Skip to main content

Descriptive and explanatory item response models

  • Chapter
Explanatory Item Response Models

Part of the book series: Statistics for Social Science and Public Policy ((SSBS))

Abstract

In this chapter we present four item response models. These four models are comparatively simple within the full range of models in this volume, but some of them are more complex than the common item response models. On the one hand, all four models provide a measurement of individual differences, but on the other hand we use the models to demonstrate how the effect of person characteristics and of item design factors can be investigated. The models range from descriptive measurement for the case where no such effects are investigated, to explanatory measurement for the case where person properties and/or item properties are used to explain the effects of persons and/or items.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adams, R.J., Wilson, M., & Wang, W. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23.

    Article  Google Scholar 

  • Adams, R.J., Wilson, M., & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22, 47–76.

    Google Scholar 

  • Akaike, M. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.

    Article  MathSciNet  MATH  Google Scholar 

  • Andersen, E.B., & Olsen, L.W. (2001). The life of Georg Rasch as a mathematician and as a statistician. In A. Boomsma, M. A. J van Duijn & T.A.B. Snijders (Eds), Essays on Item Response Theory (pp. 3–24). New-York: Springer.

    Chapter  Google Scholar 

  • Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F.M. Lord & M.R. Novick (Eds), Statistical Theories of Mental Test Scores (pp. 394–479). Reading, MA: Addison-Wesley.

    Google Scholar 

  • Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika, 46, 443–459.

    Article  MathSciNet  Google Scholar 

  • Bond, T., & Fox, C. (2001). Applying the Rasch Model: Fundamental Measurement in Human Sciences. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Bozdogan, H. (1987). Model selection for Akaike’s information criterion (AIC). Psychometrika, 53, 345–370.

    Article  MathSciNet  Google Scholar 

  • de Leeuw, J., & Verhelst, N. (1986). Maximum-likelihood estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183–196.

    Article  Google Scholar 

  • Fischer, G.H. (1968). Neue Entwicklungen in der psychologischen Testtheorie. In G.H. Fischer (Ed.), Psychologische Testtheorie (pp. 15–158). Bern: Huber.

    Google Scholar 

  • Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 3, 359–374.

    Article  Google Scholar 

  • Fischer, G.H. (1974). Einführung in die Theorie Psychologischer Tests. Bern: Huber.

    MATH  Google Scholar 

  • Fischer, G.H. (1977). Linear logistic trait models: Theory and application. In H. Spada & W.F. Kampf (Eds), Structural Models of Thinking and Learning (pp. 203–225). Bern: Huber.

    Google Scholar 

  • Fischer, G.H. (1981). On the existence and uniqueness of maximum-likelihood estimates in the Rasch model. Psychometrika, 46, 59–77.

    Article  MathSciNet  MATH  Google Scholar 

  • Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Fischer, G.H. (1989). An IRT-based model for dichotomous longitudinal data. Psychometrika, 54, 599–624.

    Article  Google Scholar 

  • Fischer, G.H. (1995). Linear logistic models for change. In G.H. Fischer & I. Molenaar (Eds), Rasch Models. Foundations, Recent Developments and Applications (pp. 157–201). New York: Springer.

    Google Scholar 

  • Fischer, G.H., & Molenaar, I. (1995) (Eds), Rasch Models. Foundations, Recent Developments, and Applications. New York: Springer.

    Google Scholar 

  • Follmann, D.A. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika, 53, 553–562.

    Article  MathSciNet  MATH  Google Scholar 

  • Fox, J.P., & Glas, C.A.W. (2003). Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika, 68, 169–191.

    Article  MathSciNet  Google Scholar 

  • Hoijtink, H., & Boomsma, A. (1995). On person parameter estimation in the dichotomous Rasch Model. In G.H. Fischer & I. Molenaar (Eds), Rasch Models. Foundations, Recent Developments and Applications (pp. 53–68). New York: Springer.

    Google Scholar 

  • Junker, B., & Sijtsma, K. (2001). Nonparametric item response theory. Special issue. Applied Psychological Measurement, 25.

    Google Scholar 

  • Masters, G.N., Adams, R.A., & Wilson, M. (1990). Charting of student progress. In T. Husen & T.N. Postlewaite (Eds), International Encyclopedia of Education: Research and Studies. Supplementary Volume 2. (pp. 628–634) Oxford: Pergamon Press.

    Google Scholar 

  • Mischel, W. (1968). Personality Assessment. New York: Wiley, 1968.

    Google Scholar 

  • Mislevy, R.J. (1987). Exploiting auxiliary information about examinees in the estimation of item parameters. Applied Psychological Measurement, 11, 81–91.

    Article  Google Scholar 

  • Molenaar, I. (1995). Estimation of item parameters. In G.H. Fischer & I. Molenaar (Eds), Rasch Models. Foundations, Recent Developments and Applications (pp. 39–57). New York: Springer.

    Google Scholar 

  • Rabe-Hesketh, S., Pickles, A., & Skrondal, A. (2001). GLLAMM Manual. Technical Report 2001/01. Department of Biostatistics and Computing, Institute of Psychiatry, King’s College, University of London.

    Google Scholar 

  • Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen, Denmark: Danish Institute for Educational Research.

    Google Scholar 

  • Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Theory of Probability (Vol. IV, pp. 321–333). Berkeley, CA: University of California Press.

    Google Scholar 

  • Rasch, G. (1967). An informal report on a theory of objectivity in comparisons. In L.J.Th. van der Kamp & C.A.J. Vlek (Eds), Psychological Measurement Theory (pp. 1–19). Proceedings of The NUFFIC international summer session. Leiden: University of Leiden.

    Google Scholar 

  • Read, T.R.C., & Cressie, N.A.C. (1988). Goodness-of-fit Statistics for Discrete Multivariate Data. New York: Springer.

    Book  MATH  Google Scholar 

  • Rost, J. (2001). The growing family of Rasch models. In A. Boomsma, M.A.J van Duijn & T.A.B. Snijders (Eds), Essays on Item Response theory (pp. 25–42). New York: Springer.

    Chapter  Google Scholar 

  • SAS Institute (1999). SAS OnlineDoc (Version 8) (software manual on CD-ROM). Cary, NC: SAS Institute.

    Google Scholar 

  • Scheiblechner, H. (1972). Das Lernen and Lösen komplexer Denkaufgaben. Zeitschrift für Experimentelle und Angewandte Psychologie, 3, 456–506.

    Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.

    Article  MathSciNet  MATH  Google Scholar 

  • Sijtsma, K., & Molenaar, I. (2002). Introduction to Nonparametric Item Response Theory. Thousand Oaks, CA: Sage.

    MATH  Google Scholar 

  • Snijders, T., & Bosker, R. (1999). Multilevel Analysis. London: Sage.

    MATH  Google Scholar 

  • Thissen, D., & Orlando, M. (2001). Item response theory for items scored in two categories. In D. Thissen & H. Wainer (Eds), Test Scoring (pp. 73–140). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Verbeke, C., & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer.

    MATH  Google Scholar 

  • Verhelst, N.D., & Eggen, T.J.H.M. (1989). Psychometrische en statistische aspecten van peilingsonderzoek (PPON rapport 4). Arnhem: Cito.

    Google Scholar 

  • Verhelst, N.D., & Glas, C.A.W. (1995). The one parameter logistic model. In G.H. Fisher & I. Molenaar (Eds), Rasch Models. Foundations, Recent Developments, and Applications (pp. 215–237). New York: Springer.

    Google Scholar 

  • Wainer, H., Vevea, J.L., Camacho, F., Reeve, B.B., Rosa, K., Nelson, L., Swygert, K., & Thissen, D. (2001). Augmented scores — “Borrowing strength” to compute scores based on small numbers of items. In D. Thissen & H. Wainer (Eds), Test Scoring (pp. 343–387). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Wald, A. (1941). Asymptotically most powerful tests of statistical hypotheses. Annals of Mathematical Statistics, 12, 1–19.

    Article  MathSciNet  Google Scholar 

  • Warm, T.A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450

    Article  MathSciNet  Google Scholar 

  • Wilson, M. (2003). On choosing a model for measuring. Methods of Psychological Research — Online, 8(3), 1–22.

    Google Scholar 

  • Wilson, M. (2005). Constructing Measures: An Item Modeling Approach. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Wright, B. (1968). Sample-free test calibration and person measurement. Proceedings 1967 Invitational Conference on Testing (pp. 85–101). Princeton: ETS.

    Google Scholar 

  • Wright, B. (1977). Solving measurement problems with the Rasch model. Journal of Educational Measurement, 14, 97–116.

    Article  Google Scholar 

  • Wright, B. (1997). A history of social science measurement. Educational Measurement: Issues and Practice, 16, 33–52.

    Article  Google Scholar 

  • Wright, B., & Stone, M. (1979). Best Test Design. Chicago, IL: MESA.

    Google Scholar 

  • Wu, M.L., Adams, R.J., & Wilson, M. (1998). ACERConquest Hawthorn, Australia: ACER Press.

    Google Scholar 

  • Zwinderman, A.H. (1991). A generalized Rasch model for manifest predictors. Psychometrika, 56, 589–600.

    Article  MATH  Google Scholar 

  • Zwinderman, A.H. (1997). Response models with manifest predictors. In W.J. van der Linden & R.K. Hambleton (Eds), Handbook of Modern Item Response Theory (pp. 245–256). New York: Springer.

    Chapter  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this chapter

Cite this chapter

Wilson, M., De Boeck, P. (2004). Descriptive and explanatory item response models. 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_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3990-9_2

  • 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

Publish with us

Policies and ethics