ibd: Binary incomplete block design for given v, b and k and...

In ibd: Incomplete Block Designs

Description

This function generates an A- and D- efficient binary incomplete block design with given number of treaments(v), number of blocks(b) and block size(k) and optionally with a specified concurrence matrix(NNP).

Usage

ibd(v,b,k,NNPo,ntrial,pbar=FALSE)

Arguments

v	number of treatments
b	number of blocks
k	block size
NNPo	optionally, desired concurrence matrix. If not specified, a nearly balanced concurrence matrix is obtained automatically.
ntrial	number of trials
pbar	progress bar

Value

v	number of treatments
b	number of blocks
k	block size
NNP	specified concurrence matrix
N	incidence matrix of the generated design
design	block contents in a b by k matrix
conc.mat	concurrence matrix of the generated design
A.efficiency	lower bound to A-efficiency of the generated design
D.efficiency	lower bound to D-efficiency of the generated design
time.taken	time taken to generate the design

Note

The function works best for values of number of treatments (v) up to 30 and block size (k) up to 10. However, for block size (k) up to 3, much larger values of number of treatments (v) may be used.

Author(s)

B N Mandal <[e-mail]>

References

Mandal, B. N., Gupta, V. K. and Parsad, R. (2013). Application of optimization techniques for construction of incomplete block designs. Project report, IASRI, New Delhi.

Mandal, B. N., Gupta, V. K., & Parsad, R. (2014). Efficient Incomplete Block Designs Through Linear Integer Programming. American Journal of Mathematical and Management Sciences, 33(2), 110-124.

Examples

v=9
b=12
k=3
ibd(v,b,k,pbar=FALSE)

Example output

Loading required package: lpSolve
Loading required package: MASS
Loading required package: car
Loading required package: carData
Loading required package: emmeans
Loading required package: multcompView
Warning message:
no DISPLAY variable so Tk is not available 
$v
[1] 9

$b
[1] 12

$k
[1] 3

$NNP
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
 [1,]    4    1    1    1    1    1    1    1    1
 [2,]    1    4    1    1    1    1    1    1    1
 [3,]    1    1    4    1    1    1    1    1    1
 [4,]    1    1    1    4    1    1    1    1    1
 [5,]    1    1    1    1    4    1    1    1    1
 [6,]    1    1    1    1    1    4    1    1    1
 [7,]    1    1    1    1    1    1    4    1    1
 [8,]    1    1    1    1    1    1    1    4    1
 [9,]    1    1    1    1    1    1    1    1    4

$N
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
 [1,]    1    0    1    0    0    1    0    0    0     0     0     1
 [2,]    0    0    0    0    0    0    0    1    1     1     0     1
 [3,]    1    0    0    0    0    0    1    0    0     1     1     0
 [4,]    0    0    0    0    1    1    1    0    1     0     0     0
 [5,]    1    0    0    1    1    0    0    1    0     0     0     0
 [6,]    0    0    1    1    0    0    0    0    1     0     1     0
 [7,]    0    1    0    0    1    0    0    0    0     0     1     1
 [8,]    0    1    0    1    0    1    0    0    0     1     0     0
 [9,]    0    1    1    0    0    0    1    1    0     0     0     0

$design
         [,1] [,2] [,3]
Block-1     1    3    5
Block-2     7    8    9
Block-3     1    6    9
Block-4     5    6    8
Block-5     4    5    7
Block-6     1    4    8
Block-7     3    4    9
Block-8     2    5    9
Block-9     2    4    6
Block-10    2    3    8
Block-11    3    6    7
Block-12    1    2    7

$conc.mat
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
 [1,]    4    1    1    1    1    1    1    1    1
 [2,]    1    4    1    1    1    1    1    1    1
 [3,]    1    1    4    1    1    1    1    1    1
 [4,]    1    1    1    4    1    1    1    1    1
 [5,]    1    1    1    1    4    1    1    1    1
 [6,]    1    1    1    1    1    4    1    1    1
 [7,]    1    1    1    1    1    1    4    1    1
 [8,]    1    1    1    1    1    1    1    4    1
 [9,]    1    1    1    1    1    1    1    1    4

$A.Efficiency
[1] 1

$D.Efficiency
[1] 1

$time.taken
   user  system elapsed 
  0.189   0.033   1.124 

ibd documentation built on May 2, 2019, 6:52 a.m.