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.
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Abdelbasit, K. M., & Plankett, R. L. (1983). Experimental design for binary data.Journal of the American Statistical Association, 78, 90–98.
Atkinson, A. C. (1982). Developments in the design of experiments.International Statistical Review, 50, 161–177.
Anderson, T. W. (1984).An Introduction to multivariate statistical analysis (2nd ed.). New York: Wiley.
Berger, M. P. F. (1989).On the efficiency of IRT models when applied to different sampling designs (Research Report 89-4). Enschede: University of Twente, Department of Education.
Berger, M. P. F. (1991). On the efficiency of IRT models when applied to different sampling designs.Applied Psychological Measurement, 15, 293–306.
Berger, M. P. F., & van der Linden, W. J. (1992). Optimality of sampling designs in item response theory models. In M. Wilson (Ed.),Objective measurement: Theory into practice (pp. 274–288). Norwood NJ: Ablex Publishing.
Cook, R. D., & Nachtsheim, C. J. (1980). A comparison of algorithms for constructing exact D-optimal designs.Technometrics, 22, 315–324.
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.
de Gruijter, D. N. M. (1988). Standard errors of item parameter estimates in incomplete designs.Applied Psychological Measurement, 12, 109–116.
Hambleton, R. K., & Swaminathan, H. (1985).Item response theory. Boston: Kluwer-Nijhoff.
Khan, M. K., & Yazdi, A. A. (1988). On D-optimal designs.Journal of Statistical Planning and Inference, 18, 83–91.
Kiefer, J. (1959). Optimum experimental designs (with discussion).Journal of the Royal Statistical Society, Series B, 21, 271–319.
Lord, F. M. (1962). Estimating norms by item-sampling.Educational and Psychological Measurement, 22, 259–267.
Lord, F. M. (1980).Applications of item response theory to practical testing problems. Hillsdale NJ: Lawrence Erlbaum.
Lord, F. M., & Wingersky, M. S. (1985). Sampling variances and covariances of parameter estimates in item response theory. In D. J. Weiss (Ed.),Proceedings of the 1982 Item Response Theory and Computerized Adaptive Testing Conference (pp. 69–88). Minneapolis: University of Minnesota.
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.
Minkin, S. (1987). Optimal designs for binary data.Journal of the American Statistical Association, 82, 1098–1103.
Pandey, T. N., & Carlson, D. (1976). Assessing payoffs in the estimation of the mean using multiple matrix sampling designs. In D. N. M. de Gruijter & L. J. van der Kamp (Eds.),Advances in psychological and educational measurement (pp. 265–275). London: John Wiley & Sons.
Shannon, C. E. (1948). A mathematical theory of communication.Bell System Technical Journal, 27, 379–423, 623–656.
Steinberg, D. M., & Hunter, W. G. (1984). Experimental design: Review and comment.Technometrics, 26, 71–130.
Thissen, D., & Wainer, H. (1982). Some standard errors in item response theory.Psychometrika, 47, 397–412.
Stocking, M. L. (1990). Specifying optimum examinees for item parameter estimation in item response theory.Psychometrika, 55, 461–475.
Vale, C. D. (1986). Linking item parameters onto a common scale.Applied Psychological Measurement, 10, 333–344.
van der Linden, W. J. (1987).IRT-based test construction (Research Report 87-2). Enschede: University of Twente, Department of Education.
van der Linden, W. J. (1988).Optimizing incomplete sampling designs for item response model parameters (Research Report 88-5). Enschede: University of Twente, Department of Education.
Wald, A. (1943). On the efficient design of statistical investigations.Annals of Mathematical Statistics, 14, 134–140.
Wingersky, M. S., & Lord (1984). An investigation of methods for reducing sampling error in certain IRT procedures.Applied Psychological Measurement, 8, 347–364.
Wynn, H. P. (1970). The sequential generation ofD-optimum experimental designs.Annals of Mathematical Statistics, 41, 1655–1664.
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.
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Berger, M.P.F. Sequential sampling designs for the two-parameter item response theory model. Psychometrika 57, 521–538 (1992). https://doi.org/10.1007/BF02294418
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DOI: https://doi.org/10.1007/BF02294418