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2 results

  • Limits on Log Odds Ratios for Unidimensional Item Response Theory Models

  • Shelby J. Haberman, Paul W. Holland, Sandip Sinharay
  • Journal:
    Psychometrika / Volume 72 / Issue 4 / December 2007
    Published online by Cambridge University Press:
    01 January 2025, pp. 551-561

  • Bounds are established for log odds ratios (log cross-product ratios) involving pairs of items for item response models. First, expressions for bounds on log odds ratios are provided for one-dimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two-parameter logistic (2PL) model. Results are also illustrated through an example from a study of model-checking procedures. The bounds obtained can provide an elementary basis for assessment of goodness of fit of these models.

  • MCMC Estimation and Some Model-Fit Analysis of Multidimensional IRT Models

  • A. A. Béguin, C. A. W. Glas
  • Journal:
    Psychometrika / Volume 66 / Issue 4 / December 2001
    Published online by Cambridge University Press:
    01 January 2025, pp. 541-561

  • A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization of the procedure to a model with multidimensional ability parameters are presented. The procedure is a generalization of a procedure by Albert (1992) for estimating the two-parameter normal ogive model. The procedure supports analyzing data from multiple populations and incomplete designs. It is shown that restrictions can be imposed on the factor matrix for testing specific hypotheses about the ability structure. The technique is illustrated using simulated and real data.