Sample selection models represent a common methodology for correcting bias induced by data missing not at random. It is well known that these models are not empirically identifiable without exclusion restrictions. In other words, some variables predictive of missingness do not affect the outcome model of interest. The drive to establish this requirement often leads to the inclusion of irrelevant variables in the model. A recent proposal uses adaptive LASSO to circumvent this problem, but its performance depends on the so-called covariance assumption, which can be violated in small to moderate samples. Additionally, there are no tools yet for post-selection inference for this model. To address these challenges, we propose two families of spike-and-slab priors to conduct Bayesian variable selection in sample selection models. These prior structures allow for constructing a Gibbs sampler with tractable conditionals, which is scalable to the dimensions of practical interest. We illustrate the performance of the proposed methodology through a simulation study and present a comparison against adaptive LASSO and stepwise selection. We also provide two applications using publicly available real data. An implementation and code to reproduce the results in this paper can be found at https://github.com/adam-iqbal/selection-spike-slab

翻译：样本选择模型是修正由非随机缺失数据引起的偏差的常用方法。众所周知，这些模型在没有排除限制的情况下无法通过经验识别。换言之，某些预测缺失的变量并不影响感兴趣的结果模型。为了满足这一要求，往往会在模型中引入无关变量。近期有提议使用自适应LASSO规避此问题，但其性能依赖于所谓的协方差假设，而该假设在小到中等样本量下可能被违反。此外，当前尚无针对该模型的选择后推断工具。为应对这些挑战，我们提出了两类尖峰- slab先验，用于在样本选择模型中执行贝叶斯变量选择。这些先验结构允许构建具有可处理条件分布的吉布斯采样器，且可扩展至实际关注的维度。我们通过模拟研究展示了所提方法的性能，并与自适应LASSO及逐步选择进行了对比。此外，我们利用公开的真实数据提供了两个应用实例。本文结果的可复现代码及实现见https://github.com/adam-iqbal/selection-spike-slab。