A Nonparametric Estimator of a Monotone Item Characteristic Curve

  • Mario LuzardoEmail author
  • Pilar Rodríguez
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 140)


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.


Nonparametric Isotone Item response theory 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of PsychologyUniversity of the RepublicMontevideoUruguay
  2. 2.University Center East RegionalUniversity of the RepublicMaldonadoUruguay

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