A Simulation Study for the Identification of Missing Data Mechanisms Using Visualisation

Understanding the cause of the missingness in data is a science of its own and is of great importance for the application of valid and unbiased analysis techniques for missing data. The distribution of missingness is defined by certain dependencies on either observed or missing values in a data set, and therefore, requires a multivariate visualisation to attempt to identify the missing data mechanism (MDM). Multivariate categorical data sets containing missing data entries can be separated into observed and unobserved (or missing) subsets by creating an additional category level (CL) for each variable with missing responses in the indicator matrix. Subset multiple correspondence analysis (sMCA) can then be applied to the recoded indicator matrix to obtain separate biplots for the observed and missing subsets. The sMCA biplot of missing categories enables the exploration of the missing values which could expose non-response patterns. Partitioning around medoids (pam) clustering is used to determine whether sufficient clustering structures can be identified in the sMCA biplot of missing responses. A simulation study consisting of data sets with different sample sizes are generated from three distributions. Artificial missingness is created by deleting values according to MAR and MCAR MDMs with different percentages of missing values. The influence of the underlying distribution on the outcome of the clustering techniques will be presented. The insight obtained from the simulation results provides guidelines for the identification of the MDM in real data applications.