Global, Parameterwise and Joint Shrinkage Factor Estimation
Global, Parameterwise and Joint Shrinkage Factor Estimation
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全局、参数化和联合收缩因子估计
DOI：
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发表时间：
2016
期刊：
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通讯作者：
G. Heinze
中科院分区：
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作者：
D. Dunkler;W. Sauerbrei;G. Heinze
通过应用收缩方法，统计模型的预测价值通常可以得到提高。这可以通过例如正则化回归或经验贝叶斯方法来实现。在获得最大似然拟合之后，也可以估计各种类型的收缩因子：全局收缩通过相同的因子修改所有回归系数，而逐参数收缩因子在回归系数之间是不同的。后者尤其在变量选择的背景下被提出。对于那些高度相关或在内容上相关的变量，例如对分类变量进行编码的虚拟变量，或者描述非线性效应的几个参数，逐参数收缩因子可能不是最佳选择。对于这种情况，我们通过所谓的“联合收缩因子”扩展了现有方法，它是全局收缩和逐参数收缩之间的一种折衷。收缩因子通常使用留一法重采样来估计。我们还讨论了一种基于重采样的收缩因子估计的计算简单且速度快得多的近似方法，在大多数用于回归分析的标准软件包中都可以很容易地获得。这种替代方法可能与模拟研究和其他计算机密集型研究相关。此外，我们提供了一个R包shrink，它为通过线性、广义线性或Cox回归拟合的模型实现了上述收缩方法，即使这些模型涉及分数多项式或受限三次样条来通过非线性函数估计连续变量的影响。通过两个例子说明了shrink包的方法和使用。
The predictive value of a statistical model can often be improved by applying shrinkage methods. This can be achieved, e.g., by regularized regression or empirical Bayes approaches. Various types of shrinkage factors can also be estimated after a maximum likelihood fit has been obtained: while global shrinkage modifies all regression coefficients by the same factor, parameterwise shrinkage factors differ between regression coefficients. The latter ones have been proposed especially in the context of variable selection. With variables which are either highly correlated or associated with regard to contents, such as dummy variables coding a categorical variable, or several parameters describing a nonlinear effect, parameterwise shrinkage factors may not be the best choice. For such cases, we extend the present methodology by so-called 'joint shrinkage factors', a compromise between global and parameterwise shrinkage. Shrinkage factors are often estimated using leave-one-out resampling. We also discuss a computationally simple and much faster approximation to resampling-based shrinkage factor estimation, can be easily obtained in most standard software packages for regression analyses. This alternative may be relevant for simulation studies and other computerintensive investigations. Furthermore, we provide an R package shrink implementing the mentioned shrinkage methods for models fitted by linear, generalized linear, or Cox regression, even if these models involve fractional polynomials or restricted cubic splines to estimate the influence of a continuous variable by a nonlinear function. The approaches and usage of the package shrink are illustrated by means of two examples.