ocheck {SOAs}

functions to evaluate low order projection properties of (O)SOAs

Description

ocheck 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.

Usage

ocheck(D, verbose = FALSE)

ocheck3(D, verbose = FALSE)

count_npairs(D, minn = 1)

count_nallpairs(ns)

Arguments

D

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

verbose

logical; if TRUE, additional information is printed (table of correlations)

minn

small integer number; the function counts pairs that are covered at least minn times

ns

vector of numbers of levels for each column

Value

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).

Author(s)

Ulrike Groemping

Examples

#' ## 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)

## 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)

## 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))