Linking Error Estimation for Mean-Geometric Mean and Pairwise Haberman Linking Across Multiple Time Points in the 2PL Model
Abstract
Longitudinal assessments link test forms through common items. Under item parameter drift, linked ability means and standard deviations depend on the item selection, adding a linking error (LE) to the standard error (SE). Treating mean-geometric mean linking and pairwise Haberman linking across three time points in the two-parameter logistic model as M-estimators, this article derives closed-form LEs and sandwich estimators of LE, SE, and total error (TE). Sandwich and item jackknife LE estimators are bias-corrected for person sampling, including dependent samples. In a simulation study, SE-based intervals undercovered increasingly with sample size, bias-corrected jackknife TE intervals reached acceptable coverage almost everywhere, and sandwich-based intervals undercovered with few items. Longitudinal mathematics data illustrate the estimators, with the LE exceeding the SE.
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BibTeX
@misc{engels2026linking,
title = {{Linking Error Estimation for Mean-Geometric Mean and Pairwise Haberman Linking Across Multiple Time Points in the 2PL Model}},
author = {Oskar Engels and Oliver Lüdtke and Alexander Robitzsch},
howpublished = {PsyArXiv},
year = {2026},
month = oct,
doi = {10.31234/osf.io/ct4my_v1},
url = {https://osf.io/preprints/psyarxiv/ct4my_v1/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linking Error Estimation for Mean-Geometric Mean and Pairwise Haberman Linking Across Multiple Time Points in the 2PL Model
AU - Oskar Engels
AU - Oliver Lüdtke
AU - Alexander Robitzsch
PY - 2026
DA - 2026/10/20
PB - PsyArXiv
DO - 10.31234/osf.io/ct4my_v1
UR - https://osf.io/preprints/psyarxiv/ct4my_v1/
AB - Longitudinal assessments link test forms through common items. Under item parameter drift, linked ability means and standard deviations depend on the item selection, adding a linking error (LE) to the standard error (SE). Treating mean-geometric mean linking and pairwise Haberman linking across three time points in the two-parameter logistic model as M-estimators, this article derives closed-form LEs and sandwich estimators of LE, SE, and total error (TE). Sandwich and item jackknife LE estimators are bias-corrected for person sampling, including dependent samples. In a simulation study, SE-based intervals undercovered increasingly with sample size, bias-corrected jackknife TE intervals reached acceptable coverage almost everywhere, and sandwich-based intervals undercovered with few items. Longitudinal mathematics data illustrate the estimators, with the LE exceeding the SE.
ER -