Comparing non-nested regression models.
Comparing non-nested regression models.
复制标题
比较非嵌套回归模型。
作者：
Patrick Royston;Simon G. Thompson
本文根据Davidson和MacKinnon（1981）的建议，在线性和非线性正态误差回归的背景下，提出了一种比较两个非嵌套模型拟合的方法。每个模型被视为一个特殊的情况下，一个人工的“超级模型”，并通过限制的值的混合参数γ为0或1。为了实现伽马的估计和假设检验，使用近似超模型，其中来自各个模型的拟合值出现在原始参数化的位置。在嵌套线性模型的情况下，所提出的检验基本上再现了标准F检验。所需的计算大部分是直接的（基本上是通过原点的线性回归）。该测试扩展到覆盖的情况下，在严重的偏见，伽玛的最大似然估计发生，简单的近似界限的偏差。两个真实的数据集被说明性地使用。
A method for comparing the fits of two non-nested models, based on a suggestion of Davidson and MacKinnon (1981), is developed in the context of linear and nonlinear regression with normal errors. Each model is regarded as a special case of an artificial "supermodel" and is obtained by restricting the value of a mixing parameter gamma to 0 or 1. To enable estimation and hypothesis testing for gamma, an approximate supermodel is used in which the fitted values from the individual models appear in place of the original parametrization. In the case of nested linear models, the proposed test essentially reproduces the standard F test. The calculations required are for the most part straight-forward (basically, linear regression through the origin). The test is extended to cover situations in which serious bias in the maximum likelihood estimate of gamma occurs, simple approximate bounds for the bias being given. Two real datasets are used illustratively throughout.