| Title: | A-Optimal Block Designs for Comparing Test Treatments with Controls |
| Version: | 0.0.3 |
| Date: | 2024-01-25 |
| Author: | Baidya Nath Mandal [aut, cre], Sukanta Dash [aut], Rajender Parsad [aut] |
| Maintainer: | Baidya Nath Mandal <mandal.stat@gmail.com> |
| Depends: | R (≥ 3.4.0), lpSolve, MASS |
| 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. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2024-01-29 05:09:59 UTC; PC |
| Repository: | CRAN |
| Date/Publication: | 2024-01-29 12:10:03 UTC |
Get an altnernate solution for particular row of incidence matrix
Description
This function returns an alternate solution for a particular row of incidence matrix with specified properties.
Usage
alternate.sol(v,b,k,r,r0,lambda,lambda0,N1,T,relaxed)Arguments
v |
number of test treatments |
b |
number of blocks |
k |
block size |
r |
number of replications of the test treatments |
r0 |
number of replications of the control |
lambda |
number of concurrences of two test treatments |
lambda0 |
number of concurrences of a test treatment with the control |
N1 |
Incidence matrix obtained till the previous row |
T |
Tabu list of deleted rows |
relaxed |
are the constraints being relaxed? |
Value
return the desired row of the incidence matrix
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Get an altnernate solution for particular row of incidence matrix
Description
This function returns an alternate solution for a particular row of incidence matrix with specified properties.
Usage
alternate.sol2(m,n,b,k,r,r0,lambda1,lambda0,N1,T,relaxed)Arguments
m |
number of rows |
n |
number of columns |
b |
number of blocks |
k |
block size |
r |
number of replications of the test treatments |
r0 |
number of replications of the control |
lambda1 |
number of concurrences of two test treatments |
lambda0 |
number of concurrences of a test treatment with the control |
N1 |
Incidence matrix obtained till the previous row |
T |
Tabu list of deleted rows |
relaxed |
are the constraints being relaxed? |
Value
return the desired row of the incidence matrix
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Get an altnernate solution for particular row of incidence matrix
Description
This function returns an alternate solution for a particular row of incidence matrix with specified properties.
Usage
alternate.sol3(v1,v2,b,k,r,r0,lambda1,lambda2,lambda12,N1,T,relaxed)Arguments
v1 |
number of test treatments |
v2 |
number of controls |
b |
number of blocks |
k |
block size |
r |
number of replications of the test treatments |
r0 |
number of replications of the control |
lambda1 |
number of concurrences of two test treatments |
lambda2 |
number of concurrences between two control treatments |
lambda12 |
number of concurrences between a test and a control treatment |
N1 |
Incidence matrix obtained till the previous row |
T |
Tabu list of deleted rows |
relaxed |
are the constraints being relaxed? |
Value
return the desired row of the incidence matrix
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
A-optimal balanced bipartite block designs
Description
This function generates A-optimal balanced bipartite block (BBPB) designs for tests vs controls comparisons with specified parameters
Usage
aoptbbpb(v1,v2,b,k,ntrial)Arguments
v1 |
number of test treatments |
v2 |
number of controls |
b |
number of blocks |
k |
block size |
ntrial |
number of trials, default is 5 |
Value
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 |
Note
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.
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
References
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.
Examples
##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)
A-optimal group divisible treatment designs
Description
This function generates A-optimal group divisible treatment (GDT) designs for test vs control comparisons with specified parameters
Usage
aoptgdtd(m,n,b,k,ntrial)Arguments
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 |
Value
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 |
Note
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.
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
References
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.
Examples
## 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)
BBPB design with given parameters
Description
This function returns incidence matrix of a BBPB design with given parameters.
Usage
bbpbwq(v1,v2,b,k,w,q,ntrial)Arguments
v1 |
number of test treatments |
v2 |
number of controls |
b |
number of blocks |
k |
block size |
w |
parameter w |
q |
parameter q |
ntrial |
number of trials |
Value
return the incidence matrix of BBPB design
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Block design from given incidence matrix
Description
This function generates the block contents from a given incidence matrix
Usage
block.design(N)Arguments
N |
incidence matrix |
Value
design |
A matrix with number of rows equal to the number of blocks and number of columns equal to block size. Constant block size is assumed. Treatments are numbered as 1, 2, ..., v |
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
BTIB design with given parameters
Description
This function returns incidence matrix of a BTIB design with given parameters.
Usage
btibts(v,b,k,t,s,alpha,rho=0,ntrial)Arguments
v |
number of test treatments |
b |
number of blocks |
k |
block size |
t |
paramter t |
s |
parameter s |
alpha |
weight of the test versus test contrasts |
rho |
rho=0 |
ntrial |
number of trials |
Value
return the incidence matrix of a BTIB design
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
g function
Description
This function checks group
Usage
check.group(m,n,x,y)Arguments
m |
number of rows |
n |
number of columns |
x |
x |
y |
y |
Value
group |
same group or different group |
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
g function
Description
This function computes the value of g for specified parameters.
Usage
g(v,b,k,x,z,alpha,rho=0)Arguments
v |
number of treatments |
b |
number of blocks |
k |
block size |
x |
x |
z |
z |
alpha |
alpha |
rho |
rho, default is 0 |
Value
g |
value of the function |
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
g function
Description
This function computes the value of g for specified parameters.
Usage
gbbpb(v1,v2,b,k,x,z)Arguments
v1 |
number of test treatments |
v2 |
number of control treatments |
b |
number of blocks |
k |
block size |
x |
x |
z |
z |
Value
value |
value of the function |
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
getr0
Description
This function returns the value of r0 for specified parameters.
Usage
getr0(v,b,k)Arguments
v |
number of test treatments |
b |
number of blocks |
k |
block size |
Value
r0star |
value of r0star |
M |
value of M |
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Get a particular row of incidence matrix
Description
This function returns a particular row of incidence matrix with specified properties.
Usage
getrow(v,b,k,r,r0,lambda,lambda0,N1,T,rownum,relaxed)Arguments
v |
number of test treatments |
b |
number of blocks |
k |
block size |
r |
number of replications of the test treatments |
r0 |
number of replications of the control |
lambda |
number of concurrences of two test treatments |
lambda0 |
number of concurrences of a test treatment with the control |
N1 |
Incidence matrix obtained till the previous row |
T |
Tabu list of deleted rows |
rownum |
the row number being obtained |
relaxed |
are the constraints being relaxed? TRUE or FALSE |
Value
return the desired row of the incidence matrix
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Get a particular row of incidence matrix
Description
This function returns a particular row of incidence matrix with specified properties.
Usage
getrow2(m,n,b,k,r,r0,lambda1,lambda0,N1,T,rownum,relaxed)Arguments
m |
number of rows |
n |
number of columns |
b |
number of blocks |
k |
block size |
r |
number of replications of the test treatments |
r0 |
number of replications of the control |
lambda1 |
number of concurrences of two test treatments |
lambda0 |
number of concurrences of a test treatment with the control |
N1 |
Incidence matrix obtained till the previous row |
T |
Tabu list of deleted rows |
rownum |
the row number being obtained |
relaxed |
are the constraints being relaxed? TRUE or FALSE |
Value
return the desired row of the incidence matrix
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Get a particular row of incidence matrix
Description
This function returns a particular row of incidence matrix with specified properties.
Usage
getrow3(v1,v2,b,k,r,r0,lambda1,lambda2,lambda12,N1,T,rownum,relaxed)Arguments
v1 |
number of test treatments |
v2 |
number of controls |
b |
number of blocks |
k |
block size |
r |
number of replications of the test treatments |
r0 |
number of replications of the control |
lambda1 |
number of concurrences of two test treatments |
lambda2 |
number of concurrences between two control treatments |
lambda12 |
number of concurrences between a test and a control treatment |
N1 |
Incidence matrix obtained till the previous row |
T |
Tabu list of deleted rows |
rownum |
the row number being obtained |
relaxed |
are the constraints being relaxed? TRUE or FALSE |
Value
return the desired row of the incidence matrix
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Value of t and s which minimize g function
Description
This function gives the value of t and s which minimize the g function.
Usage
getts(v,b,k,alpha,rho)Arguments
v |
number of treatments |
b |
number of blocks |
k |
block size |
alpha |
weight |
rho |
rho is zero throughout. |
Value
return the values of t and s
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Value of w and q which minimize g function
Description
This function gives the value of w and q which minimize the g function.
Usage
getwq(v1,v2,b,k)Arguments
v1 |
number of test treatments |
v2 |
number of controls |
b |
number of blocks |
k |
block size |
Value
return the values of w and q
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
Weighted A-optimal balanced treatment incomplete block designs
Description
This function generates weighted A-optimal balanced treatment incomplete block design for test vs control comparisons with specified parameters
Usage
wtaoptbtib(v,b,k,alpha,rho=0,ntrial=5)Arguments
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 |
Value
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 |
Note
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.
Author(s)
Baidya Nath Mandal <mandal.stat@gmail.com>
References
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.
Examples
##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)