redundancies {ThurMod}

Determine the number of redundancies

Description

This function determines the number of redundancies among the tetrachoric correlations and thresholds.

Usage

redundancies(blocks, warn = TRUE)

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.

warn

Logical. Should warning messages be returned? Defaults to 'TRUE'.

Details

If a ranking design is used (variances of binary indicators is zero) there are redundancies among the thresholds and tetrachoric correlations to be estimated. This is the case, whenever the number of items per block is larger than two. In these cases the degrees of freedom must be corrected by subtracting the redundancies. For more details see Jansen and Schulze (2023) and Maydeu-Olivares (1999).

Value

Returns an integer of the number of redundancies.

References

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

Maydeu-Olivares, A. (1999). Thurstonian modeling of ranking data via mean and covariance structure analysis. Psychometrika, 64(3), 325-340. doi:10.1007/BF02294299

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,10)

# Determine the redundancies
redundancies(blocks)