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Item Parameter Estimation and Item Fit Analysis

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Elements of Adaptive Testing

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

Abstract

Computer-based testing (CBT), as computerized adaptive testing (CAT), is based on the availability of a large pool of calibrated test items. Usually, the calibration process consists of two stages.

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References

  • Ackerman, T. A. (1996a). Developments in multidimensional item response theory. Applied Psychological Measurement, 20, 309–310.

    Article  Google Scholar 

  • Ackerman, T. A. (1996b). Graphical representation of multidimensional item response theory analyses. Applied Psychological Measurement, 20, 311–329.

    Article  Google Scholar 

  • Aitchison, J. & Silvey, S. D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813–828.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Bock, R. D., Gibbons, R. D. & Muraki, E. (1988). Full-information factor analysis. Applied Psychological Measurement, 12, 261–280.

    Article  Google Scholar 

  • Bock, R. D. & Zimowski, M. F. (1997). Multiple group IRT. In W. J. van der Linden and R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 433–448). New York: Springer-Verlag.

    Google Scholar 

  • Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. R. Statist. Soc. B. 39, 1–38.

    MATH  MathSciNet  Google Scholar 

  • Efron, B. (1977). Discussion on maximum likelihood from incomplete data via the EM algorithm (by A. Dempster, N. Laird, and D. Rubin). J. R. Statist. Soc. B., 39, 1–38.

    Google Scholar 

  • Fischer, G. H. & Scheiblechner, H. H. (1970). Algorithmen und Programme für das probabilistische Testmodell von Rasch. Psychologische Beiträge, 12, 23–51.

    Google Scholar 

  • Glas, C. A. W. (1992). A Rasch model with a multivariate distribution of ability. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 1) (pp. 236–258). Norwood, NJ: Ablex Publishing Corporation.

    Google Scholar 

  • Glas, C. A. W. (1988). The Rasch Model and multi-stage testing. Journal of Educational Statistics, 13, 45–52.

    Article  Google Scholar 

  • Glas, C. A. W. (1998). Detection of differential item functioning using Lagrange multiplier tests. Statistica Sinica, 8, 647–667.

    MATH  MathSciNet  Google Scholar 

  • Glas, C. A. W. (1999). Modification indices for the 2-PL and the nominal response model. Psychometrika, 64, 273–294.

    Article  Google Scholar 

  • Glas, C. A. W. & Suarez-Falcon, J.C. (2003). A comparison of item-fit statistics for the three-parameter logistic model. Applied Psychological Measurement, 27, 87–106.

    Article  MathSciNet  Google Scholar 

  • Kiefer, J. & Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Annals of Mathematical Statistics, 27, 887–903.

    Article  MATH  MathSciNet  Google Scholar 

  • Kingsbury, G. G. & Zara, A. R. (1989). Procedures for selecting items for computerized adaptive tests. Applied Measurement in Education, 2, 359–375.

    Article  Google Scholar 

  • Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233.

    MATH  MathSciNet  Google Scholar 

  • Mislevy, R. J. (1984). Estimating latent distributions. Psychometrika, 49, 359–381.

    Article  MATH  Google Scholar 

  • Mislevy, R. J. (1986). Bayes modal estimation in item response models. Psychometrika, 51, 177–195.

    Article  MATH  MathSciNet  Google Scholar 

  • Mislevy, R. J. & Chang, H.-H. (2000). Does adaptive testing violate local independence? Psychometrika, 65, 149–156.

    Article  MathSciNet  Google Scholar 

  • Mislevy, R. J. & Wu, P. K. (1996). Missing responses and IRT ability estimation: Omits, choice, time limits, and adaptive testing (Research Report RR-96-30-ONR). Princeton, NJ: Educational Testing Service.

    Google Scholar 

  • Neyman, J. & Scott, E. L. (1948). Consistent estimates, based on partially consistent observations. Econometrica, 16, 1–32.

    Article  MathSciNet  Google Scholar 

  • Rao, C. R. (1947). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society, 44, 50–57.

    Google Scholar 

  • Reckase, M. D. (1985). The difficulty of test items that measure more than one ability. Applied Psychological Measurement, 9, 401–412.

    Article  Google Scholar 

  • Reckase, M. D. (1997). A linear logistic multidimensional model for dichotomous item response data. In W. J. van der Linden and R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 271–286). New York: Springer-Verlag.

    Google Scholar 

  • Rigdon S. E. & Tsutakawa, R. K. (1983). Parameter estimation in latent trait models. Psychometrika, 48, 567–574.

    Article  MATH  MathSciNet  Google Scholar 

  • Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–592.

    Article  MATH  MathSciNet  Google Scholar 

  • Stocking, M. L. (1993). Controlling exposure rates in a realistic adaptive testing paradigm (Research Report 93-2). Princeton, NJ: Educational Testing Service.

    Google Scholar 

  • Stocking, M. L. & Swanson, L. (1993). A method for severely constrained item selection in adaptive testing. Applied Psychological Measurement, 17, 277–292.

    Article  Google Scholar 

  • Sympson, J. B. & Hetter, R. D. (1985). Controlling item-exposure rates in computerized adaptive testing. Proceedings of the 27th Annual meeting of the Military Testing Association (pp. 973–977). San Diego: Navy Personnel Research and Development Center.

    Google Scholar 

  • Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175–186.

    Article  MATH  Google Scholar 

  • Veerkamp, W. J. J. (1996). Statistical methods for computerized adaptive testing. Unpublished doctoral thesis, Twente University, the Netherlands.

    Google Scholar 

  • Wetherill, G. B. (1977). Sampling inspection and statistical quality control (2nd ed.). London: Chapman and Hall.

    Google Scholar 

  • Wilson, D. T., Wood, R. & Gibbons, R. D. (1991) TESTFACT: Test scoring, item statistics, and item factor analysis (computer software). Chicago: Scientific Software International, Inc.

    Google Scholar 

  • Wright, B. D. & Panchapakesan, N. (1969). A procedure for sample-free item analysis. Educational and Psychological Measurement, 29, 23–48.

    Article  Google Scholar 

  • Zimowski, M. F., Muraki, E., Mislevy, R. J. & Bock, R. D. (1996). Bilog MG: Multiple-group IRT analysis and test maintenance for binary items. Chicago: Scientific Software International, Inc.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Research Methodology, Measurement, and Data Analysis, University of Twente, 217, 7500, AE, Enschede, The Netherlands

    Cees A. W. Glas

Authors
  1. Cees A. W. Glas
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Editors and Affiliations

  1. CTB/McGraw-Hill LLC, Ryan Ranch Road 20, Monterey, 93940, U.S.A.

    Wim J. van der Linden

  2. Fac. Behavioural Sciences, Twente University, Enschede, Netherlands

    Cees A.W. Glas

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Glas, C.A.W. (2009). Item Parameter Estimation and Item Fit Analysis. In: van der Linden, W., Glas, C. (eds) Elements of Adaptive Testing. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85461-8_14

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