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Optimal dichotomization of bimodal Gaussian mixtures

Author

Listed:
  • Yan-ni Jhan

    (National Changhua University of Education)

  • Wan-cen Li

    (National Changhua University of Education)

  • Shin-hui Ruan

    (National Changhua University of Education)

  • Jia-jyun Sie

    (National Changhua University of Education)

  • Iebin Lian

    (National Changhua University of Education)

Abstract

Despite criticism for loss of information and power, dichotomization of variables is still frequently used in social, behavioral, and medical sciences, mainly because it yields more interpretable conclusions for research outcomes and is useful for decision making. However, the artificial choice of cut-points can be controversial and needs proper justification. In this work, we investigate the properties of point-biserial correlation after dichotomization with underlying bimodal Gaussian mixture distributions. We propose a dichotomous grouping procedure that considers the largest standardized difference in group mean while minimizing information loss.

Suggested Citation

  • Yan-ni Jhan & Wan-cen Li & Shin-hui Ruan & Jia-jyun Sie & Iebin Lian, 2024. "Optimal dichotomization of bimodal Gaussian mixtures," Statistical Papers, Springer, vol. 65(5), pages 3285-3301, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01521-1
    DOI: 10.1007/s00362-023-01521-1
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    References listed on IDEAS

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    1. S. L. Prince Nelson & V. Ramakrishnan & P. J. Nietert & D. L. Kamen & P. S. Ramos & B. J. Wolf, 2017. "An evaluation of common methods for dichotomization of continuous variables to discriminate disease status," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10823-10834, November.
    2. Jian Zhou & Yifei Mo & Hong Li & Xingwu Ran & Wenying Yang & Qiang Li & Yongde Peng & Yanbing Li & Xin Gao & Xiaojun Luan & Weiqing Wang & Yun Xie & Weiping Jia, 2013. "Relationship between HbA1c and Continuous Glucose Monitoring in Chinese Population: A Multicenter Study," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-6, December.
    3. Carlo V. Fiorio & Vassilis A. Hajivassiliou & Peter C. B. Phillips, 2010. "Bimodal t-ratios: the impact of thick tails on inference," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 271-289, July.
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