Homogeneity-Pursuit Calibration of Item Response Theory Models with Limited Samples and Sparse Response Data

Calibrating item response theory models is challenging when item banks are large relative to available sample sizes and response data are sparsely observed, as commonly occurs in classroom assessment, low-stakes testing, and early-stage item bank development. These challenges are particularly pronounced for the two-parameter logistic model, where unconstrained estimation often yields unstable or extreme item parameter estimates. To address this problem, we propose a new calibration framework based on homogeneity pursuit (HP), which stabilizes estimation by adaptively pooling information across items with similar psychometric properties. Rather than aiming to recover exact latent groupings, HP reduces effective model complexity through data-driven equality constraints, improving finite-sample estimation accuracy. We develop two variants of the proposed framework-HP-Scott and HP-Silhouette-that differ in the criteria used to guide adaptive pooling. Three simulation studies evaluate the performance of HP under idealized and realistic item-bank settings, including continuous parameter variation, small sample sizes, and high missing-response rates. Across these conditions, HP consistently reduces estimation error and mitigates extreme parameter estimates compared with baseline approaches. A real classroom assessment application with over 60% missing responses further demonstrates that HP produces more plausible item parameter estimates and superior model fit.