Population and network boundary
Identifying a network boundary is a tricky business in network analysis, and more details of ways of doing this can be found in Wasserman and Faust, 1994. We used snowball sampling, but also, to draw the boundary, we made use of theoretical justifications for stopping the sampling process; as described in the article, we were mainly interested in uncovering the social networks of JAC members, to compare this kind of social structure with that of stakeholder categories to see which structure correlated most strongly with land management views. As such, ‘rolling a snowball’ until no more new names were nominated was not deemed necessary in the context of our research, although we did discover that names did, indeed, start to repeat. In the end, we interviewed all JAC members, and we interviewed 20 of 30 new names these JAC members nominated, as described in the paper.
There were some other issues we encountered: certain answers provided by the second round of respondents were problematic, in that some respondents felt uncomfortable offering an actual name. Thus, some respondents nominated categories of stakeholders such as ‘farmers’, or ‘neighbours’ or ‘county officials’ as opposed to actual persons. As such, we tended to disregard nominations that were not linked to actual persons. Thus, the two shortcomings of our sample, therefore, were that we were unable to contact 10 of 30 nominated names, and we had no means of ascertaining whether certain responses such as ‘neighbours’ or ‘farmers’ may or may have been JAC members.
Use of permutation tests and p-values for analysing data derived from social networks
Complete social network data (as opposed to ego-network data) are assumed to be interdependent, i.e. that respondents are not independent of one another. And this interdependency assumption is seen as the very nature of social network data. As such, theoretical distribution models (such as a normal curve) can not be used for making inferences on network data. Thus, network analysts often make use of a form of non-parametric testing called permutation tests (also referred to as boot-strapping). Although permutation tests typically are used for deriving p-values, they do not work so well for deriving confidence intervals or for attaining coefficient values (Good 2005). Thus, one can only comment on the significance of the relationship in question, and not on the strength of that relationship, and this is the reason why coefficient values are absent from Table 1. Finally, permutation tests were used not only for the Geary C statistic in computing network autocorrelations (Table 1), but also for the regression model used for analyzing the attribute data of social actors (Table 2).
Use of the Geary C statistic for network autocorrelation
This statistic is a measure of spatial autocorrelation, and as such, focuses on the proximity of observations in time (Geary 1954). In this case, the proximities translate into two observations in a two-dimensional space. As social network data correlated with individual attribute data can be conceptualized as this sort of two-dimensional space, the Geary C statistic was used. In addition, Geary C was chosen, as it is more sensitive to local network structure than other procedures, for example Moran I.
Creating a binary matrix
To test for the relationship(s) between the presence of a social tie and similiarity in views, we transformed our valued data reflecting the frequency of communication between stakeholders to binary data. In transforming valued data to binary data, we in essence reduced the social network data to a recording of the mere presence or absence of a communication tie between any two pair of stakeholders, where a 1 represented the presence of a tie and 0 the absence of a tie.
Creating a strength-of-tie matrix.
The strength-of-tie matrix was created by aggregating i) the communication matrix containing valued data reflecting the frequency of contact between individuals (with 1 = rarely and 5 =daily); and ii) the six binary matrices that reflected the six potential relationships between individuals (friendship, colleague, boss, employee, neighbor, other). Thus, if an individual actor was recorded as both a ‘friend’ and a ‘colleague,’ that person received a score of 1 in each matrix representing the different relation, and 0s in the matrices representing the other relations. The strength of tie matrix was then created through aggregating these different matrices. Thus, for example, the data gathered from a respondent who nominated another person as a ‘friend’ and ‘colleague,’ and who also stated they had ‘daily’ communication contact with that person (rated 5), was thus aggregated to one score, that of 7, in the new strength-of-tie matrix.
We are aware that this way of handling relationships glosses over qualitative differences in kinds of ties, e.g. an employer-employee relationship is different from a friendship one. However, for present purposes, we were interested in capturing the idea that a relationship could contain more than one kind of dimension. Future research can explore in more depth the qualitative differences in these stakeholder relations.
Creating a Simmelian ties matrix
We made use of the binary communication matrix (described above). Here, we used UCINET’s procedure for creating a Simmelian ties matrix. In essence, this procedure extracts only those ties from an observed network matrix, where the ties in question are embedded in a closed triad, as shown in Figure 3. Thus, the resulting matrix generally has considerably fewer ties than the original matrix, as these other structure features are considered in making the extractions.
Geary, R. C. 1954. The contiguity ratio and statistical mapping. The Incorporated Statistician 5:115-145.
Good, P. I. 2005. Permutation, parametric and bootstrap tests of hypotheses, 3rd edition. Springer, New York.