Karthika Mohan

Graphical Representation of Missing Data Problems

Rubin’s classic missingness mechanisms are central to handling missing data and minimizing biases that can arise due to missingness. However, the formulaic expressions that posit certain independencies among missing and observed data are difficult to grasp. As a result, applied researchers often rely on informal translations of these assumptions. We present a graphical representation of missing data mechanism, formalized in Mohan, Pearl, and Tian (2013). We show that graphical models provide a tool for comprehending, encoding, and communicating assumptions about the missingness process. Furthermore, we demonstrate on several examples how graph-theoretical criteria can determine if biases due to missing data might emerge in some estimates of interests and which auxiliary variables are needed to control for such biases, given assumptions about the missingness process.

Recoverability and Testability of Missing Data: Introduction and Summary of Results

This is an expository paper, aimed to provide a gentle introduction to missing data problems as viewed from graphical modeling perspective. Aside from producing new theoretical results, the graphical perspective oers researchers a transparent language in which to understand, articulate and analyze missing data problems. Users can specify graphical features of their problems before choosing software or algorithms, and methodological researchers can use graph-based tools to develop software and algorithms that either exploit modeling assumptions or stand robust to such assumptions. The text of this paper is written around as set of 11 slides (marked 59-69) presented at the JSM-13 meeting, on August 6, 3013.

Estimation with Incomplete Data: The Linear Case

Traditional methods for handling incomplete data, including Multiple Imputation and Maximum Likelihood, require that the data be Missing At Random (MAR). In most cases, however, missingness in a variable depends on the underlying value of that variable. In this work, we devise model-based methods to consistently estimate mean, variance and covariance given data that are Missing Not At Random (MNAR). While previous work on MNAR data require variables to be discrete, we extend the analysis to continuous variables drawn from Gaussian distributions. We demonstrate the merits of our techniques by comparing it empirically to state of the art software packages.

Missing Data from a Causal Perspective

This paper applies graph based causal inference procedures for recovering information from missing data. We establish conditions that permit and prohibit recoverability. In the event of theoretical impediments to recoverability, we develop graph based procedures using auxiliary variables and external data to overcome such impediments. We demonstrate the perils of model-blind recovery procedures both in determining whether or not a query is recoverable and in choosing an estimation procedure when recoverability holds.