Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To avoid the misspecification, we propose semiparametric Bayesian estimation in which an outcome model is parametric, but the response model is semiparametric in that we do not assume any parametric form for the nonresponse variable. We adopt penalized spline methods to estimate the unknown function. We also consider a fully nonparametric approach to modeling the response mechanism by using radial basis function methods. Using Pólya–gamma data augmentation, we developed an efficient posterior computation algorithm via Gibbs sampling in which most full conditional distributions can be obtained in familiar forms. The performance of the proposed method is demonstrated in simulation studies and an application to longitudinal data.

无响应的统计推断非常具有挑战性，尤其是在响应机制不可忽略的情况下。在这种情况下，统计推断的有效性取决于响应模型的不可测试的正确规范。为了避免错误指定，我们提出了半参数贝叶斯估计，其中结果模型是参数化的，但是响应模型是半参数的，因为我们不对无响应变量采用任何参数形式。我们采用惩罚样条方法来估计未知函数。我们还考虑了使用径向基函数方法对响应机制进行建模的完全非参数方法。使用Pólya-gamma数据扩充，我们通过Gibbs采样开发了一种有效的后验计算算法，该算法可以以熟悉的形式获得大多数完整的条件分布。