Abstract

In the context of a Gaussian multiple regression model, we address the problem of variable selection when in the list of potential predictors there are factors, that is, categorical variables. We adopt a model selection perspective, that is, we approach the problem by constructing a class of models, each corresponding to a particular selection of active variables. The methodology is Bayesian and proceeds by computing the posterior probability of each of these models. We highlight the fact that the set of competing models depends on the dummy variable representation of the factors, an issue already documented by Fernández et al. in a particular example but that has not received any attention since then. We construct methodology that circumvents this problem and that presents very competitive frequentist behavior when compared with recently proposed techniques. Additionally, it is fully automatic, in that it does not require the specification of any tuning parameters.

摘要

在高斯多元回归模型的背景下，我们解决了当潜在预测变量列表中存在因素（即分类变量）时的变量选择问题。我们采用模型选择的观点，即我们通过构建一类模型来解决问题，每个模型对应于特定的活动变量选择。该方法是贝叶斯方法，通过计算每个模型的后验概率来进行。我们强调了一个事实，即一组竞争模型取决于因素的虚拟变量表示，Fernández 等人已经记录了一个问题。在一个特定的例子中，但从那时起就没有受到任何关注。我们构建了规避这个问题的方法，与最近提出的技术相比，它呈现出非常有竞争力的常客行为。此外，它是全自动的，因为它不需要指定任何调整参数。