Analysis of Complex Networks

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] = σ² = 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 ...