Bayesian variable selection with related predictors
Bayesian variable selection with related predictors
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DOI：
10.2307/3315687
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发表时间：
1996-03-01
影响因子：
0.6
通讯作者：
Chipman, H
中科院分区：
文献类型：
--
作者：
Chipman, H
在具有许多预测因子的数据集中，经常使用用于识别预测因子的良好子集的算法。大多数这样的算法不允许预测器之间的任何关系。例如，逐步回归可能选择包含交互作用AB但不包含主效应A或B的模型。本文开发的数学表示的预测，这可能会被纳入模型选择过程中的这种关系和其他关系。贝叶斯方法，超越了标准的独立变量选择之前，并解释为先验信息的偏好某些模型。先验相关的任意相互作用和多项式，虚拟变量的分类因素，竞争的预测，并限制模型的大小。由于开发的关系是先验的，它们可以被纳入任何类型的线性模型的任何贝叶斯变量选择算法。通过乔治和McCulloch（1993）的随机搜索变量选择算法来说明本文方法的应用，该算法被修改以利用新的先验。该方法的性能示出了两个构造的例子和计算机性能数据集。
In data sets with many predictors, algorithms for identifying a good subset of predictors are often used. Most such algorithms do not allow for any relationships between predictors. For example, stepwise regression might select a model containing an interaction AB but neither main effect A or B. This paper develops mathematical representations of this and other relations between predictors, which may then be incorporated in a model selection procedure. A Bayesian approach that goes beyond the standard independence prior for variable selection is adopted, and preference for certain models is interpreted as prior information. Priors relevant to arbitrary interactions and polynomials, dummy variables for categorical factors, competing predictors, and restrictions on the size of the models are developed. Since the relations developed are for priors, they may be incorporated in any Bayesian variable selection algorithm for any type of linear model. The application of the methods here is illustrated via the stochastic search variable selection algorithm of George and McCulloch (1993), which is modified to utilize the new priors. The performance of the approach is illustrated with two constructed examples and a computer performance dataset.