Abstract
The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.
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The research reported in this paper was supported by Grants APA320 and A4035 from the Natural Sciences and Engineering Research Council of Canada. It was also supported by Contract No. F41689-82-C-10020 from the Air Force Human Resources Laboratory to Educational Testing Service. The author wishes to thank M. Abrahamowicz for his assistance and R. Darrell Bock for providing the parameters for the items used in the simulations.
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Ramsay, J.O., Winsberg, S. Maximum marginal likelihood estimation for semiparametric item analysis. Psychometrika 56, 365–379 (1991). https://doi.org/10.1007/BF02294480
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DOI: https://doi.org/10.1007/BF02294480