count.xblocks {ThurMod}

Determine the number of extra blocks

Description

This function determines the minimal number of extra blocks needed in order to link all blocks.

Usage

count.xblocks(blocks)

Arguments

blocks

A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block.

Details

The matrix of blocks must be constructed so that the number of columns corresponds to the number of items per block. The number of rows corresponds to the number of blocks for the specific measure. If $p$ is the number of blocks, and $k$ is the number of items per block (e.g. $k=3$ for triplets), then the number of extra blocks can be determined by (see also Jansen & Schulze, 2023)

\lceil\frac{p-1}{k-1}\rceil

Value

An integer corresponding to the number of extra blocks needed.

References

Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.

Examples

# Define a matrix of blocks
blocks <- matrix(1:15,ncol=3, byrow=TRUE)

# Determine the number of extra blocks needed
count.xblocks(blocks)