Direct and indirect effects for neighborhood-based clustered and longitudinal data.

Definitions of direct and indirect effects are given for settings in which individuals are clustered in groups or neighborhoods and in which treatments are administered at the group level. A particular intervention may affect individual outcomes both through its effect on the individual and by changing the group or neighborhood itself. Identification conditions are given for controlled direct effects and for natural direct and indirect effects. The interpretation of these identification conditions are discussed within the context of neighborhood research and multilevel modeling. Interventions at a single point in time and time-varying interventions are both considered. The definition of direct and indirect effects requires certain stability or no-interference conditions; some discussion is given as to how these no-interference conditions can be relaxed.