#> 3 1.3416408 1 0.4472136 -0.4472136 -1 1.3416408
#> 4 -0.4472136 -1 1.3416408 0.4472136 -1 -1.3416408
#> 5 -0.4472136 -1 1.3416408 -0.4472136 -1 1.3416408
#> 6 1.3416408 1 0.4472136 0.4472136 -1 -1.3416408
#> 7 0.4472136 -1 -1.3416408 -1.3416408 1 -0.4472136
#> 8 -1.3416408 1 -0.4472136 1.3416408 1 0.4472136
#> 9 0.4472136 -1 -1.3416408 0.4472136 -1 -1.3416408
#> 10 -1.3416408 1 -0.4472136 -0.4472136 -1 1.3416408
#> 11 -0.4472136 -1 1.3416408 1.3416408 1 0.4472136
#> 12 1.3416408 1 0.4472136 -1.3416408 1 -0.4472136
#> 13 1.3416408 1 0.4472136 1.3416408 1 0.4472136
#> 14 -0.4472136 -1 1.3416408 -1.3416408 1 -0.4472136
#> 15 -1.3416408 1 -0.4472136 0.4472136 -1 -1.3416408
#> 16 0.4472136 -1 -1.3416408 -0.4472136 -1 1.3416408