GPAbin: unifying visualizations of multiple imputations for missing values

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.

Keywords:

• Biplots
• missing data
• multiple correspondence analysis
• multivariate categorical data
• Procrustes analysis