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Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application

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  • Steven Andrew Culpepper

    (University of Illinois at Urbana-Champaign)

Abstract

There has been renewed interest in Barton and Lord’s (An upper asymptote for the three-parameter logistic item response model (Tech. Rep. No. 80-20). Educational Testing Service, 1981) four-parameter item response model. This paper presents a Bayesian formulation that extends Béguin and Glas (MCMC estimation and some model fit analysis of multidimensional IRT models. Psychometrika, 66 (4):541–561, 2001) and proposes a model for the four-parameter normal ogive (4PNO) model. Monte Carlo evidence is presented concerning the accuracy of parameter recovery. The simulation results support the use of less informative uniform priors for the lower and upper asymptotes, which is an advantage to prior research. Monte Carlo results provide some support for using the deviance information criterion and $$\chi ^{2}$$ χ 2 index to choose among models with two, three, and four parameters. The 4PNO is applied to 7491 adolescents’ responses to a bullying scale collected under the 2005–2006 Health Behavior in School-Aged Children study. The results support the value of the 4PNO to estimate lower and upper asymptotes in large-scale surveys.

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  • Steven Andrew Culpepper, 2016. "Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1142-1163, December.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:4:d:10.1007_s11336-015-9477-6
    DOI: 10.1007/s11336-015-9477-6
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    Cited by:

    1. Justin L. Kern & Steven Andrew Culpepper, 2020. "A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 575-599, September.
    2. Justin L. Kern, 2024. "Extending an Identified Four-Parameter IRT Model: The Confirmatory Set-4PNO Model," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 368-402, June.
    3. Steven Andrew Culpepper, 2019. "An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 921-940, December.
    4. Christian A. Gregory, 2020. "Are We Underestimating Food Insecurity? Partial Identification with a Bayesian 4-Parameter IRT Model," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 632-655, October.
    5. Xiangyi Liao & Daniel M. Bolt, 2021. "Item Characteristic Curve Asymmetry: A Better Way to Accommodate Slips and Guesses Than a Four-Parameter Model?," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 753-775, December.
    6. Steven Andrew Culpepper & Yinghan Chen, 2019. "Development and Application of an Exploratory Reduced Reparameterized Unified Model," Journal of Educational and Behavioral Statistics, , vol. 44(1), pages 3-24, February.
    7. Steven Andrew Culpepper, 2017. "The Prevalence and Implications of Slipping on Low-Stakes, Large-Scale Assessments," Journal of Educational and Behavioral Statistics, , vol. 42(6), pages 706-725, December.
    8. Chanjin Zheng & Shaoyang Guo & Justin L Kern, 2021. "Fast Bayesian Estimation for the Four-Parameter Logistic Model (4PLM)," SAGE Open, , vol. 11(4), pages 21582440211, October.
    9. Steven Andrew Culpepper, 2019. "Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 333-357, June.

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