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Estimating parameters of dichotomous and ordinal item response models with gllamm

  • Xiaohui Zheng


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

  • Sophia Rabe-Hesketh

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

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.

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Article provided by StataCorp LP in its journal Stata Journal.

Volume (Year): 7 (2007)
Issue (Month): 3 (September)
Pages: 313-333

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Handle: RePEc:tsj:stataj:v:7:y:2007:i:3:p:313-333
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  1. Aeilko Zwinderman, 1991. "A generalized rasch model for manifest predictors," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 589-600, December.
  2. 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.
  3. Jean-Benoit Hardouin, 2007. "Rasch analysis: Estimation and tests with raschtest," Stata Journal, StataCorp LP, vol. 7(1), pages 22-44, February.
  4. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
  5. 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.
  6. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
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