Title: Visualizations of multiple imputations using generalized orthogonal procrustes analysis
Authors: Johane Nienkemper-Swanepoel - Stellenbosch University (South Africa) [presenting]
Niel Le Roux - Stellenbosch University (South Africa)
Sugnet Lubbe - University of Cape Town (South Africa)
Abstract: Multiple imputation based on multiple correspondence analysis (MIMCA) has been suggested for dealing with missing values in categorical data sets. The MIMCA procedure is visually investigated using simulated data sets with different patterns of missing data. Multiple correspondence analysis (MCA) biplots of the multiple imputations are constructed and optimally aligned using Generalized orthogonal Procrustes analysis (GOPA). GOPA allows the comparison of several configurations with a group average configuration or predetermined target configuration. The aligned biplots allow a detailed description of the consistencies and idiosyncrasies among the various imputed data sets. An average configuration can be obtained from the optimally aligned configurations, which is intuitively associated to the well-known combination rules of Rubin used for combining estimates from multiple imputed data sets. It is proposed to use the distances between the samples and category level points (CLPs) of the average configuration to predict final CLPs for the missing samples. This proposal will result in a final combined data set for further analysis, as opposed to multiple data sets with separate analyses. Finally visualizations of the predicted data set are compared to visualizations of the original complete simulated data set. Different measures for the goodness of fit within the Procrustes framework will be used to validate the proposed procedures.