Abstract
In the present chapter, the focus is on extending item response models on the item side. Item and item group predictors are included as external factors and the item parameters β i are considered as random effects. When the items are modeled to come from one common distribution, the models are descriptive on the item side. When item predictors of the property type are included, the models are explanatory on the item side. Item groups are a special case of item properties. They refer to binary, non-overlapping properties indicating group membership. The resulting models with item properties can all be described as linear logistic test models (LLTM; Fischer, 1995) with an error term in the prediction of item difficulty. When this random item variation is combined with random person variation, models with crossed random effects are obtained. All models in this chapter are of that kind.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Albert, J.H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17, 251–269.
Béguin, A.A. & Glas, C.A.W. (2001). MCMC estimation and some model-fit analyses of multidimensional IRT models. Psychometrika, 66, 541–561.
Bejar, I.I. (2002). Generative testing: Prom conception to implementation. In S.H. Irvine & P.C. Kyllonen (Eds), Generating Items from Cognitive Tests: Theory and Practice (pp. 199–217). Mahwah, NJ: Lawrence Erlbaum.
Bradlow, E.T., Wainer, H. & Wang, X. (1999). A Bayesian random effects model for testlets. Psychometrika, 64, 153–168.
Embretson, S.E. (1999). Generating items during testing: Psychometric issues and models. Psychometrika, 64, 407–433.
Fischer, G.H. (1995). The linear logistic test model. In G.H. Fischer & I.W. Molenaar (Eds), Rasch Models: Foundations, Recent Developments, and Applications (pp. 131–155). New York: Springer.
Gelman, A. (1995). Inference and monitoring convergence. In W.R. Gilks, S. Richardson & D.J. Spiegelhalter (Eds), Markov Chain Monte Carlo in Practice (pp. 131–143). New York: Chapman & Hall.
Gelman, A., Carlin, J.B., Stern, H.S. & Rubin, D.B. (1995). Bayesian Data Analysis. New York: Chapman & Hall.
Gelman, A., Meng, X.L. & Stern, H.S. (1996). Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Sta-tistica Sinica, 6, 733–807.
Gilks, W.R., Richardson, S. & Spiegelhalter, D.J.E. (1996). Markov Chain Monte Carlo in Practice. New York: Chapman & Hall.
Glas, C.A.W. & Van der Linden, W. (2002). Modeling variability in item response models. (Research Report.) University of Twente, Faculty of Educational Science and Technology, Department of Educational Measurement and Data Analysis.
Glas, C.A.W., Wainer, H. & Bradlow, E.T. (2000). MML and EAP estimates for the testlet response model. In W.J. Van der Linden & C.A.W. Glas (Eds), Computerized Adaptive Testing: Theory into Practice (pp. 271–287). Boston, MA: Kluwer-Nijhoff.
Haberman, S.J. (1997). Maximum likelihood estimates in exponential response models. Annals of Statistics, 5, 815–841.
Janssen, R., De Boeck, P. & Schepers, J. (2003). The random-effects version of the linear logistic test model. Manuscript submitted for publication.
Janssen, R., Tuerlinckx, F., Meulders, M. & De Boeck, P. (2000). A hierarchical IRT model for criterion-referenced measurement. Journal of Educational and Behavioral Statistics, 25, 285–306.
Maris, G. & Maris, E. (2002). A MCMC-method for models with continuous latent responses. Psychometrika, 67, 335–350.
Meng, X.L. (1994). Posterior predictive p-values. Annals of Statistics, 22, 1142–1160.
Mislevy, R.J. (1988). Exploiting auxiliary information about items in the estimation of Rasch item difficulty parameters. Applied Psychological Measurement, 12, 725–737.
Patz, R.J. & Junker, B.W. (1999). A straightforward approach to Markov Chain Monte Carlo methods for item response models. Journal of Educational and Behavioral Statistics, 24, 146–178.
Sheehan, K. & Mislevy, R.J. (1990). Integrating cognitive and psychometric models to measure document literacy. Journal of Educational Measurement, 27, 255–277.
Swaminathan, H. & Gifford, J. (1982). Bayesian estimation in the Rasch model. Journal of Educational Statistics, 7, 175–191.
Tanner, M.A. (1996). Tools for statistical inference: Methods for the exploration of posterior distributions and likelihood functions (3rd ed.). New York: Springer.
Van den Noortgate, W., De Boeck, P. & Meulders, M. (2003). Cross-classification multilevel logistic models in psychometrics. Journal of Educational and Behavioral Statistics. Manuscript accepted for publication.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Janssen, R., Schepers, J., Peres, D. (2004). Models with item and item group predictors. In: De Boeck, P., Wilson, M. (eds) Explanatory Item Response Models. Statistics for Social Science and Public Policy. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3990-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3990-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2323-3
Online ISBN: 978-1-4757-3990-9
eBook Packages: Springer Book Archive