## 16.7 Binary Choice Model

We now turn to modeling organizational collaboration choices in order to examine how specific individual characteristics, spatial effects, and network effects determine the choice of collaboration (the theoretical underpinnings are described in Ref. [29]). We will build upon the survey data and the subnetwork constructed there from (Section 16.3). While this restricts us to only 191 organizations, we have considerably more information about these organizations than for the complete networks.

### 16.7.1 **The Empirical Model**

In our analytical framework, the constitution of a collaboration *Y*_{ij} between two organizations (*i*) and (*j*) will depend on an unobserved continuous variable *Y*^{*} that corresponds to the profit that two organizations (*i*) and (*j*)_{ij} receive when they collaborate. Since we cannot observe *Y*^{*}_{ij} but only its dichotomous realizations *Y*_{ij}, we assume *Y*_{ij} =1 if *Y*^{*}_{ij} > 0 and *Y*_{ij} = 0 if (*Y*^{*}_{ij} ≤ 0. *Y*_{ij} is assumed to follow a Bernoulli distribution so that *Y*_{ij} can take the values one and zero with probabilities π_{ij} and 1– π_{ij}, respectively. The probability function can be written as

with (*E [Y*_{ij}] = μ_{ij} = π_{ij} and (Var [*Y*_{ij}] = σ^{2} = π_{ij} (1– π_{ij})), where μ_{ij} denotes some mean value.

The next step in defining the model concerns the systematic structure – we would like the probabilities π_{ij} to depend on a matrix of observed covariates. Thus, we let the probabilities ...