Single World Object Oriented Plates (SWOOPs): A Graphical Framework for Causal Reasoning in Multivariate, Multilevel, and Longitudinal Settings

• Activity Number: 362
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Roddy Theobald* and Thomas S. Richardson
• Companies: University of Washington and University of Washington
• Keywords: graphical models ; causal inference ; value-added ; education

Abstract

We introduce a graphical framework called Single World Object Oriented Plates (SWOOPs), an extension of Directed Acyclic Graphs (DAGs) that facilitates causal reasoning in multivariate, multilevel, and longitudinal settings. SWOOPs can be derived from DAGs in three steps: by aggregating related variables into "objects" (e.g. Koller and Pfeffer, 1997); by arranging objects within a level of data into "plates" (Buntine, 1994); and, following Richardson and Robins (2013), by introducing a "node-splitting" operation that allows for the inclusion of potential outcomes on the graph. We prove that conditional independence relationships in SWOOPs imply conditional independence relationships in any underlying DAG, and demonstrate how SWOOPs can be used to communicate and verify the assumptions that justify causal conclusions from observational data. As an application, we discuss value-added models (VAMs) of teacher effectiveness, and show that SWOOPs can be used to connect the substantive conditions (Rothstein, 2009) and the counterfactual conditions (Reardon and Raudenbush, 2009) that justify causal conclusions from different VAMs.