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.
utils::install.packages(pkgs = "shortr")
base::library(package = "shortr")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
)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:
\[ \max_{K \subset N,\ |K| = k} \sum_{i \in K} \sum_{j \in K^c} |a_{ij}| \]
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).
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 1.0.2) [Computer software]. https://doi.org/10.32614/CRAN.package.shortr