| Summary: | Bock and Aitkin (1981) developed an EM algorithm for the maximum marginal likelihood estimation of parametric item response curves, such that these estimates could be obtained in the absence of the estimation of examinee parameters. Using functional data analytic techniques described by Ramsay and Silverman (1997), this algorithm is extended to achieve nonparametric estimates of item response functions. Unlike their parametric counterparts, nonparametric functions have the freedom to adopt any possible shape, making the current approach an attractive alternative to the popular three-parameter logistic model. A basis function expansion is described for the item response functions, as is a roughness penalty which mediates a compromise between the fit of the data and the smoothness of the estimate. The algorithm is developed and applied to both actual and simulated data to illustrate its performance, and how the nonparametric estimates compare to results obtained through more classical methods.
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