# Model Specification

## Independent Bivariate Attribute Analysis

A considerable section of the interlocking directorates research does not go beyond descriptive statistics similar to those in Table 20.1. The purpose of these studies is to find over- or underrepresented groups by comparing directorships across groups and with a baseline random distribution.

## Purely Structural Effects

In our bipartite ERGM, up to five structural effects are used in various combinations: the edge parameter [L], alternating *k*-stars for directors [K- Sp] and corporations [K-Sa], and alternating k-cycles for directors [K-Cp] and corporations [K-Ca]. The edge parameter [L] represents the baseline probability of forming a tie and is similar to the intercept in a classic regression model. The star effects can be thought of as a “popularity” effect or a “rich get richer” effect (also called the “Matthew effect”), whereby actors with ties have an increased likelihood of receiving further ties. In this chapter, we use the alternating *k*-star parameters described in Chapter 10 (see Figure 10.8; the rationale for the alternating version of these statistics is given in Chapter 6). The alternating k-cycles ([K- Cp] and [K-Ca]) parameters capture the propensity of directors (p) and corporations (a) to be part of 4-cycles (i.e., to engage in closed bipartite network structures) (see Chapter 10 and Figure 10.11).