Estimating Causal Effects From Multilevel Group-Allocation Data

In group-allocation studies for comparing behavioral, social, or educational inter-ventions, subjects in the same group necessarily receive the same treatment, whereby a group and/or group-dynamic effect can confound the treatment effect. General counterfactual outcomes that depend on group characteristics, group membership, and treatment are developed to provide a structure for specifying causal effects of treatment in the multilevel setting. An average causal effect of treatment cannot be specified, however, without a simplifying assumption of group-membership invariance (i.e., no group-dynamic effect). Under group-membership invariance and ignorability assumptions, the average causal effect is then con-nected to estimable quantities of the hierarchical linear model (HLM). Further-more, it is shown that the typical specification of the HLM involves conditional independence assumptions that actually preclude the group-dynamic effect