Causal Inference, Social Networks and Chain Graphs

Abstract

Traditionally, statistical inference and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as social networks, where individuals may interact with one another such that treatments may spill over from the treated individual to their social contacts and outcomes may be contagious. Existing models proposed for causal inference using observational data from networks of interacting individuals have two major shortcomings. First, they often require a level of granularity in the data that is infeasible in practice to collect in most settings and, second, the models are high dimensional and often too big to fit to the available data. We illustrate and justify a parsimonious parameterization for network data with interference and contagion. Our parameterization corresponds to a particular family of graphical models known as chain graphs. We argue that, in some settings, chain graph models approximate the marginal distribution of a snapshot of a longitudinal data-generating process on interacting units. We illustrate the use of chain graphs for causal inference about collective decision making in social networks by using data from US Supreme Court decisions between 1994 and 2004 and in simulations.

Does deforestation drive visceral leishmaniasis transmission? A causal analysis

“…Causal mechanisms have been studied within the framework of causal inference in the presence of interference, allowing for partial interference between units [28][29][30]. More recently, methods have been developed to allow for full interference by assuming that the data can be described as a network [26,[31][32][33], and representing the data as chain graphs [47,48] that allow inferences about the parameters of the joint distribution of the observed data. A chain graph is a mixed graph that enables a network to be constructed from both the directed relationship of the variables (as in figure 2), and the undirected relationship of the study units (i.e.…”

“…infection), the so-called dependent happenings. Only fairly recently methods to allow for such dependence in causal inference contexts became available [26][27][28][29][30][31][32][33].…”

Information Theoretic Causal Effect Quantification

“…Similar considerations have led to the extension of DAGs to chain graphs as graphical models for causality. Potential presence of associations between variables which cannot be attributed to an underlying causal process (e.g., because the direction of causality cannot be established with available measurements, there exists an unmeasured confounding variable or a feed-back mechanism) motivated a causal interpretation of chain graphs [ 52 , 53 ] analogous to the causal interpretation of DAGs introduced in Section 2.1 . The said non-causal direct associations are modelled with undirected adges between variables.…”

“…Analogously to Equations ( 2 ) and ( 3 ), the data generating process as well as interventional distribution have been defined for CGs. We follow the approach put forward in [ 52 , 53 ].…”

“…Secondly, within every chain component, every node depends on all the other nodes without any specified direction of the dependence (which can be modelled as Gibbs sampling of the nodes in the chain component until the pdfs of the nodes reach an equilibrium). This interpretation of chain graphs’ data generating process and Markov properties was proposed by Lauritzen and Wermuth [ 48 , 50 , 51 ] and later used as a basis for modelling causal relationships [ 52 , 53 ]. We build on this interpretation of chain graphs in Section 3 .…”