Resumen de GPAbin for data visualization in the presence of missing observations
N.J. le Roux, J. Nienkemper Swanepoel, S. Lubbe
Multiple imputation is a well-established and favored technique for analyzing data containing missing values. It consists of analyzing each imputed data set separately and then combining the estimates for inference. However, the exploratory analysis options of multiple imputed data sets are limited. Biplots provide a simultaneous configuration of both samples and variables in a two- or three dimensional display. Therefore, a visualization for each of the multiple imputed data sets can be constructed and interpreted individually, but in order to formulate an unbiased conclusion, the multiple visualizations have to be combined for a unified interpretation. We propose the GPAbin technique to address this challenge for multivariate categorical data sets. The biplots for the multiple imputations are first aligned to a centroid configuration using generalized orthogonal Procrustes analysis (GPA) and then combined by obtaining the mean coordinate matrices from the aligned configurations. The combining step is inspired by Rubin’s rules (Rubin, 1987) for combining estimates obtained from analyses applied to multiple imputed data sets. The name GPAbin is derived from the amalgamation of GPA and Rubin’s rules. Simulation studies have confirmed the usefulness of the GPAbin method for categorical data in the context of multiple correspondence analysis (MCA) based biplots. The GPAbin methodology is extended to compositional data containing missing values. This extension replaces MCA based biplots with log-ratio biplots. The extended GPAbin method is illustrated by creating artificial missingness in a complete compositional example data set. A comparison between the GPAbin- and log-ratio biplots is presented to illustrate the usage of the technique.
