Abstract
In group-allocation studies for comparing behavioral, social, or educational interventions, 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 connected to estimable quantities of the hierarchical linear model (HLM). Furthermore, it is shown that the typical specification of the HLM involves conditional independence assumptions that actually preclude the group-dynamic effect.
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