Hostname: page-component-6898cfcb55-kwdml Total loading time: 0 Render date: 2026-11-11T14:51:08.340Z Has data issue: false hasContentIssue false
  • English
  • Français

Sequential Sampling Designs for the Two-Parameter Item Response Theory Model

Published online by Cambridge University Press:  01 January 2025

Martijn P. F. Berger
Martijn P. F. Berger*
Affiliation:
University of Twente, The Netherlands
*
Requests for reprints should be sent to Martijn P. F. Berger, University of Twente, Department of Education, PO Box 217, 7500 AE Enschede, THE NETHERLANDS.
Get accessRights & Permissions [Opens in a new window]

Abstract

In optimal design research, designs are optimized with respect to some statistical criterion under a certain model for the data. The ideas from optimal design research have spread into various fields of research, and recently have been adopted in test theory and applied to item response theory (IRT) models. In this paper a generalized variance criterion is used for sequential sampling in the two-parameter IRT model. Some general principles are offered to enable a researcher to select the best sampling design for the efficient estimation of item parameters.

Keywords

sequential sampling designefficiencyitem response theory modelstwo-parameter logistic modeloptimality criteria

Information

Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 4 , December 1992, pp. 521 - 538
Copyright
Copyright © 1992 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abdelbasit, K. M., Plankett, R. L. (1983). Experimental design for binary data. Journal of the American Statistical Association, 78, 90–98.CrossRefGoogle Scholar
Atkinson, A. C. (1982). Developments in the design of experiments. International Statistical Review, 50, 161–177.CrossRefGoogle Scholar
Anderson, T. W. (1984). An Introduction to multivariate statistical analysis 2nd ed.,, New York: Wiley.Google Scholar
Berger, M. P. F. (1989). On the efficiency of IRT models when applied to different sampling designs, Enschede: University of Twente, Department of Education.Google Scholar
Berger, M. P. F. (1991). On the efficiency of IRT models when applied to different sampling designs. Applied Psychological Measurement, 15, 293–306.CrossRefGoogle Scholar
Berger, M. P. F., van der Linden, W. J. (1992). Optimality of sampling designs in item response theory models. In Wilson, M. (Eds.), Objective measurement: Theory into practice (pp. 274–288). Norwood NJ: Ablex Publishing.Google Scholar
Cook, R. D., Nachtsheim, C. J. (1980). A comparison of algorithms for constructing exact D-optimal designs. Technometrics, 22, 315–324.CrossRefGoogle Scholar
de Gruijter, D. N. M. (1985). A note on the asymptotic variance-covariance matrix of item parameter estimates in the Rasch model. Psychometrika, 50, 247–249.CrossRefGoogle Scholar
de Gruijter, D. N. M. (1988). Standard errors of item parameter estimates in incomplete designs. Applied Psychological Measurement, 12, 109–116.CrossRefGoogle Scholar
Hambleton, R. K., Swaminathan, H. (1985). Item response theory, Boston: Kluwer-Nijhoff.CrossRefGoogle Scholar
Khan, M. K., Yazdi, A. A. (1988). On D-optimal designs. Journal of Statistical Planning and Inference, 18, 83–91.CrossRefGoogle Scholar
Kiefer, J. (1959). Optimum experimental designs (with discussion). Journal of the Royal Statistical Society, Series B, 21, 271–319.CrossRefGoogle Scholar
Lord, F. M. (1962). Estimating norms by item-sampling. Educational and Psychological Measurement, 22, 259–267.CrossRefGoogle Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale NJ: Lawrence Erlbaum.Google Scholar
Lord, F. M., Wingersky, M. S. (1985). Sampling variances and covariances of parameter estimates in item response theory. In Weiss, D. J. (Eds.), Proceedings of the 1982 Item Response Theory and Computerized Adaptive Testing Conference (pp. 69–88). Minneapolis: University of Minnesota.Google Scholar
McLaughlin, M. E., Drasgow, F. (1987). Lord's chi-square test of item bias with estimated and with known person parameters. Applied Psychological Measurement, 11, 162–173.CrossRefGoogle Scholar
Minkin, S. (1987). Optimal designs for binary data. Journal of the American Statistical Association, 82, 1098–1103.CrossRefGoogle Scholar
Pandey, T. N., Carlson, D. (1976). Assessing payoffs in the estimation of the mean using multiple matrix sampling designs. In de Gruijter, D. N. M., van der Kamp, L. J. (Eds.), Advances in psychological and educational measurement (pp. 265–275). London: John Wiley & Sons.Google Scholar
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.CrossRefGoogle Scholar
Steinberg, D. M., Hunter, W. G. (1984). Experimental design: Review and comment. Technometrics, 26, 71–130.CrossRefGoogle Scholar
Thissen, D., Wainer, H. (1982). Some standard errors in item response theory. Psychometrika, 47, 397–412.CrossRefGoogle Scholar
Stocking, M. L. (1990). Specifying optimum examinees for item parameter estimation in item response theory. Psychometrika, 55, 461–475.CrossRefGoogle Scholar
Vale, C. D. (1986). Linking item parameters onto a common scale. Applied Psychological Measurement, 10, 333–344.CrossRefGoogle Scholar
van der Linden, W. J. (1987). IRT-based test construction, Enschede: University of Twente, Department of Education.Google Scholar
van der Linden, W. J. (1988). Optimizing incomplete sampling designs for item response model parameters, Enschede: University of Twente, Department of Education.Google Scholar
Wald, A. (1943). On the efficient design of statistical investigations. Annals of Mathematical Statistics, 14, 134–140.CrossRefGoogle Scholar
Wingersky, M. S., Lord, (1984). An investigation of methods for reducing sampling error in certain IRT procedures. Applied Psychological Measurement, 8, 347–364.CrossRefGoogle Scholar
Wynn, H. P. (1970). The sequential generation of D-optimum experimental designs. Annals of Mathematical Statistics, 41, 1655–1664.CrossRefGoogle Scholar
Yen, W. M., Burket, G. R., Sykes, R. C. (1991). Nonunique solutions to the likelihood equation for the three-parameter logistic model. Psychometrika, 56, 39–54.CrossRefGoogle Scholar