Sparse Estimation and Uncertainty with Application to Subgroup Analysis∗

We introduce a Bayesian method, LASSOplus, that unifies recent contributions in the sparse modeling literatures, while substantially extending pre-existing estimators in terms of both performance and flexibility. Unlike existing Bayesian variable selection methods, LASSOplus both selects and estimates effects while returning estimated confidence intervals among discovered effects. Furthermore, we show how LASSOplus easily extends to modeling repeated observations and permits a simple Bonferroni correction to control coverage on confidence intervals among discovered effects. We situate LASSOplus in the literature on how to estimate sub-group effects, a topic that often leads to a proliferation of estimation parameters. We also offer a simple pre-processing step that draws on recent theoretical work to estimate higherorder effects that can be interpreted independent of their lower-order terms. A simulation study illustrates the method’s performance relative to several existing variable selection methods. In addition, we apply LASSOplus to an existing study on public support for climate treaties to illustrate the method’s ability to discover substantive and relevant effects. Software implementing the method is publicly available in the R package sparsereg.