Fong Youyi
Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Department of Biostatistics, University of Washington, Seattle, WA 98109.
J Comput Graph Stat. 2019;28(2):466-470. doi: 10.1080/10618600.2018.1537927. Epub 2019 Feb 13.
Continuous threshold regression is a common type of nonlinear regression that is attractive to many practitioners for its easy interpretability. More widespread adoption of thresh-old regression faces two challenges: (i) the computational complexity of fitting threshold regression models and (ii) obtaining correct coverage of confidence intervals under model misspecification. Both challenges result from the non-smooth and non-convex nature of the threshold regression model likelihood function. In this paper we first show that these two issues together make the ideal approach for making model-robust inference in continuous threshold linear regression an impractical one. The need for a faster way of fitting continuous threshold linear models motivated us to develop a fast grid search method. The new method, based on the simple yet powerful dynamic programming principle, improves the performance by several orders of magnitude.
连续阈值回归是一种常见的非线性回归类型，因其易于解释而受到许多从业者的青睐。阈值回归更广泛的应用面临两个挑战：（i）拟合阈值回归模型的计算复杂性，以及（ii）在模型设定错误的情况下获得正确的置信区间覆盖范围。这两个挑战都源于阈值回归模型似然函数的非光滑和非凸性质。在本文中，我们首先表明，这两个问题共同使得在连续阈值线性回归中进行模型稳健推断的理想方法变得不切实际。对更快拟合连续阈值线性模型方法的需求促使我们开发了一种快速网格搜索方法。这种新方法基于简单而强大的动态规划原理，性能提高了几个数量级。
