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Locally Weighted Score Estimation for Quantile Classification in Binary Regression Models

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  • John D. Rice

    () (University of Michigan)

  • Jeremy M. G. Taylor

    (University of Michigan)

Abstract

Abstract One common use of binary response regression methods is classification based on an arbitrary probability threshold dictated by the particular application. Since this is given to us a priori, it is sensible to incorporate the threshold into our estimation procedure. Specifically, for the linear logistic model, we solve a set of locally weighted score equations, using a kernel-like weight function centered at the threshold. The bandwidth for the weight function is selected by cross validation of a novel hybrid loss function that combines classification error and a continuous measure of divergence between observed and fitted values; other possible cross-validation functions based on more common binary classification metrics are also examined. This work has much in common with robust estimation, but differs from previous approaches in this area in its focus on prediction, specifically classification into high- and low-risk groups. Simulation results are given showing the reduction in error rates that can be obtained with this method when compared with maximum likelihood estimation, especially under certain forms of model misspecification. Analysis of a melanoma dataset is presented to illustrate the use of the method in practice.

Suggested Citation

  • John D. Rice & Jeremy M. G. Taylor, 2016. "Locally Weighted Score Estimation for Quantile Classification in Binary Regression Models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 333-350, October.
  • Handle: RePEc:spr:stabio:v:8:y:2016:i:2:d:10.1007_s12561-016-9147-y
    DOI: 10.1007/s12561-016-9147-y
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    References listed on IDEAS

    as
    1. Junhui Wang & Xiaotong Shen & Yufeng Liu, 2008. "Probability estimation for large-margin classifiers," Biometrika, Biometrika Trust, vol. 95(1), pages 149-167.
    2. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    3. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407.
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