NPBBBdesigns (version 1.0.0)

construct_method1: Construct an NPBBB Design by Composing a PBBB Design with an NBIB Design

Description

Implements Method 1 of Vinayaka et al. (2026). Each block of a partially balanced bipartite block (PBBB) design of size \(k^\prime\) is replaced by a copy of a nested balanced incomplete block (NBIB) design on \(v^{*} = k^\prime\) symbols, by identifying the \(k^\prime\) symbols of the NBIB design with the \(k^\prime\) entries of the PBBB block.

Usage

construct_method1(pbbb_blocks, nbib_subblocks, q, v2 = 2)

Value

An object of class "npbbb": 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

pbbb_blocks

A list of integer vectors of common length \(k^\prime\), the blocks of a PBBB design, with test treatments labelled 1, ..., v1 and controls v1 + 1, ..., v1 + v2.

nbib_subblocks

A list of integer vectors over the symbols \(1, \ldots, k^\prime\) giving the sub-blocks of an NBIB design, supplied in block order (q sub-blocks per block).

q

Number of sub-blocks per block of the NBIB design.

v2

Number of control treatments in the PBBB design (default 2).

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).

Examples

# PBBB design: 4 test treatments (1-4), 2 controls (5, 6); block size k' = 4
pbbb <- list(c(1,2,5,6), c(1,3,5,6), c(1,4,5,6),
             c(2,3,5,6), c(2,4,5,6), c(3,4,5,6))
# NBIB on k' = 4 symbols from a one-factorisation of K4 (q = 2 sub-blocks/block)
nbib <- list(c(1,2), c(3,4),  c(1,3), c(2,4),  c(1,4), c(2,3))
d <- construct_method1(pbbb, nbib, q = 2, v2 = 2)
d