R/utilitiesEvaluate.R
ocheck.Rdocheck and ocheck3 evaluate pairwise or 3-orthogonality of columns,
count_npairs evaluates the number of level pairs in 2D projections,
count_nallpairs calculates corresponding total numbers of pairs.
ocheck(D, verbose = FALSE)
ocheck3(D, verbose = FALSE)
count_npairs(D, minn = 1)
count_nallpairs(ns)a matrix with factor levels or an object of class SOA;
factor levels can start with 0 or with 1, and need to be consecutively numbered
logical; if TRUE, additional information is printed
(table of correlations)
small integer number; the function counts pairs that are covered at least minn times
vector of numbers of levels for each column
Functions ocheck and ocheck3 return a logical.
Functions count_npairs returns a vector of
counts for level combinations covered in factor pairs (in the order of the columns of
DoE.base:::nchoosek(ncol(D),2)) for the array in D,
function count_nallpairs provides the total number of level combinations for
designs with numbers of levels given in ns (and thus can be used to obtain
a denominator for count_npairs).
#' ## Shi and Tang strength 3+ construction in 7 8-level factors for 32 runs
D <- SOAs_8level(32, optimize=FALSE)
## is an OSOA
ocheck(D)
#> [1] TRUE
## an OSOA of strength 3 with 3-orthogonality
## 4 columns in 27 levels each
## second order model matrix
D_o <- OSOAs_LiuLiu(DoE.base::L81.3.10, optimize=FALSE)
ocheck3(D_o)
#> [1] TRUE
## benefit of 3-orthogonality for second order linear models
colnames(D_o) <- paste0("X", 1:4)
y <- stats::rnorm(81)
mylm <- stats::lm(y~(X1+X2+X3+X4)^2 + I(X1^2)+I(X2^2)+I(X3^2)+I(X4^2),
data=as.data.frame(scale(D_o, scale=FALSE)))
crossprod(stats::model.matrix(mylm))
#> (Intercept) X1 X2 X3 X4 I(X1^2) I(X2^2) I(X3^2) I(X4^2)
#> (Intercept) 81 0 0 0 0 4914 4914 4914 4914
#> X1 0 4914 0 0 0 0 0 0 0
#> X2 0 0 4914 0 0 0 0 0 0
#> X3 0 0 0 4914 0 0 0 0 0
#> X4 0 0 0 0 4914 0 0 0 0
#> I(X1^2) 4914 0 0 0 0 535626 289368 315612 289368
#> I(X2^2) 4914 0 0 0 0 289368 535626 298116 289368
#> I(X3^2) 4914 0 0 0 0 315612 298116 535626 289368
#> I(X4^2) 4914 0 0 0 0 289368 289368 289368 535626
#> X1:X2 0 0 0 0 0 38880 -38880 0 39852
#> X1:X3 0 0 0 0 0 8748 74844 2916 -1458
#> X1:X4 0 0 0 0 0 0 -4266 13014 0
#> X2:X3 0 0 0 0 0 34668 -26244 26244 4212
#> X2:X4 0 0 0 0 0 -486 2916 79218 -4374
#> X3:X4 0 0 0 0 0 78246 -972 38880 -38880
#> X1:X2 X1:X3 X1:X4 X2:X3 X2:X4 X3:X4
#> (Intercept) 0 0 0 0 0 0
#> X1 0 0 0 0 0 0
#> X2 0 0 0 0 0 0
#> X3 0 0 0 0 0 0
#> X4 0 0 0 0 0 0
#> I(X1^2) 38880 8748 0 34668 -486 78246
#> I(X2^2) -38880 74844 -4266 -26244 2916 -972
#> I(X3^2) 0 2916 13014 26244 79218 38880
#> I(X4^2) 39852 -1458 0 4212 -4374 -38880
#> X1:X2 289368 34668 -486 74844 -4266 4401
#> X1:X3 34668 315612 78246 0 4401 13014
#> X1:X4 -486 78246 289368 4401 39852 -1458
#> X2:X3 74844 0 4401 298116 -972 79218
#> X2:X4 -4266 4401 39852 -972 289368 4212
#> X3:X4 4401 13014 -1458 79218 4212 289368