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Estimating parameters of dichotomous and ordinal item response models with gllamm

Author

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  • Xiaohui Zheng

    () (Graduate School of Education, University of California, Berkeley)

  • Sophia Rabe-Hesketh

    (Graduate School of Education, University of California, Berkeley)

Abstract

Item response theory models are measurement models for categorical responses. Traditionally, the models are used in educational testing, where responses to test items can be viewed as indirect measures of latent ability. The test items are scored either dichotomously (correct–incorrect) or by using an ordinal scale (a grade from poor to excellent). Item response models also apply equally for measurement of other latent traits. Here we describe the one- and two-parameter logit models for dichotomous items, the partial-credit and rating scale models for ordinal items, and an extension of these models where the latent variable is regressed on explanatory variables. We show how these models can be expressed as generalized linear latent and mixed models and fitted by using the user-written command gllamm. Copyright 2007 by StataCorp LP.

Suggested Citation

  • Xiaohui Zheng & Sophia Rabe-Hesketh, 2007. "Estimating parameters of dichotomous and ordinal item response models with gllamm," Stata Journal, StataCorp LP, vol. 7(3), pages 313-333, September.
  • Handle: RePEc:tsj:stataj:v:7:y:2007:i:3:p:313-333
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    References listed on IDEAS

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    1. Jean-Benoit Hardouin, 2007. "Rasch analysis: Estimation and tests with raschtest," Stata Journal, StataCorp LP, vol. 7(1), pages 22-44, February.
    2. Anders Skrondal & Sophia Rabe-Hesketh, 2003. "Multilevel logistic regression for polytomous data and rankings," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 267-287, June.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    4. Aeilko Zwinderman, 1991. "A generalized rasch model for manifest predictors," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 589-600, December.
    5. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    6. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
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    Cited by:

    1. repec:zbw:rwirep:0378 is not listed on IDEAS
    2. Raileanu Szeles, Monica & Fusco, Alessio, 2009. "Item response theory and the measurement of deprivation: Evidence from PSELL-3," IRISS Working Paper Series 2009-05, IRISS at CEPS/INSTEAD.
    3. Olugbenga Ajilore & Gayle Alberda, 2017. "Peer Effects and Political Participation: What is the Role of Coursework Clusters?," The Review of Regional Studies, Southern Regional Science Association, vol. 47(1), pages 47-62, Winter.
    4. FAYE Ousmane & BASCHIERI Angela & FALKINGHAM Jane & MUINDI Kanyiva, 2010. "Hunger and Food Insecurity in Nairobi's Slums: An assessment using IRT models'," LISER Working Paper Series 2010-33, LISER.
    5. Michaelsen, Maren M., 2012. "Mental Health and Labour Supply – Evidence from Mexico's Ongoing Violent Conflicts," Ruhr Economic Papers 378, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    6. Jean-Benoit Hardouin & Angelique Bonnaud-Antignac & Veronique Sebille, 2011. "Nonparametric item response theory using Stata," Stata Journal, StataCorp LP, vol. 11(1), pages 30-51, March.
    7. Monica Szeles & Alessio Fusco, 2013. "Item response theory and the measurement of deprivation: evidence from Luxembourg data," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(3), pages 1545-1560, April.
    8. Maren M. Michaelsen, 2012. "Mental Health and Labour Supply – Evidence from Mexico‘s Ongoing Violent Conflicts," Ruhr Economic Papers 0378, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    9. repec:spr:soinre:v:133:y:2017:i:2:d:10.1007_s11205-016-1383-5 is not listed on IDEAS

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