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Fitting Item Characteristic Curves With Spline Functions IRT

Thissen, David; Wainer, Howard; Winsberg, Suzanne
Publication Year:
Report Number:
RR-84-40, PSRTR-84-40, PSRTR-84-52
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Natural Sciences and Engineering Research Council of Canada, United States Air Force Human Resources Laboratory, Item Analysis, Item Response Theory (IRT), Maximum Likelihood Statistics, Statistical Analysis


In most item response theory models a particular mathematical form is assumed for all item characteristic curves, e.g., a logistic function. It could be desirable, however, to estimate the shape of the item characteristic curves without prior restrictive assumptions about its mathematical form. We have developed a practical method of estimating the shape of item response functions leading to smooth flexible functions and numerically stable calculations. In our approach the probability of success of an item is represented as a monotone function of the ability evaluated by the item. The function is represented as a monotone spline. We use the technique developed by Bock and Aitkin (1981) for marginal maximum likelihood estimation of the item parameters. Examples of real and artificial data are presented. (AUTHOR). (25pp.)

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