irtlink: IRT Linking and Linking Error Estimation Across Time Points and
Groups
Estimation of trends in the mean and standard deviation
of latent ability distributions across the time points of
educational assessments, and of ability distribution differences
across linked groups, for unidimensional item response theory
(IRT) models (1PL, 2PL, 3PL, partial credit, and generalized
partial credit). Groups connected through common items, with
independent or dependent person samples, are calibrated on an
internal marginal maximum likelihood EM engine, separately,
concurrently, with fixed item parameters, or with regularized
calibration. Linking methods include mean-mean and mean-geometric
mean linking, Haberman linking (Haberman, 2009,
<doi:10.1002/j.2333-8504.2009.tb02197.x>) with robust Lp loss and
a pairwise variant (Robitzsch, 2025,
<doi:10.3390/appliedmath5010007>), and the response function
methods of Haebara and Stocking-Lord. Under differential item
functioning (DIF), the linked estimates depend on the selected
common items, and the package estimates this linking error
together with the standard error by jackknife and sandwich
estimators, including bias-corrected variants (Robitzsch, 2024,
<doi:10.3390/stats7030036>). RMSD and likelihood-ratio DIF
diagnostics with iterative purification are included.
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