Decomposition of effect of self-excluded model (3a) and its re-parameterized form (3b).

aAs explained in the main text, yij is an observed outcome of individual i in group j, xij is an individual-level social capital score of individual i in group j,  =  is the mean of social capital scores of all individuals in group j, nj is the size of the group j, and  =  is the mean of social capital scores of all individuals (excluding individual i) in group j.