Keywords
Item Response Theory, Quantile Regression, Graded Response Model, Generalized Partial Credit Model, Robust estimation
Abstract
This dissertation investigates robust estimation of linking coefficients in Item Response Theory (IRT) using quantile regression and its extensions. Linking procedures are essential for placing item and ability parameters from different test forms onto a common scale, thereby ensuring comparability of examinee scores across administrations. Traditional approaches such as moment methods, characteristic curve methods, and mean-based regression procedures like Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) perform adequately under ideal conditions but tend to lose accuracy when ability distributions deviate from normality or include outliers.
To address these limitations, this research proposes a quantile-based regression framework that estimates conditional quantiles rather than means, offering robustness against asymmetry and heavy-tailed distributions. Two major IRT models were investigated: the Graded Response Model (GRM) and the Generalized Partial Credit Model (GPCM). Simulation studies under a variety of non-normal latent trait distributions including Gamma, Weibull, and Cauchy were conducted to compare the performance of Quantile Regression (QR), Composite Quantile Regression (CQR), and Weighted Composite Quantile Regression (WCQR) with traditional OLS, GLS, and characteristic-curve methods.
The results consistently demonstrate that quantile-based estimators, particularly WCQR, yield more stable and accurate estimates of the linking coefficients under skewed and heavy-tailed distributions. These methods substantially reduce bias and standard error compared to mean-based approaches, especially when sample sizes are small or the number of common items is limited. The findings were further validated through application to real-world assessment data, confirming the practical utility of quantile regression in large-scale testing contexts.
Overall, this dissertation provides theoretical and empirical evidence supporting quantile regression as a robust alternative for IRT scale linking. By enhancing the reliability of score transformations under realistic data conditions, the proposed framework contributes to more accurate and equitable score interpretations in educational and psychological measurement.
Completion Date
2026
Semester
Spring
Committee Chair
Larry Tang
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Statistics and Data Science
Document Type
Thesis
Identifier
DP0053120
STARS Citation
Almansour, Ibrahim, "Robust Linking Estimation in Item Response Theory Using Quantile Regression: Applications to the Graded Response and Generalized Partial Credit Models" (2026). Graduate Studies Theses and Dissertations 2026. 10.
https://stars.library.ucf.edu/gradstudies_etd_2026/10
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