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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.

Suggested Citation

  • 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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    References listed on IDEAS

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    1. Hua-Hua Chang & Zhiliang Ying, 2008. "To Weight or Not to Weight? Balancing Influence of Initial Items in Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 441-450, September.
    2. D. Holmes, 1990. "The robustness of the usual correction for restriction in range due to explicit selection," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 19-32, March.
    3. Ogasawara, Haruhiko, 2012. "Supplement to the paper“ Asymptotic expansions for the ability estimator in item response theory”," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 63(2/3), pages 329-336.
    4. Richard J. Patz & Brian W. Junker, 1999. "Applications and Extensions of MCMC in IRT: Multiple Item Types, Missing Data, and Rated Responses," Journal of Educational and Behavioral Statistics, , vol. 24(4), pages 342-366, December.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Jorge Mendoza, 1993. "Fisher transformations for correlations corrected for selection and missing data," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 601-615, December.
    7. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    8. Richard J. Patz & Brian W. Junker, 1999. "A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models," Journal of Educational and Behavioral Statistics, , vol. 24(2), pages 146-178, June.
    9. James H. Albert, 1992. "Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 17(3), pages 251-269, September.
    10. Haruhiko Ogasawara, 2012. "Asymptotic expansions for the ability estimator in item response theory," Computational Statistics, Springer, vol. 27(4), pages 661-683, December.
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    Cited by:

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    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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