| Title: | A-Optimal Block Designs for Comparing Test Treatments with Controls |
|---|---|
| Description: | A collection of functions to construct A-optimal block designs for comparing test treatments with one or more control(s). Mainly A-optimal balanced treatment incomplete block designs, weighted A-optimal balanced treatment incomplete block designs, A-optimal group divisible treatment designs and A-optimal balanced bipartite block designs can be constructed using the package. The designs are constructed using algorithms based on linear integer programming. To the best of our knowledge, these facilities to construct A-optimal block designs for comparing test treatments with one or more controls are not available in the existing R packages. For more details on designs for tests versus control(s) comparisons, please see Hedayat, A. S. and Majumdar, D. (1984) <doi:10.1080/00401706.1984.10487989> A-Optimal Incomplete Block Designs for Control-Test Treatment Comparisons, Technometrics, 26, 363-370 and Mandal, B. N. , Gupta, V. K., Parsad, Rajender. (2017) <doi:10.1080/03610926.2015.1071394> Balanced treatment incomplete block designs through integer programming. Communications in Statistics - Theory and Methods 46(8), 3728-3737. |
| Authors: | Baidya Nath Mandal [aut, cre], Sukanta Dash [aut], Rajender Parsad [aut] |
| Maintainer: | Baidya Nath Mandal <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.0.3 |
| Built: | 2025-02-01 05:43:20 UTC |
| Source: | https://github.com/cran/Aoptbdtvc |
This function generates A-optimal balanced bipartite block (BBPB) designs for tests vs controls comparisons with specified parameters
aoptbbpb(v1,v2,b,k,ntrial)aoptbbpb(v1,v2,b,k,ntrial)
v1 |
number of test treatments |
v2 |
number of controls |
b |
number of blocks |
k |
block size |
ntrial |
number of trials, default is 5 |
It either returns a text message or a design. If a design is found, it returns a list with following components
parameters |
parameters of the design |
design |
generated A-optmal BBPB design |
N |
incidence matrix of the generated A-optmal BBPB design |
NNP |
concurrence matrix of the generated design |
Aeff |
A-efficiency of the design |
type |
R- type or S- type design |
The function is useful to construct A-optimal BBPB designs for v1+v2 <= 30 and up to block size 10. May not be very useful beyond v1+v2 > 30. For k<=3, designs with larger v1+v2 may be obtained.
Baidya Nath Mandal <[email protected]>
Jaggi, S., Gupta, V. and Parsad, R. (1996). A-efficient block designs for comparing two disjoint sets of treatments, Communications in Statistics-Theory and Methods 25(5), 967-983.
Mandal, B. N., Parsad, R. and Dash, S. (2017). A-optimal block designs for comparing test treatments with control treatment(s) - an algorithmic approach, upcoming project report, ICAR-Indian Agricultural Statistics Research Institute, New Delhi, India.
##construct an A-optimal BBPB design with 5 test treatments and 3 control treatments in ##12 blocks each of size 5 aoptbbpb(v1=5,v2=3,b=12,k=5) ##construct an A-optimal BBPB design with 6 test treatments and 3 control treatments in ##6 blocks each of size 8 aoptbbpb(v1=6,v2=3,b=6,k=8) ##Design does not exist #not run aoptbbpb(3,2,9,3) aoptbbpb(6,3,9,4) #Design not found ## Not run: aoptbbpb(3,3,12,4)##construct an A-optimal BBPB design with 5 test treatments and 3 control treatments in ##12 blocks each of size 5 aoptbbpb(v1=5,v2=3,b=12,k=5) ##construct an A-optimal BBPB design with 6 test treatments and 3 control treatments in ##6 blocks each of size 8 aoptbbpb(v1=6,v2=3,b=6,k=8) ##Design does not exist #not run aoptbbpb(3,2,9,3) aoptbbpb(6,3,9,4) #Design not found ## Not run: aoptbbpb(3,3,12,4)
This function generates A-optimal group divisible treatment (GDT) designs for test vs control comparisons with specified parameters
aoptgdtd(m,n,b,k,ntrial)aoptgdtd(m,n,b,k,ntrial)
m |
number of rows such that m*n = number of test treatments |
n |
number of columns such that m*n = number of test treatments |
b |
number of blocks |
k |
block size |
ntrial |
number of trials, default is 5 |
It either returns a text message or a design. If a design is found, it returns a list with following components
parameters |
parameters of the design |
design |
generated A-optmal GDT design |
N |
incidence matrix of the generated A-optmal GDT design |
NNP |
concurrence matrix of the generated design |
The function is useful to construct A-optimal GDT designs for number of test treatments <= 30 and up to block size 10. May not be very useful for m*n > 30. For k<=3, designs with larger number of test treatment may be obtained.
Baidya Nath Mandal <[email protected]>
Jacroux, M. (1989). The A-optimality of block designs for comparing test treatments with a control, Journal of the American Statistical Association 84(405), 310-317.
Mandal, B. N., Parsad, R. and Dash, S. (2017). A-optimal block designs for comparing test treatments with control treatment(s) - an algorithmic approach, upcoming project report, ICAR-Indian Agricultural Statistics Research Institute, New Delhi, India.
## construct an A-optimal GDT design with 12 (= 4 x 3) test treatments ##in 12 blocks each of size 6 aoptgdtd(m=4,n=3,b=12,k=6) ## construct an A-optimal GDT design with 8 (= 4 x 2) test treatments ##in 8 blocks each of size 4 aoptgdtd(m=4,n=2,b=8,k=4) ##design does not exist aoptgdtd(4,2,8,2) ##Design not found ## Not run: aoptgdtd(3,3,15,3)## construct an A-optimal GDT design with 12 (= 4 x 3) test treatments ##in 12 blocks each of size 6 aoptgdtd(m=4,n=3,b=12,k=6) ## construct an A-optimal GDT design with 8 (= 4 x 2) test treatments ##in 8 blocks each of size 4 aoptgdtd(m=4,n=2,b=8,k=4) ##design does not exist aoptgdtd(4,2,8,2) ##Design not found ## Not run: aoptgdtd(3,3,15,3)
This function generates weighted A-optimal balanced treatment incomplete block design for test vs control comparisons with specified parameters
wtaoptbtib(v,b,k,alpha,rho=0,ntrial=5)wtaoptbtib(v,b,k,alpha,rho=0,ntrial=5)
v |
number of test treatments |
b |
number of blocks |
k |
block size |
alpha |
Weight for test versus test comparisons. Should be between 0 to 1 |
rho |
rho=0 |
ntrial |
number of trials, default is 5 |
It either returns a text message or a design. If a design is found, it returns a list with following components
parameters |
parameters of the design |
design |
generated weighted A-optmal BTIB design |
N |
incidence matrix of the generated weighted A-optmal BTIB design |
NNP |
concurrence matrix of the generated design |
The function is useful to construct weighted A-optimal BTIB designs upto 30 test treatments and up to block size 10. May not be very useful beyond 30 test treatments. For k<=3, designs with larger number of test treatments may be obtained.
Baidya Nath Mandal <[email protected]>
Gupta, V., Ramana, D. and Parsad, R. (1999). Weighted A-efficiency of block designs for making treatment-control and treatment-treatment comparisons, Journal of statistical planning and inference 77(2), 301-319.
Mandal, B. N., Parsad, R. and Dash, S. (2017). A-optimal block designs for comparing test treatments with control treatment(s) - an algorithmic approach, upcoming project report, ICAR-Indian Agricultural Statistics Research Institute, New Delhi, India.
##construct a weighted A-optimal BTIB design with 4 test treatments in 6 blocks each of size 4 ##with weights to test vs test treatments comparisons as 0.6 wtaoptbtib(v=4,b=6,k=4,alpha=0.6,rho=0) ##construct an A-optimal BTIB design with 9 test treatments in 12 blocks each of size 4 ##with weights to test vs test treatments comparisons as 0 wtaoptbtib(v=9,b=12,k=4,alpha=0,rho=0) ##design not found ## Not run: wtaoptbtib(v=3,b=6,k=5,alpha=0.2,rho=0) ##BTIB design does not exist for these parameters #Not run wtaoptbtib(3,4,3,0.2,0)##construct a weighted A-optimal BTIB design with 4 test treatments in 6 blocks each of size 4 ##with weights to test vs test treatments comparisons as 0.6 wtaoptbtib(v=4,b=6,k=4,alpha=0.6,rho=0) ##construct an A-optimal BTIB design with 9 test treatments in 12 blocks each of size 4 ##with weights to test vs test treatments comparisons as 0 wtaoptbtib(v=9,b=12,k=4,alpha=0,rho=0) ##design not found ## Not run: wtaoptbtib(v=3,b=6,k=5,alpha=0.2,rho=0) ##BTIB design does not exist for these parameters #Not run wtaoptbtib(3,4,3,0.2,0)