The Hierarchical Rater Model for Rated Test Items and its Application to Large-Scale Educational Assessment Data

Abstract

Open-ended or “constructed” student responses to test items have become a stock component of standardized educational assessments. Digital imaging of examinee work now enables a distributed rating process to be flexibly managed, and allocation designs that involve as many as six or more ratings for a subset of responses are now feasible. In this article we develop Patz’s (1996) hierarchical rater model (HRM) for polytomous item response data scored by multiple raters, and show how it can be used to scale examinees and items, to model aspects of consensus among raters, and to model individual rater severity and consistency effects. The HRM treats examinee responses to open-ended items as unobsered discrete varibles, and it explicitly models the “proficiency” of raters in assigning accurate scores as well as the proficiency of examinees in providing correct responses. We show how the HRM “fits in” to the generalizability theory framework that has been the traditional tool of analysis for rated item response data, and give some relationships between the HRM, the design effects correction of Bock, Brennan and Muraki (1999), and the rater bundle model of Wilson and Hoskens (2002). Using simulated and real data, we compare the HRM to the conventional IRT Facets model for rating data (e.g., Linacre, 1989; Engelhard, 1994, 1996), and we explore ways that information from HRM analyses may improved the quality of the rating process.