A Note on the Item Information Function of the Four-Parameter Logistic Model

David Magis

44 citations0/0 files storedApplied Psychological Measurement

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

This article focuses on four-parameter logistic (4PL) model as an extension of the usual three-parameter logistic (3PL) model with an upper asymptote possibly different from 1. For a given item with fixed item parameters, Lord derived the value of the latent ability level that maximizes the item information function under the 3PL model. The purpose of this article is to extend this result to the 4PL model. A generic and algebraic method is developed for that purpose. The result is practically illustrated by an example and several potential applications of this result are outlined.

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References

1969Statistical Theories of Mental Test Scores 2012Applications of Item Response Theory To Practical Testing Problems 1968Some latent trait models and their use in inferring an examinee's ability 1984Item Response Theory: Principles and Applications 1985Item Response Theory 1986Basic Algebra I.2002Analyzing Multiple-Item Measures of Crime and Deviance I: Item Response Theory Scaling 1981AN UPPER ASYMPTOTE FOR THE THREE‐PARAMETER LOGISTIC ITEM‐RESPONSE MODEL*

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2022Some thoughts on analytical choices in the scaling model for test scores in international large-scale assessment studies 2017Bayesian Modal Estimation of the Four-Parameter Item Response Model in Real, Realistic, and Idealized Data Sets 2017The Prevalence and Implications of Slipping on Low-Stakes, Large-Scale Assessments

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