使用多元高斯聚类加权建模填补缺失数据
Imputation of missing data using multivariate Gaussian Linear Cluster-Weighted Modeling
AI总结：
本文提出一种基于多元高斯聚类加权建模的完全贝叶斯填补方法，利用完全观测的辅助变量联合建模响应变量，以提升缺失数据填补能力，并通过模拟和真实数据验证其优于现有方法。
摘要：
当某些感兴趣变量的值未被记录或观测到时，就会出现缺失数据。然而，大多数统计理论都假设数据是完整可用的。为了处理不完整的数据库，一种方法是根据特定准则填补与缺失信息相对应的空白，这被称为填补（imputation）。在本研究中，我们提出了一种针对含有无响应单元的数据库的新型填补方法，通过利用完全观测的辅助变量所提供的额外信息来实现。我们假设数据库中包含的变量是连续的，并且完全观测的辅助变量有助于提高模型的填补能力。在一个完全贝叶斯框架内，我们的方法利用灵活的多元正态分布混合来联合建模响应变量和辅助变量。通过运用高斯聚类加权建模（Gaussian Cluster-Weighted modeling）的原理，我们构建了一个预测模型，利用协变量的信息来填补缺失值。我们给出了模拟研究和一个真实数据示例，以展示我们的方法在各种场景下的填补能力，并将其与文献中的其他方法进行了比较。
英文摘要：
Missing data arises when certain values are not recorded or observed for variables of interest. However, most of the statistical theory assume complete data availability. To address incomplete databases, one approach is to fill the gaps corresponding to the missing information based on specific criteria, known as imputation. In this study, we propose a novel imputation methodology for databases with non-response units by leveraging additional information from fully observed auxiliary variables. We assume that the variables included in the database are continuous and that the auxiliary variables, which are fully observed, help to improve the imputation capacity of the model. Within a fully Bayesian framework, our method utilizes a flexible mixture of multivariate normal distributions to jointly model the response and auxiliary variables. By employing the principles of Gaussian Cluster-Weighted modeling, we construct a predictive model to impute the missing values by leveraging information from the covariates. We present simulation studies and a real data illustration to demonstrate the imputation capacity of our method across various scenarios, comparing it to other methods in the literature
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