utilitiesPB: Internal utility functions

Description

Internal functions, mainly for calculation of Plackett-Burman and other non-regular screening designs. They need not be accessed for normal use of the package.

Usage

circ.mat(gen) 
double.des(des)
normalize.col.first(mat)
normalize.row.last(mat)
williamson(A,B,C,D)
taguchi(nruns)
boxtyssedal(nruns,k)
des.recode(var, recodes, as.factor.result, char)

Arguments

gen

~~Generating vector for circular design matrix (used in Plackett-Burman construction)

des

~~numeric design matrix (elements -1 / +1 ) to be doubled

mat

~~numeric design matrix (elements -1 / +1 ) to be normalized

~~numeric square matrix (elements -1 / +1 ) to be combined with B, C, and D by Williamson construction. Although the function combines any square matrices of identical dimension, the matrices must observe a special structure to in order to yield a useful design matrix.

~~numeric square matrix (elements -1 / +1 ) with same dimensions as A

nruns

number of runs; currently has to be 12 for taguchi and 16 for boxtyssedal.

number of factors; for up to 12 factors, a different design is picked. For 15 factors, a warning against perfect aliasing (of the last columnn) is issued.

var

variable

recodes

character string specifying recodes, so far only used in the principal form “-1=level[1];1=level[2]”

as.factor.result

logical that specifies whether or not results are to be coerced to factor. The default is that factors are coerced to factor, while numeric variables with numeric recodes are kept numeric.

char

logical: should replacement be treated as character string (TRUE) or evaluated? default is FALSE

Value

All functions return except des.recode return a numeric matrix, circ.mat a square matrix of dimension length(gen), double.des a matrix with 2*nrow(des) rows and 2*ncol(des)+1 columns (full foldover), the normalize... functions a matrix of the same dimenensions as mat, and williamson a square matrix of dimension 4*nrow(A). taguchi returns the Plackett-Burman array in 12 runs in Taguchi order (it is isomorphic to the standard version), and boxtyssedal returns the suitable version of the 16 run Hadamard matrix described by Box and Tyssedal, which is more appropriate for screening than the standard 16 run factorial.

des.recode returns a numeric vector or factor, depending on the type of var and the setting of as.factor.result. This function is identical to the function in package DoE.base and will eventually be deleted in package FrF2.

Details

Function des.recode has been adapted to the needs of this package from function recode of package car.

References

Box, G.E.P. and Tyssedal, J. (2001) Sixteen Run Designs of High Projectivity for Factor Screening. Communications in Statistics - Simulation and Computation 30, 217-228.

Hedayat, A.S., Sloane, N.J.A. and Stufken, J. (1999) Orthogonal Arrays: Theory and Applications, Springer, New York.

Plackett, R.L.; Burman, J.P. (1946) The design of optimum multifactorial experiments. Biometrika 33, 305-325.