construct_method6: Construct an NPBBB Design by Expanding the Size-2 Blocks of a PBIB Design
Description
Implements Method 6 of Vinayaka et al. (2026) (specific to
v2 = 2). Each block \((x_1, x_2)\) of a PBIB design with block size 2
is expanded, with the two controls \(0_1, 0_2\), into three blocks of size 4
(two sub-blocks of size 2): \([(x_1, x_2);(0_1, 0_2)]\),
\([(x_1, 0_1);(x_2, 0_2)]\) and \([(x_1, 0_2);(x_2, 0_1)]\).
Usage
construct_method6(pbib_blocks)
Value
An object of class "npbbb" with v2 = 2: a list with the
following components:
method: a character string naming the construction used.
v1, v2: numbers of test and control treatments.
parameters: a list of the design parameters
v1, v2, b1, b2, r1, r2, k1, k2, q.
block_design: an integer matrix with b1 rows and
k1 columns; each row is a block written as its concatenated
sub-blocks.
subblock_design: an integer matrix with b2 rows and
k2 columns; each row is a sub-block.
E1, E2: block and sub-block A-efficiencies.
efficiency: an object of class "npbbb_efficiency"
holding the underlying A-values and optimal references.
Arguments
pbib_blocks
A list of integer vectors of length 2, the blocks of a PBIB
design with test treatments labelled 1, ..., v1.
References
Vinayaka, Parsad R, Mandal BN, LN Vinaykumar (2026) Nested partially balanced bipartite block designs for comparing test treatments with multiple controls. Journal of Statistical Theory and Practice. (In press).