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：样本选择模型是纠正非随机缺失数据导致偏差的常用方法。众所周知，若无排除限制条件，这些模型在经验上不可识别。换言之，部分预测缺失的变量不会影响感兴趣的结果模型。建立这一要求的努力常导致模型中包含无关变量。近期研究提出使用自适应LASSO来解决该问题，但其性能依赖于所谓的协方差假设，该假设在小样本至中等样本中可能不成立。此外，该模型尚无用于选择后推断的工具。为应对这些挑战，我们提出两类尖峰-厚尾先验，用于在样本选择模型中进行贝叶斯变量选择。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，该采样器可扩展至实际感兴趣的维度。通过模拟研究展示了所提方法的性能，并与自适应LASSO及逐步选择法进行了对比。我们还使用公开可用的真实数据给出了两个应用案例。本文结果的复现代码及实现可见于https://github.com/adam-iqbal/selection-spike-slab。