Logistic Approximation to the Normal: The KL Rationale |
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| Authors: | Victoria Savalei |
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| Institution: | (1) University of California, Los Angeles;(2) Department of Psychology, University of California, Los Angeles, CA 90095, USA |
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| Abstract: | A rationale is proposed for approximating the normal distribution with a logistic distribution using a scaling constant based
on minimizing the Kullback–Leibler (KL) information, that is, the expected amount of information available in a sample to
distinguish between two competing distributions using a likelihood ratio (LR) test, assuming one of them is true. The new
constant 1.749, computed assuming the normal distribution is true, yields an approximation that is an improvement in fit of
the tails of the distribution as compared to the minimax constant of 1.702, widely used in item response theory (IRT). The
minimax constant is by definition marginally better in its overall maximal error. It is argued that the KL constant is more
statistically appropriate for use in IRT.
The author would like to thank Sebastian Schreiber for his generous assistance with this project. |
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| Keywords: | IRT logistic approximation Kullback-Leibler information |
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