| Title: | Response Surface Designs with Neighbour Effects (rsdNE) |
|---|---|
| Description: | Response surface designs with neighbour effects are suitable for experimental situations where it is expected that the treatment combination administered to one experimental unit may affect the response on neighboring units as well as the response on the unit to which it is applied. Integrating these effects in the response surface model improves the experiment's precision (Jaggi, S., Sarika and Sharma, V.K. (2010)<http://krishi.icar.gov.in/jspui/handle/123456789/4364>; Verma A., Jaggi S., Varghese, E.,Varghese, C.,Bhowmik, A., Datta, A. and Hemavathi M. (2021)<DOI: 10.1080/03610918.2021.1890123>). This package includes sym(), asym1(), asym2() functions that generates response surface designs which are rotatable under a polynomial model of a given order without interaction term incorporating neighbour effects. |
| Authors: | Ashutosh Dalal [aut, cre], Seema Jaggi [aut, ctb], Eldho Varghese [aut, ctb], Subhasish Sarkar [aut], Arpan Bhowmik [aut], Cini Varghese [aut], Anindita Datta [aut], Soumen Pal [aut] |
| Maintainer: | Ashutosh Dalal <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.1.0 |
| Built: | 2025-02-14 03:09:24 UTC |
| Source: | https://github.com/cran/rsdNE |
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.
asym1(n1, n2, c)asym1(n1, n2, c)
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 |
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.
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.
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.
Verma et al.2021, Communication in Statistics – Simulation and Computation
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"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"
This function generates asymmetrical rotatable response surface designs in the presence of neighbour effects for (n1 + n2) factors, n1 factors at s1 levels and another n2 factors at s2 levels.
asym2(s1, n1, s2, n2, c)asym2(s1, n1, s2, n2, c)
s1 |
Number of levels of n1 factors, 1<s1<=8 |
n1 |
Number of factors, 1<=n1<=4 |
s2 |
Number of levels of n2 factors, 1<s2<=8 |
n2 |
Number of factors, 1<=n2<=4 |
c |
Value of alpha (Coefficient of neighbour effects), 0<=c<=1 |
his function generates rotatable designs as well as Z_prime_Z matrix, inv(Z_primeZ) matrix and variance estimated response for the (s1^n1 * s2^n2) factorial combination.
Here s1 and s2 both not even at the same time and s1 not equal to s2.
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.
Dalal, 2021, Unpublished M.Sc. Thesis, IARI, New Delhi
library(rsdNE) asym2(2,2,5,2,0.5)library(rsdNE) asym2(2,2,5,2,0.5)
This function generates symmetrical rotatable response surface designs in the presence of neighbour effects for n1 factors each at s1 levels.
sym(s1, n1, c)sym(s1, n1, c)
s1 |
Number of levels of n1 factors, 1<s1<=6 |
n1 |
Number of factors, 1<n1<=4 |
c |
Value of alpha (Coefficient of neighbour effects), 0<=c<=1 |
his function generates rotatable designs as well as Z_prime_Z matrix, inv(Z_primeZ) matrix and variance estimated response for the (s1^n1) factorial combination.
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.
Sarika et al.2009, Communications in Statistics-Theory and Methods; Sarika et al.2013, Ars Combinatoria
library(rsdNE) sym(2,2,0.5) ##output: ## X matrix # [,1] [,2] [,3] # [1,] 1 -1 -1 # [2,] 1 1 1 # [3,] 1 1 -1 # [4,] 1 -1 1 # [5,] 1 -1 -1 # [6,] 1 1 1 # [7,] 1 -1 1 # [8,] 1 1 -1 # [9,] 1 -1 -1 #[10,] 1 1 1 ## Z prime Z matrix # [,1] [,2] [,3] #[1,] 32 0 0 #[2,] 0 4 0 #[3,] 0 0 4 ## Z prime Z inverse matrix # [,1] [,2] [,3] #[1,] 0.03125 0.00 0.00 #[2,] 0.00000 0.25 0.00 #[3,] 0.00000 0.00 0.25 #[1] "total number of runs" "8" #[1] "variance of esitmated response" "0.5312"library(rsdNE) sym(2,2,0.5) ##output: ## X matrix # [,1] [,2] [,3] # [1,] 1 -1 -1 # [2,] 1 1 1 # [3,] 1 1 -1 # [4,] 1 -1 1 # [5,] 1 -1 -1 # [6,] 1 1 1 # [7,] 1 -1 1 # [8,] 1 1 -1 # [9,] 1 -1 -1 #[10,] 1 1 1 ## Z prime Z matrix # [,1] [,2] [,3] #[1,] 32 0 0 #[2,] 0 4 0 #[3,] 0 0 4 ## Z prime Z inverse matrix # [,1] [,2] [,3] #[1,] 0.03125 0.00 0.00 #[2,] 0.00000 0.25 0.00 #[3,] 0.00000 0.00 0.25 #[1] "total number of runs" "8" #[1] "variance of esitmated response" "0.5312"