Abstract

Missing data are a common occurrence in analyses of multivariate data, including in multilevel modeling. Bayesian approaches to handling missing data in multilevel modeling have garnered increasing attention, either on their own or in service of multiple imputation. However, these applications are largely confined to specific models or missingness patterns. The current work provides a coherent account of Bayesian analysis of multilevel models in the presence of missing data on the outcomes, level-1 predictors, and level-2 predictors, that covers the main aspects of the models and missingness. In doing so, this work provides a grounding for estimation in fully Bayesian approaches that employ Gibbs sampling, and provides an account of how to generate the imputations in the first phase of a multiple imputation approach.

摘要

缺失数据在多变量数据分析（包括多级建模）中很常见。处理多级建模中缺失数据的贝叶斯方法无论是单独使用还是用于多重插补，都引起了越来越多的关注。然而，这些应用程序很大程度上局限于特定模型或缺失模式。当前的工作在结果、1 级预测变量和 2 级预测变量存在缺失数据的情况下，对多级模型的贝叶斯分析提供了连贯的说明，涵盖了模型和缺失的主要方面。在此过程中，这项工作为采用吉布斯采样的完全贝叶斯方法的估计提供了基础，并提供了如何在多重插补方法的第一阶段中生成插补的说明。