Figure 3.

Causal directed acyclic graphs for linear data-generating models with one-sided exposure-to-outcome sibling spillover and spillover from outcomes. Subscripts i and j denote family and sibling, respectively. T_ij is the exposure, Y_ij is the outcome, D_i is the gain-score, and U_i is an unobserved family-level confounder. Greek letters denote effects. (3A) has outcome-to-exposure spillover, and (3B) and (3C) have outcome-to-outcome spillover. The gain-score method does not identify the spillover effect θ (T_i1 → Y_i2) in any of the three models.