The Scaling Constant D in Item Response Theory - Open Journal of Statistics

OJS > Vol.7 No.5, October 2017

The Scaling Constant D in Item Response Theory ()

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DOI: 10.4236/ojs.2017.75055 2,596 Downloads 5,253 Views Citations

Author(s)

Gregory Camilli

Affiliation(s)

Graduate School of Education, Rutgers University, New Brunswick, NJ, USA.

ABSTRACT

In item response theory (IRT), the scaling constant D = 1.7 is used to scale a discrimination coefficient a estimated with the logistic model to the normal metric. Empirical verification is provided that Savalei’s [1] proposed a scaling constant of D = 1.749 based on Kullback-Leibler divergence appears to give the best empirical approximation. However, the understanding of this issue as one of the accuracy of the approximation is incorrect for two reasons. First, scaling does not affect the fit of the logistic model to the data. Second, the best scaling constant to the normal metric varies with item difficulty, and the constant D = 1.749 is best thought of as the average of scaling transformations across items. The reason why the traditional scaling with D = 1.7 is used is simply because it preserves historical interpretation of the metric of item discrimination parameters.

KEYWORDS

Item Response Theoru, IRT, Scaling Constant, D

Share and Cite:

Camilli, G. (2017) The Scaling Constant D in Item Response Theory. Open Journal of Statistics, 7, 780-785. doi: 10.4236/ojs.2017.75055.

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