FITTING BENT LINES TO DATA, WITH APPLICATIONS TO ALLOMETRY
FITTING BENT LINES TO DATA, WITH APPLICATIONS TO ALLOMETRY
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DOI：
10.1016/s0022-5193(89)80141-9
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发表时间：
1989-05-22
影响因子：
2
通讯作者：
CHAPPELL, R
中科院分区：
文献类型：
--
作者：
CHAPPELL, R
变点模型在异速生长和其他类型的建模中越来越重要。变点模型通过允许线性或非线性关系在事先不固定的点发生变化来推广线性或非线性关系。通常，变更点是“通过眼睛”选择的，并且为每个结果子域运行单独的回归。然而，由于以下原因，该程序是有缺陷的：首先，没有使用可重复和客观的程序来估计变化点；其次，后续分析通常没有考虑到从数据中估计变化点这一事实；最后，忽略了通常期望的变化点连续性要求。本文介绍了从数据中联合估计线性关系和中间变点的各种方法。在最简单的情况下，对于正态误差和一个变量对另一个变量的线性关系，这相当于通过最小二乘技术拟合一条“弯曲线”。此外，还介绍了变更点存在的测试和图形诊断。给出了陆地哺乳动物奔跑速度随体型变化的变化点和坡度的计算实例。过去，这些数据都是用直线或抛物线拟合的。这表明，优越的拟合和可解释性实现使用一个变化点模型。
Change-point models, in which a linear or non-linear relation is generalized by allowing it to change at a point not fixed in advance, are of growing importance in allometric and other types of modeling. Frequently, the change-point is picked "by eye" and separate regressions are run for each resultant subdomain. This procedure is deficient, however, for the following reasons: first, a repeatable and objective procedure for estimating the change-point has not been used; second, the subsequent analysis usually does not take into account the fact that the change-point is estimated from the data; and last, the usually desirable requirement of continuity at the change-point is ignored. This paper describes various methods for jointly estimating linear relations and the intervening change-point from the data. In the simplest case, with normal errors and a linear relation of one variable upon another, this amounts to fitting a "bent line" via least squares techniques. In addition, tests and graphical diagnostic for the presence of change-points are presented. An example is given where a change-point and slopes are estimated for the relation of running speed with size among land mammals. In the past, these data have been fit with a straight line or a parabola. It is shown here that superior fit and interpretability are achieved using a change-point model.