TITLE:
The Scaling Constant D in Item Response Theory
AUTHORS:
Gregory Camilli
KEYWORDS:
Item Response Theoru, IRT, Scaling Constant, D
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.5,
October
13,
2017
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.