Abstract
This paper presents a nonparametric approach to estimating item characteristic curves (ICCs) when they should be monotonic. First, it addresses the uni-dimensional case; before generalizing it to the multidimensional case.
This is a two-stage process. The first stage uses a nonparametric estimator of the ICC by means of nonparametric kernel regression; the second uses the above result to estimate the density function of the inverse ICC.
By integrating this density function, we obtain an isotonic estimator of the inverse ICC: symmetrized with respect to the bisector of the unit square, to obtain the ICC estimator. We also present the multidimensional case, in which we proceed on a coordinate-by-coordinate basis.
Keywords
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Luzardo, M., Rodríguez, P. (2015). A Nonparametric Estimator of a Monotone Item Characteristic Curve. In: van der Ark, L., Bolt, D., Wang, WC., Douglas, J., Chow, SM. (eds) Quantitative Psychology Research. Springer Proceedings in Mathematics & Statistics, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-319-19977-1_8
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DOI: https://doi.org/10.1007/978-3-319-19977-1_8
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