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On the Sampling Theory Roundations of Item Response Theory Models

Published online by Cambridge University Press:  01 January 2025

Paul W. Holland
Paul W. Holland*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Paul W. Holland, Educational Testing Service, Rosedale Road 21-T, Princeton, NJ 08541.
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Abstract

Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the “stochastic subject” versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating θ versus estimating θ-predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.

Keywords

stochastic subjectsmarginal maximum likelihood (MML)conditional maximum likelihood (CML)unconditional maximum likelihood (UML)joint maximum likelihood (JML)probability simplexloglinear modelsrobustness
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 577 - 601
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

A presidential address can serve many different functions. This one is a report of investigations I started at least ten years ago to understand what IRT was all about. It is a decidedly one-sided view, but I hope it stimulates controversy and further research. I have profited from discussions of this material with many people including: Brian Junker, Charles Lewis, Nicholas Longford, Robert Mislevy, Ivo Molenaar, Donald Rock, Donald Rubin, Lynne Steinberg, Martha Stocking, William Stout, Dorothy Thayer, David Thissen, Wim van der Linden, Howard Wainer, and Marilyn Wingersky. Of course, none of them is responsible for any errors or misstatements in this paper. The research was supported in part by the Cognitive Science Program, Office of Naval Research under Contract No. Nooo14-87-K-0730 and by the Program Statistics Research Project of Educational Testing Service.

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