Salvaging Data Records with Missing Data: Data Imputation using the Multivariate t Distribution

Abstract

When doing multivariate data analysis, one common obstacle is the presence of incomplete observations, i.e., observations for which one or more key fields are missing data. Missing data is often countered by deleting entire observations that contain missing data. The negative effects of deleting entire observations are multiple: deleting observations reduces sample size and can also result in biased inferences even if data is missing at random. In addition, knowledge contained within incomplete observations is knowledge lost when they are deleted- and the effort spent collecting that knowledge is effort wasted. Data imputation methods, or methods of statistically “filling-in” missing data, can help combat small sample sizes by using the existing information in partially complete observations with the end goal of producing less biased and higher confidence inferences. When a sample from a multivariate normal population is only partially complete, and the missing data meets appropriate assumptions (missing at random), robust data imputation of the missing data can be implemented with monotone data augmentation (MDA) using the multivariate t distribution. Missing data imputation is applied to data from the NASA Instrument Cost Model (NICM) using the MDA algorithm under the assumption of having a multivariate t distribution with fixed degrees of freedom. A sensitivity analysis to the degrees of freedom parameter is presented to demonstrate robustness of the multivariate t distribution when dealing with small samples as compared to the multivariate normal distribution.