Abstract
In this chapter we consider the inclusion of person-by-item predictors into the model. Unlike person predictors or item predictors, person-by-item predictors vary both within and between persons. The inclusion of person-by-item predictors besides person predictors or item predictors is relevant for modeling various phenomena such as differential item functioning (DIF) and local item dependencies (LID) (see Zwinderman, 1997). To describe models with person-by-item predictors we will distinguish between static and dynamic interaction models. We concentrate here on models for DIF and LID, but the interaction concept is of course more general.
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References
Arnold, B.C. & Press, S.J. (1989). Compatible conditional distributions. Journal of the American Statistical Association, 84, 152–156.
Diggle, P.J., Heagerty, P., Liang, K. & Zeger, S.L. (2002). Analysis of Longitudinal Data (2nd ed.). New York: Oxford University Press.
Dorans, N.J. & Holland, P.W. (1993). DIF detection and description: Mantel-Haenszel and standardization. In P.W. Holland & W. Howard (Eds), Differential Item Functioning (pp. 35–66). Hillsdale, NJ: Lawrence Erlbaum.
Dorans, N.J. & Kulick, E. (1986). Demonstrating the utility of the standardization approach to assessing unexpected differential item performance on the scholastic aptitude test. Journal of Educational Measurement, 23, 355–368.
Engelhard, G. (1992). The measurement of writing ability with a many-faceted Rasch model. Applied Measurement in Education, 5, 171–191.
Fahrmeir, L. & Tutz, G. (2001). Multivariate Statistical Modeling Based on Generalized Linear Models (2nd ed.). New York: Springer.
Gelman, A. & Speed, T.P. (1993). Characterizing a joint probability distribution by conditionals. Journal of the Royal Statistical Society. Series B, 55, 185–188.
Holland, P.W. & Thayer, D.T. (1988). Differential item functioning and the Mantel-Haenszel procedure. In H. Wainer & H.I. Braun (Eds), Test Validity (pp. 129–145). Hillsdale, NJ: Lawrence Erlbaum.
Holland, P.W. & Wainer, H. (1993). Differential Item Functioning. Hillsdale, NJ: Lawrence Erlbaum.
Hoskens, M. & De Boeck, P. (1995). Componential IRT models for polytomous items. Journal of Educational Measurement, 32, 364–384.
Hoskens, M. & De Boeck, P. (1997). A parametric model for local dependence among test items. Psychological Methods, 2, 261–277.
Hunt, L.A. & Jorgensen, M.A. (1999). Mixture model clustering: A brief introduction to the MULTIMIX program. Australian and New Zealand Journal of Statistics, 41, 153–171.
Ip, E.H., Wang, J.W., De Boeck, P. & Meulders, M. (2003). Locally dependent latent trait models for polytomous responses. Psychometrika. Manuscript accepted for publication.
Jannarone, R.J. (1986). Conjunctive item response theory kernels. Psychometrika, 51, 357–373.
Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49, 223–245.
Kelderman, H. (1989). Item bias detection using loglinear IRT. Psychometrika, 54, 681–697.
Klauer, K.C. & Sydow, H. (2001). Dynamic IRT models. In A. Boomsma, M.A.J. van Duijn & T.A.B. Snijders (Eds), Essays on Item Response Theory (pp. 69–87). New York: Springer.
Li, H. & Stout, W. (1996). A new procedure for detection of crossing DIF. Psychometrika, 61, 647–677.
Lord, F.M. (1980). Applications of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: Lawrence Erlbaum.
Mellenbergh, G.J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7, 105–118.
Millsap, R.E. & Everson, H.T. (1993). Methodology review: Statistical approaches for assessing measurement bias. Applied Psychological Measurement, 17, 297–334.
Moore, S.M. (1996). Estimating differential item functioning in the polytomous case with the RCML model. In G. Engelhard & M. Wilson (Eds), Objective Measurement: Theory into Practice (Vol.3) (pp. 219–240). Norwoord, NJ: Ablex.
Muraki, E. (1999). Stepwise analysis of differential item functioning based on multiple-group partial credit model. Journal of Educational Measurement, 36, 217–232.
Raju, N.S. (1988). The area between two item characteristic curves. Psychometrika, 53, 495–502.
Rosenbaum, P.R. (1988). Item bundles. Psychometrika, 53, 349–359.
Scheuneman, J.D. (1979). A method of assessing bias in test items. Journal of Educational Measurement, 16, 143–152.
Shealy, R. & Stout, W. (1993a). An item response theory model for test bias and differential item functioning. In P.W. Holland & W. Howard (Eds), Differential Item Functioning (pp. 197–239). Hillsdale, NJ: Lawrence Erlbaum.
Shealy, R. & Stout, W. (1993b). A model-based standardization approach that separates true bias/DIF from group ability differences and detects test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159–194.
Swaminathan, H. & Rogers, H.J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27, 361–370.
Thissen, D., Steinberg, L. & Wainer, H. (1988). Use of item-response theory in the study of group differences in trace lines. In H. Wainer & H.I. Braun (Eds), Test Validity (pp. 147–169). Hillsdale, NJ: Lawrence Erlbaum.
Verguts, T. & De Boeck, P. (2000). A Rasch model for learning while solving an intelligence test. Applied Psychological Measurement, 24, 151–162.
Verhelst, N.D. & Glas, C.A.W. (1993). A dynamic generalization of the Rasch model. Psychometrika, 58, 395–415.
Verhelst, N.D. & Glas, C.A.W. (1995). Dynamic generalizations of the Rasch model. In G.H. Fischer & I.W. Molenaar (Eds), Rasch Models: Foundations, Recent Developments, and Applications (pp. 181–201). New York: Springer.
Wainer, H., Sireci, S.G., & Thissen, D. (1991). Differential test let functioning: Definitions and detection. Journal of Educational Measurement, 28, 197–219.
Wainer, H. & Kiely, G. (1987). Item clusters and computerized adaptive testing: A case for testlets. Journal of Educational Measurement, 24, 185–201.
Wilson, M. & Adams, R.A. (1995). Rasch models for item bundles. Psychometrika, 60, 181–198.
Zimowski, F., Muraki, E., Mislevy, R.J. & Bock, R.D. (1994). BIMAIN 2: Multiple group IRT analysis and test maintenance for binary items. Chicago: Scientific Software International.
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.
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Meulders, M., Xie, Y. (2004). Person-by-item 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_7
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DOI: https://doi.org/10.1007/978-1-4757-3990-9_7
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