NPBBBdesigns (version 1.0.0)

info_matrix: Information Matrix of a (Sub-)Block Design for Test-Versus-Control Comparisons

Description

Computes the reduced (treatment) information matrix \(C = R - N K^{-1} N^\prime\) for a single classification (blocks or sub-blocks) of a nested partially balanced bipartite block (NPBBB) design. Here \(R\) is the diagonal matrix of treatment replications, \(N\) is the treatment-by-(sub-)block incidence matrix and \(K\) is the diagonal matrix of (sub-)block sizes. Control treatments may occur more than once in a (sub-)block (for example, designs obtained by merging rows of a group-divisible scheme); such multiplicities are counted in \(N\) so that \(C\) is the correct information matrix under the homoscedastic fixed-effects nested model. For more details see Vinayaka et al. (2026).

Usage

info_matrix(design, v1, v2)

Value

A numeric (v1 + v2) by (v1 + v2) information matrix

\(C\).

Arguments

design

A matrix (or data frame) whose rows are the blocks or sub-blocks and whose entries are the treatment labels. Test treatments must be labelled 1, ..., v1 and control treatments v1 + 1, ..., v1 + v2.

v1

Number of test treatments.

v2

Number of control treatments.

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

# Two blocks of size 4 on 4 test treatments (1-4) and 2 controls (5, 6)
d <- rbind(c(1, 2, 5, 6), c(3, 4, 5, 6))
info_matrix(d, v1 = 4, v2 = 2)