Develop Concise but Comprehensive Shortened Versions of Psychometric Instruments

Operationalizes the identification problem of which subset of items should be kept in the shortened version of a said psychometric instrument to best represent the set of items comprised in the original version of the said psychometric instrument.

shortr: Develop Concise but Comprehensive Shortened Versions of Psychometric Instruments

Description

shortr operationalizes the identification problem of which subset of items should be kept in the shortened version of a said psychometric instrument to best represent the set of items comprised in the original version of the said psychometric instrument.

Installation

utils::install.packages(pkgs = "shortr")

base::library(package = "shortr")

Usage

shortr::shortr(
  n.mat = lavaan::lavCor(object = DATA, ordered = TRUE), 
  k = 5, 
  algorithm = "brute.force"
)

shortr::shortr(
  n.mat = lavaan::lavCor(object = DATA, ordered = TRUE), 
  k = 5, 
  algorithm = "simulated.annealing", 
  start.temp = 1, 
  cool.fact = 0.999, 
  stop.temp = 0.001, 
  n.runs = 1000, 
  seed = 5107
)

Formulation

Let $N$ denote the indices corresponding to the set of items comprised in the original version of a said psychometric instrument, and let $n = |N|$ denote its cardinality, with $n \in \mathbb{N}$. Let $i, j \in N$ denote arbitrary indices. Let $K \subset N$ denote the indices corresponding to the subset of items to be comprised in the shortened version of the said psychometric instrument, and let $k = |K|$ denote its cardinality, with $k \in {1, \ldots, n-1}$. Let $A = (a_{ij}) \in \mathbb{R}^{n \times n}$ denote a symmetric matrix of associations (e.g., of zero-order polychoric correlation coefficients) computed from the set of items comprised in the original version of the said psychometric instrument, satisfying $A = A^\top \Leftrightarrow a_{ij} = a_{ji}$ for all $i, j \in N$. Each element $a_{ij}$ represents an association (e.g., a zero-order polychoric correlation coefficient) between the items indexed by $i$ and $j$. Let $K^c = N \setminus K$ denote the complement of $K$ in $N$, with $|K^c| = n - k$. The objective is to identify the subset of indices $K \subset N$ of cardinality $|K| = k$ that maximizes the sum of the absolute values of the associations $a_{ij}$ for all $i \in K$ and $j \in K^c$. Formally, such an identification problem is expressed as follows:

$$ \max_{K \subset N,\ |K| = k} \sum_{i \in K} \sum_{j \in K^c} |a_{ij}| $$

Operationalization

To operationalize the said identification problem, we developed and released the R function shortr::shortr() of the R package shortr (Fournier et al., 2026), which is publicly shared under a GNU General Public License on the Comprehensive R Archive Network (https://doi.org/10.32614/CRAN.package.shortr).

Citation

utils::citation(package = "shortr")

Fournier, L., Heeren, A., Baggio, S., Clark, L., Verdejo-García, A., Perales, J. C., & Billieux, J. (2026). shortr: Develop concise but comprehensive shortened versions of psychometric instruments (R package version 1.0.3) [Computer software]. https://doi.org/10.32614/CRAN.package.shortr