# Model Specification

## Modeling Issues

The data pose two major modeling challenges. The first is that we have no previous knowledge of the structure of leadership networks, and thus do not know which parameters to include in the model. We therefore started with the customary social circuit parameters (see Table 13.1 in Section 13.2), and by examination of goodness of fit (GOF) statistics (see Section 13.3), added new parameters.

The second problem is that our data is restricted by the presence of distinct and nonoverlapping groups: Recruits are embedded within teams. Moreover, the selection process is structured so that interaction between teams is not possible: recruits only interact with (and can therefore select) others from their own team. Estimating the model needs to account for this complexity. We take this into account by using structural zeros, thus specifying only specific actors (allocated into the same team) with whom interaction is possible. In essence, this approach takes all six teams and examines them in a single ERGM. By fixing “structural zeroes” in the ties between groups, nominations between groups are specifically disavowed.^{[1]} The model estimates apply to all six groups. This means that we make the implicit assumption that the same endogenous processes apply in all teams. As great care is taken during selection to standardize the groups, this assumption with respect to endogenous factors is not unreasonable. We show later that this approach is warranted empirically because no differences were found between teams. An alternative would have been to allow the parameters to be different for the different groups, and afterward combining the estimates using the approach of Lubbers and Snijders (2007).

- [1] We note that the “structural zero” is the fixing of ties, where in PNet “0”means a tiecannot vary, and “1” means it can. We have fixed ties here using this process so that theycan never be present, but it is also possible to fix network ties using the same process sothat they are always present.