Abstract

Multiple imputation is a well-established technique for analyzing missing data. Multiple imputed data sets are obtained and analyzed separately using standard complete data techniques. The estimates from the separate analyses are then combined for the purpose of statistical inference. However, the exploratory analysis options of multiple imputed data sets are limited. Biplots are regarded as generalized scatterplots which provide a simultaneous configuration of both samples and variables. A visualization for each of the multiple imputed data sets can be constructed and interpreted individually, but this can become cumbersome and several plots make a unified interpretation challenging. Analogous to multiple imputation, the coordinates of the visualizations can now be regarded as the estimates which are to be pooled in an unbiased manner to construct a final visualization. We propose a GPAbin biplot for a final single visualization after multiple imputation. In a first step, generalized orthogonal Procrustes analysis is used to align the individual biplots before combining their separate coordinate sets into an average coordinate matrix. Finally, this average coordinate matrix is then utilized to construct a single biplot called a GPAbin biplot. A simulation study is used to establish the properties of the final combined GPAbin biplot for varying data characteristics.

摘要

多重插补是分析缺失数据的成熟技术。使用标准完整数据技术分别获得和分析多个估算数据集。然后将单独分析的估计值合并起来以进行统计推断。然而，多个估算数据集的探索性分析选项是有限的。双图被视为广义散点图，它提供样本和变量的同时配置。可以单独构建和解释每个多个估算数据集的可视化，但这可能会变得很麻烦，并且多个图使得统一解释具有挑战性。类似于多重插补，可视化的坐标现在可以被视为以无偏的方式汇集以构建最终可视化的估计。我们提出了 GPAbin 双图，用于多重插补后的最终单一可视化。第一步，在将单独的坐标集组合成平均坐标矩阵之前，使用广义正交 Procrustes 分析来对齐各个双图。最后，利用这个平均坐标矩阵构建一个称为 GPAbin 双标图的双标图。模拟研究用于确定不同数据特征的最终组合 GPAbin 双图的属性。广义正交 Procrustes 分析用于在将各个双标图组合成平均坐标矩阵之前对齐各个双标图。最后，利用这个平均坐标矩阵构建一个称为 GPAbin 双标图的双标图。模拟研究用于确定不同数据特征的最终组合 GPAbin 双图的属性。广义正交 Procrustes 分析用于在将各个双标图组合成平均坐标矩阵之前对齐各个双标图。最后，利用这个平均坐标矩阵构建一个称为 GPAbin 双标图的双标图。模拟研究用于确定不同数据特征的最终组合 GPAbin 双图的属性。