Cluster allocation design networks

Abstract

When planning and designing a policy intervention and evaluation, it is important to differentiate between (future) policy interventions we want to evaluate, $F_{T}$, affecting "the world," and experimental allocations, $A_{T}$, affecting "our picture of the world." The policy maker usually has to define a strategy that involves policy assignment and recording mechanisms that will affect the (conditional independence) structure of the data available. Causal inference is sensitive to the specification of these mechanisms. Influence diagrams have been used for causal reasoning within a Bayesian decision-theoretic framework that introduces interventions as decision nodes (Dawid 2002). Design Networks expand this framework by including experimental design decision nodes (Madrigal and Smith 2004). They provide semantics to discuss how a design decision strategy (such as a cluster randomised study) might assist the identification of intervention causal effects. The Design Network framework is extended to Cluster Allocation. It is used to assess identifiability when the experimental unit's level is different from the analysis unit's level, and to discuss the evaluation of cluster- and individual-level future policies. Cases of 'pure' cluster (all individuals in a cluster receiving the same intervention) and 'non-pure' cluster (only a subset receiving the policy) are discussed in terms of causal effects. The representation and analysis of a simplified version of a Mexican social policy programme to alleviate poverty (Progresa) is performed as an illustration of the use of Bayesian hierarchical models to make causal inferences relating to household and community level interventions.