Advertisement

Descriptive and explanatory item response models

  • Mark Wilson
  • Paul De Boeck
Part of the Statistics for Social Science and Public Policy book series (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.

Keywords

Item Response Theory Person Property Item Parameter Verbal Aggression Trait Anger 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Adams, R.J., Wilson, M., & Wang, W. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23.CrossRefGoogle Scholar
  2. 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
  3. Akaike, M. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 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.CrossRefGoogle Scholar
  5. 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
  6. Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika, 46, 443–459.MathSciNetCrossRefGoogle Scholar
  7. Bond, T., & Fox, C. (2001). Applying the Rasch Model: Fundamental Measurement in Human Sciences. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  8. Bozdogan, H. (1987). Model selection for Akaike’s information criterion (AIC). Psychometrika, 53, 345–370.MathSciNetCrossRefGoogle Scholar
  9. de Leeuw, J., & Verhelst, N. (1986). Maximum-likelihood estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183–196.CrossRefGoogle Scholar
  10. Fischer, G.H. (1968). Neue Entwicklungen in der psychologischen Testtheorie. In G.H. Fischer (Ed.), Psychologische Testtheorie (pp. 15–158). Bern: Huber.Google Scholar
  11. Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 3, 359–374.CrossRefGoogle Scholar
  12. Fischer, G.H. (1974). Einführung in die Theorie Psychologischer Tests. Bern: Huber.zbMATHGoogle Scholar
  13. 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
  14. Fischer, G.H. (1981). On the existence and uniqueness of maximum-likelihood estimates in the Rasch model. Psychometrika, 46, 59–77.MathSciNetzbMATHCrossRefGoogle Scholar
  15. Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–26.MathSciNetzbMATHCrossRefGoogle Scholar
  16. Fischer, G.H. (1989). An IRT-based model for dichotomous longitudinal data. Psychometrika, 54, 599–624.CrossRefGoogle Scholar
  17. 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
  18. Fischer, G.H., & Molenaar, I. (1995) (Eds), Rasch Models. Foundations, Recent Developments, and Applications. New York: Springer.Google Scholar
  19. Follmann, D.A. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika, 53, 553–562.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Fox, J.P., & Glas, C.A.W. (2003). Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika, 68, 169–191.MathSciNetCrossRefGoogle Scholar
  21. 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
  22. Junker, B., & Sijtsma, K. (2001). Nonparametric item response theory. Special issue. Applied Psychological Measurement, 25. Google Scholar
  23. 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
  24. Mischel, W. (1968). Personality Assessment. New York: Wiley, 1968.Google Scholar
  25. Mislevy, R.J. (1987). Exploiting auxiliary information about examinees in the estimation of item parameters. Applied Psychological Measurement, 11, 81–91.CrossRefGoogle Scholar
  26. 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
  27. 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
  28. Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen, Denmark: Danish Institute for Educational Research.Google Scholar
  29. 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
  30. 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
  31. Read, T.R.C., & Cressie, N.A.C. (1988). Goodness-of-fit Statistics for Discrete Multivariate Data. New York: Springer.zbMATHCrossRefGoogle Scholar
  32. 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.CrossRefGoogle Scholar
  33. SAS Institute (1999). SAS OnlineDoc (Version 8) (software manual on CD-ROM). Cary, NC: SAS Institute.Google Scholar
  34. Scheiblechner, H. (1972). Das Lernen and Lösen komplexer Denkaufgaben. Zeitschrift für Experimentelle und Angewandte Psychologie, 3, 456–506.Google Scholar
  35. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.MathSciNetzbMATHCrossRefGoogle Scholar
  36. Sijtsma, K., & Molenaar, I. (2002). Introduction to Nonparametric Item Response Theory. Thousand Oaks, CA: Sage.zbMATHGoogle Scholar
  37. Snijders, T., & Bosker, R. (1999). Multilevel Analysis. London: Sage.zbMATHGoogle Scholar
  38. 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
  39. Verbeke, C., & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer.zbMATHGoogle Scholar
  40. Verhelst, N.D., & Eggen, T.J.H.M. (1989). Psychometrische en statistische aspecten van peilingsonderzoek (PPON rapport 4). Arnhem: Cito.Google Scholar
  41. 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
  42. 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
  43. Wald, A. (1941). Asymptotically most powerful tests of statistical hypotheses. Annals of Mathematical Statistics, 12, 1–19.MathSciNetCrossRefGoogle Scholar
  44. Warm, T.A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450MathSciNetCrossRefGoogle Scholar
  45. Wilson, M. (2003). On choosing a model for measuring. Methods of Psychological Research — Online, 8(3), 1–22.Google Scholar
  46. Wilson, M. (2005). Constructing Measures: An Item Modeling Approach. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  47. Wright, B. (1968). Sample-free test calibration and person measurement. Proceedings 1967 Invitational Conference on Testing (pp. 85–101). Princeton: ETS.Google Scholar
  48. Wright, B. (1977). Solving measurement problems with the Rasch model. Journal of Educational Measurement, 14, 97–116.CrossRefGoogle Scholar
  49. Wright, B. (1997). A history of social science measurement. Educational Measurement: Issues and Practice, 16, 33–52.CrossRefGoogle Scholar
  50. Wright, B., & Stone, M. (1979). Best Test Design. Chicago, IL: MESA.Google Scholar
  51. Wu, M.L., Adams, R.J., & Wilson, M. (1998). ACERConquest Hawthorn, Australia: ACER Press.Google Scholar
  52. Zwinderman, A.H. (1991). A generalized Rasch model for manifest predictors. Psychometrika, 56, 589–600.zbMATHCrossRefGoogle Scholar
  53. 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.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Mark Wilson
  • Paul De Boeck

There are no affiliations available

Personalised recommendations