asym1 {rsdNE}

This generates a class of asymmetric rotatable response surface designs with neighbour effects under a second order model

Description

This function generates asymmetrical rotatable response surface designs in the presence of neighbour effects for 2n factors, n factors at 2 levels and another n factors at 3 levels.

Usage

asym1(n1, n2, c)

Arguments

n1

n1 factors having 2 levels, 1<=n1<=5

n2

n2 factors having 3 levels, 1<=n2<=5

c

Value of alpha (Coefficient of neighbour effects), 0<=c<=1

Value

This function generates rotatable designs as well as Z_prime_Z matrix, inv(Z_primeZ) matrix and variance estimated response for the (2^n1 * 3^n2) factorial combination.

Note

Here 3 types of cases have been considered: (2^n1*3^n2), where, n1=n2=n; (2^n1*3), where, n1=n and n2=1; (2*3^n2), where, n1=1 and n2=n.

Author(s)

Ashutosh Dalal, Division of Design of Experiments,ICAR-IASRI, New Delhi. Seema Jaggi, Education Division, ICAR, Krishi Anusandhan Bhawan - II, Pusa, New Delhi. Eldho Varghese,Fishery Resources Assessment Division,ICAR-CMFRI, Kochi. Subhasish Sarkar, Division of Computer Application,ICAR-IASRI, New Delhi. Arpan Bhowmik, Division of Design of Experiments,ICAR-IASRI, New Delhi. Cini Varghese, Division of Design of Experiments,ICAR-IASRI, New Delhi. Anindita Datta, Division of Design of Experiments,ICAR-IASRI, New Delhi. Soumen Pal, Division of Computer Application,ICAR-IASRI, New Delhi.

References

Verma et al.2021, Communication in Statistics – Simulation and Computation

Examples

library(rsdNE)
asym1(1,1,0.5)
##X matrix
#      [,1] [,2] [,3] [,4]
#[1,]    1   -1   -1    1
#[2,]    1    1    1    1
#[3,]    1    1    0    0
#[4,]    1    1   -1    1
#[5,]    1   -1    1    1
#[6,]    1   -1    0    0
#[7,]    1   -1   -1    1
#[8,]    1    1    1    1
##Z prime Z matrix
#      [,1] [,2] [,3] [,4]
#[1,]   24    0    0   16
#[2,]    0   12    0    0
#[3,]    0    0    1    0
#[4,]   16    0    0   11
##Z prime Z imverse matrix
#      [,1]       [,2]   [,3]  [,4]
#[1,]  1.375 0.00000000    0   -2
#[2,]  0.000 0.08333333    0    0
#[3,]  0.000 0.00000000    1    0
#[4,] -2.000 0.00000000    0    3
#[1] "total number of runs" "6"
#[1] "variance of esitmated response" "1.4583"