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 Polya-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.
翻译:不答复的统计推论相当具有挑战性,特别是在反应机制不可忽略的情况下。在这种情况下,统计推论的有效性取决于无法检验的反应模型的正确规格。为了避免区分错误,我们提议半对数贝伊斯估计,结果模型是参数,但反应模型是半对数的,因为我们不为不反应变量假定任何参数形式。我们采用惩罚性的样板方法来估计未知功能。我们还认为,使用辐射基函数法来模拟反应机制的模型是完全非对数的。我们利用Polica-gamma数据扩增,通过Gibbs取样开发了高效的后方计算算法,其中最完整的有条件分布可以以熟悉的形式获得。拟议方法的性能在模拟研究和对长方数据的应用中得到了证明。