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Property of the diagnostic odds ratio based on various kinds of accuracy measures
Journal of the Korean Data & Information Science Society 2021;32:1281-94
Published online November 30, 2021;  https://doi.org/10.7465/jkdi.2021.32.6.1281
© 2021 Korean Data and Information Science Society.

Chong Sun Hong1 · Se Hyeon Oh2

12Department of Statistics, Sungkyunkwan University
Correspondence to: 1 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-Ro, Jongno-Gu, Seoul, 03063, Korea. E-mail: cshong@skku.edu
2 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul, 03063, Korea.
Received September 1, 2021; Revised October 1, 2021; Accepted October 9, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
There exist many statistical methods to estimate the optimal threshold for binary classification in a mixed group which is consisted of default (positive) and non-default (negative) states in credit (diagnostic) evaluation. These are based on minimizing type I and II errors and their error sum. By expanding for the optimal threshold based on DOR (Diagnostic odds ratio) and Log(DOR) which are functions of the positive and negative likelihood ratios including information on the sensitivity and specificity, the values of DOR and Log(DOR) are obtained from the six categories classified by many optimal thresholds, and their relationship with discriminant power is explored after setting the distribution functions of default and non-default as various normal mixtures. This method can explore whether the general assumption of the binary classification model holds, and has the advantage that it can be clearly interpreted since these are composed of the odds ratios. Therefore, it is found that more rational and accurate explanations can be made by using both DOR and various kinds of existing accuracy measures for selecting the optimal threshold as a criterion for minimizing type I and II errors and their error sum.
Keywords : Default, discriminant, sensitivity, specificity, threshold.