Skip to main content
SpringerLink
Log in

Adaptive Mastery Testing Using a Multidimensional IRT Model

  • Chapter
  • First Online:
Elements of Adaptive Testing

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

Abstract

Mastery testing concerns the decision to classify a student as a master or as a nonmaster. In the previous chapter, adaptive mastery testing (AMT) using item response theory (IRT) and sequential mastery testing (SMT) using Bayesian decision theory were combined into an approach labeled adaptive sequential mastery testing (ASMT). This approach is based on the one-parameter logistic model (1PLM; Rasch, 1960) and three-parameter logistic model (3PLM; Birnbaum, 1968). In the present chapter, ASMT is applied to a multidimensional IRT (MIRT) model.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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

  • Ackerman, T. A. (1987). A comparison study of the unidimensional IRT estimation of compensatory and noncompensatory multidimensional item response data (ACT Research Report Series 87-12). Iowa City, IA: ACT Inc.

    Google Scholar 

  • 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 

  • Adams, R. J., Wilson, M. R. & Wang, W. C. (1997). The random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–25.

    Article  Google Scholar 

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

    Google Scholar 

  • Andersen, E. B. (1985). Estimating latent correlations between repeated testings. Psychometrika, 50, 3–16.

    Article  MATH  MathSciNet  Google Scholar 

  • Béguin, A. A. & Glas, C. A. W. (2001). MCMC estimation and some fit analysis of multidimensional IRT models. Psychometrika, 66, 541–562.

    Article  MathSciNet  Google Scholar 

  • Bellman, R. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Birnbaum, A. (1968). Some latent trait models. In F. M. Lord & M.R. Novick (Eds.), Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

    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 

  • Bradlow, E. T., Wainer, H. & Wang, X. (1999). A Bayesian random effects model for testlets. Psychometrika, 64, 153–168.

    Article  Google Scholar 

  • Coombs, C. H. (1960). A theory of data. Ann Arbor, MI: Mathesis Press.

    Google Scholar 

  • Coombs, C. H. & Kao, R. C. (1955). Nonmetric factor analysis. [Engng. Res. Bull., No.38]. Ann Arbor, MI: University of Michigan Press.

    Google Scholar 

  • DeGroot, M. H. (1970). Optimal statistical decisions. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Embretson, S. (1980). Multicomponent latent trait models for ability tests. Psychometrika, 45, 479–494.

    Article  Google Scholar 

  • Embretson, S. (1984). A general latent trait model for response processes. Psychometrika, 49, 175–186.

    Article  Google Scholar 

  • Ferguson, T. S. (1967). Mathematical statistics: A decision theoretic approach. New York: Academic Press.

    MATH  Google Scholar 

  • Fraser, C & McDonald, R. P. (1988). NOHARM: Least Squares item factor analysis. Multivariate Behavioral Research, 23, 267–269.

    Article  Google Scholar 

  • Glas, C. A. W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika, 53, 525–546.

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Glas, C. A. W. & Verhelst, N. D. (1995). Testing the Rasch model. In G. H.Fischer & I. W.Molenaar (Eds.), Rasch models: foundations, recent developments and applications (pp.69–96). New York, NJ: Springer-Verlag.

    Google Scholar 

  • 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.), Computer adaptive testing: Theory and practice (pp.271–287). Boston: Kluwer-Nijhoff Publishing.

    Google Scholar 

  • Lewis, C. & Sheehan, K. (1990). Using Bayesian decision theory to design a computerized mastery test. Applied Psychological Measurement, 14, 367–386.

    Article  Google Scholar 

  • Lindgren, B. W. (1976). Statistical theory (3rd ed.). New York: Macmillan.

    MATH  Google Scholar 

  • Lord, F. M. & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  • Luecht, R. M. (1996). Multidimensional computerized adaptive testing in a certification or licensure context. Applied Psychological Measurement, 20, 389–404.

    Article  Google Scholar 

  • Luecht, R. M. & Nungester, R. J. (1998). Some practical examples of computer-adaptive sequential testing. Journal of Educational Measurement, 35, 239–249.

    Google Scholar 

  • Luecht, R. M. & Nungester, R. J. (2000). Computer-adaptive sequential testing. In W. J. van der Linden & C. A. W.Glas (eds.). Computerized adaptive testing: Theory and practice. (pp. 117–128). Boston: Kluwer-Nijhof Publishing.

    Google Scholar 

  • Maris, E. (1993). Additive and multiplicative models for gamma distributed random variables, and their application as psychometric models for response times. Psychometrika, 58, 445–470.

    Article  MATH  Google Scholar 

  • Maris, E. (1995). Psychometric latent response models. Psychometrika, 60, 523–548.

    Article  MATH  Google Scholar 

  • McDonald, R. P. (1967). Nonlinear factor analysis. Psychometric monographs, No. 15.

    Google Scholar 

  • McDonald, R. P. (1997). Normal-ogive multidimensional model. In W. J. van der Linden and R. K. Hambleton (Eds.). Handbook of Modern Item Response Theory (pp.257–269). New York: Springer-Verlag.

    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. (1988). Exploiting auxiliary information about items in the estimation of Rasch item difficulty parameters. Applied Psychological Measurement, 12, 281–296.

    Article  Google Scholar 

  • Novick, M. R. & Jackson, P. H. (1974). Statistical methods for educational and psychological research. New York, NJ: McGraw-Hill.

    Google Scholar 

  • Novick, M. R. & Lindley, D. V. (1979). The use of more realistic utility functions in educational applications. Journal of Educational Measurement, 15, 81–191.

    Google Scholar 

  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

    Google Scholar 

  • Reckase, M. D. (1983). A procedure for decision making using tailored testing. In D. J. Weiss (Ed.). New horizons in testing: Latent trait test theory and computerized adaptive testing (pp. 237–257). New York: Academic Press.

    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 

  • Robbins, H. (1964). The empirical Bayes approach to statistical decision problems. Annals of Mathematical Statistics, 35, 1–20.

    Article  MATH  MathSciNet  Google Scholar 

  • Segall, D. O. (1996). Multidimensional adaptive testing. Psychometrika, 61, 331–354.

    Article  MATH  Google Scholar 

  • Spray, J. A., Davey, D. C., Reckase, M. D., Ackerman, T. A. & Carlson, J. E. (1990). Comparison of two logistic multidimensional item response theory models (ACT Research Report Series ONR90-8). Iowa City, IA: ACT Inc.

    Google Scholar 

  • Sympson, J. B. (1978). A model for testing with multidimensional items. In D. J. Weiss (Ed.), Proceedings of the 1977 Computerized Adaptive Testing Conference (pp. 82–98). Minneapolis: University of Minnesota.

    Google Scholar 

  • van der Linden, W. J. (1999). Empirical initialization of the trait estimator in adaptive testing. Applied Psychological Measurement, 23, 21–29.

    Article  Google Scholar 

  • van der Linden, W. J. & Reese, L. M. (1998). A model for optimal constrained adaptive testing. Applied Psychological Measurement, 22, 259–270.

    Article  Google Scholar 

  • Verhelst, N. D., Glas, C. A. W. & Verstralen, H. H. F. M. (1995). OPLM: Computer program and manual. Arnhem: Cito.

    Google Scholar 

  • Wainer, H. (Ed.). (1990). Computerized adaptive testing: A primer. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Wainer, H, Bradlow, E. T. & Du, Z. (2000). Testlet response theory: An analogue for the 3-PL useful in testlet-based adaptive testing. In W. J. van der Linden & C. A. W.Glas (Eds.). Computer adaptive testing: Theory and practice (pp. 245–269). Boston: Kluwer-Nijhoff Publishing.

    Google Scholar 

  • Weiss, D. J. (Ed.). (1983). New horizons in testing. New York: Academic Press.

    Google Scholar 

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

    Google Scholar 

  • Winston, W. L. (1994). Operations research: Applications and algorithms. Belmont, CA: Wadsworth.

    MATH  Google Scholar 

  • Wu, M. L., Adams, R. J. & Wilson, M. R. (1997). ConQuest: Generalized item response modelling software. Australian Counsil for Educational Research.

    Google Scholar 

Download references

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 & Hans J. Vos

Authors
  1. Cees A. W. Glas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans J. Vos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

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

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Glas, C.A.W., Vos, H.J. (2009). Adaptive Mastery Testing Using a Multidimensional IRT Model. 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_21

Download citation

Publish with us

Policies and ethics

Search

Navigation