extended · other · 2024

Random pairing MLE for estimation of item parameters in Rasch model

Yuepeng Yang; Cong Ma; John M. Linacre

The Rasch model, a classical model in the item response theory, is widely used in psychometrics to model the relationship between individuals' latent traits and their binary responses to assessments or questionnaires. In this paper, we introduce a new likelihood-based estimator -- random pairing maximum likelihood estimator ($\mathrm{RP\text{-}MLE}$) and its bootstrapped variant multiple random pairing MLE ($\mathrm{MRP\text{-}MLE}$) which faithfully estimate the item parameters in the Rasch model. The new estimators have several appealing features compared to existing ones. First, both work for sparse observations, an increasingly important scenario in the big data era. Second, both estimators are provably minimax optimal in terms of finite sample $\ell_{\infty}$ estimation error. Lastly, both admit precise distributional characterization that allows uncertainty quantification on the it...