Linking Error Estimation for Mean-Geometric Mean and Pairwise Haberman Linking Across Multiple Time Points in the 2PL Model
Year: 2026
Type: preprint
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.
Source: PsyArXiv (OSF Preprints)
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7223027003