Visualising Incomplete Data with Subset Multiple Correspondence Analysis

Determining the cause of missing values is a challenge, but an important task in order to select correct analysis techniques for missing data. This paper presents a new approach to identify the missing data mechanism (MDM) by applying cluster analysis to biplots of data having missing observations. Subset multiple correspondence analysis (sMCA) enables an isolated analysis of a chosen subset while preserving the scaffolding of the original data set. Multivariate categorical data sets are frequently represented in a coded dummy matrix, referred to as an indicator matrix. Additional category levels can be created for the indicator matrix to account for the unobserved information which has the advantage of not forfeiting any observed information. The extended indicator matrix easily partitions a data set into observed and unobserved subsets. sMCA biplots are used for the visual exploration of the subsets. Configurations of the incomplete subsets enable the recognition of non-response patterns which could aid in the identification of a particular MDM. The missing at random (MAR) MDM refers to missing responses that are dependent on the observed information and is expected to be identified by patterns and groupings occurring in the incomplete sMCA biplot. ... mehrThe missing completely at random (MCAR) MDMstates that all observations have the same probability of not being captured which could be identified by a random cloud of points in the incomplete sMCA biplot. The partitioning around mediods (pam) clustering technique is used to establish the number of available clusters in an incomplete sMCA biplot. A simulation study confirmed that there is a difference in the number of sufficient clusters that can by identified from MAR and MCAR simulated data sets. A real data set is also explored and the MDM is identified using the results of the simulation study as guidelines.