Home Sociology Exponential Random Graph Models for Social Networks Theory, Methods, and Applications
For comparability purposes, I transformed the behavioral and recall networks into binary and symmetric matrices using the procedure explained by Bernard et al. (1979). I used the dichotomization thresholds (K) indicated in Bernard at al. (198, table 2) and reported in Table 21.1. For the recall networks, ranked data were dichotomized by allocating 1 to all dyads with a value inferior or equal to K and 0 to all others, and scaled data were dichotomized by allocating 1 to all dyads greater than or equal to K and 0 to all other values. For the behavioral networks, the frequency of interaction had to be ranked from the most frequent to the least frequent before it could be dichotomized. I obtained density results that are similar to those reported by Bernard et al.1 After having dichotomized the networks, I symmetrized them such that if at least one tie is present in one dyad, then the edge is said to be present (Bernard et al.).
I begin by modeling each network individually because the univariate models serve as a baseline to understand the changes in significance levels
1 There is a difference between Bernard et al.’s (1979) density of the behavioral network of the Off data set and my results. It can be explained by the fact that Bernard et al. made some undocumented judgment calls during the ranking procedure of the behavioral data.
in the next stages of modeling (models with dyadic covariate and multivariate models), as well as providing information about the structure of the networks. Then, I model the recall networks using the behavioral networks as a covariate, effectively asking the question of the extent to which recall deviates from a dyadic association to behavior. Finally, I model the recall and behavioral networks together (multivariate networks) to provide further insights into their patterns of association and into the structural differences between the two.
Because there are no actor attributes in the data, the exponential random graph models (ERGMs) presented here focus only on structural parameters for these nondirected networks. A similar set of parameters has been used for all networks in order to improve the comparability of the results. Most models include an Edge parameter, although for some networks the density was fixed to assist convergence (see the comments about conditional estimation in Section 12.4.2). For the sparser networks, the inclusion of an Isolates parameter in the model was needed. The alternating Star parameter [A-S] is included to control for the degree distribution in the networks; in some models, inclusion of a Markov 2- star parameter assisted convergence. The Path Closure parameter [AT-T] and the counterpart Multiple Connectivity parameter [A2P-T] were also used. For the covariate models, the behavioral network was included as a dyadic attribute (covariate edge) in each model (see Chapter 8). Finally, in the multivariate models (see Chapter 10), different configurations representing the association between networks have been included. Similar to the covariate models, the inclusion of the Edge B-R parameter captures the extent to which the two networks align at a dyadic level. Then, more complex forms of associations are explored. Alternating triangle AT-BRB (see Figure 10.4 in Chapter 10) represents the extent to which two individuals who communicate with the same alters tend to report communication with each other. In contrast, alternating triangle AT- RBR captures the extent to which individuals who recall communicating with the same alters tend to communicate together.
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