A multiple indicator approach to blockmodeling signed networks

Regardless of whether the eation of concrete social sensitivity to poor quality the details of specific netw tions where choices cann of tackling these problem of an underlying affect di moment correlations and the sum of observed relat used to show the value of relations are replaced by u also within a broader pro made for future work. Following the introduction of blockmodeling by Lorrain and White (1971), an explosion of work followed (Hummon and Carley, 1993) that: (i) explored its mathematical foundations (e.g. Schwartz, 1977; White and Reitz, 1983; Batagelj, 1997; Doreian et al., 2005); (ii) provided practical computer algorithms to perform blockmodeling (e.g. Breiger et al., 1975; Burt, 1976; Batagelj et al., 1992); (iii) explored detailed role structures (e.g. White et al., 1976); (iv) provided algebraic interpretations of role structures (e.g. Bonacich, 1979; Winship and Mandel, 1983; Mandel, 1983) and (v) provided many empirical applications of blockmodeling. Generalized blockmodeling was presented as a general framework permittingmanydifferentblock typeswithnewtypesofblockmodels and direct fitting of blockmodels to social relational data that included blockmodels for signed relations (Doreian et al., 2005). Regardless of whether the focus is on algebraic structures, elaborating role structures or the simple delineation of concrete social structures, there are at least two vulnerabilities for this approach: (1) possible poor quality of the relational data analyzed and (2) the risk of over fitting a blockmodel to the details of a specific network. This paper presents one way of tackling both problems through the use of multiple indicators for signed social relations. Section 1 introduces the problem more fully. The methods and the data are described in Section 2. These methods are applied to the data and the results are interpreted in Section 3. The final section disE-mail address: [email protected]. 0378-8733/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.socnet.2008.03.005 States is on algebraic structures, elaborating role structures or the simple delintures, generalized blockmodeling faces a pair of vulnerabilities. One is he relational data and the other is a risk of over fitting blockmodels to . Over fitting blockmodels can lead to multiple equally well fitting partimade between them on a principled basis. This paper presents a method viewing (when possible) observed social relations as multiple indicators ion. Quadratic assignment methods using matching coefficients, product man and Kruskal’s gamma are used to assess the appropriateness of using s input for applying generalized blockmodeling. Data for four groups are pproach within whichmultiple equally well fitting blockmodels for single e (or near-unique) partitions of the summed data. This strategy is located of blockmodeling three-dimensional networks data and suggestions are © 2008 Elsevier B.V. All rights reserved. cusses the empirical results, presents some suggestions concerning blockmodelingbothsignedandunsignedsocial relationsand three1. Signed social relations and blockmodeling When studying sociometric structure, the modal strategy uses positive social relations. Yet, many social relations carry both positive and negative affect and the dynamics of signed affect ties between people are different to those of positive relations alone. Fortunately, there are signed network data sets available to explore these issues. For signed relations, one focus – informed by thework ofCartwright andHarary (1956) andofDavis (1967)– is ondelineating the group structure in the sense of identifying mutually hostile subgroups where each subgroup is held together by positive ties. Structural balance theory has its origins1 in the work of Heider (1946). Cartwright and Harary (1956) generalized structural balance theory in threeways by: (a) removing the distinction between signed social relations and signed unit formation relations to study, simply, signed relations; (b)moving fromstudying signed triples (in the minds of actors) to studying signed social networks (of actors) (Doreian, 2004); (c) providing a compelling statement of the global 1 While there are many variants of ‘consistency theories’, for example, Newcomb (1961, 1968), Festinger (1957) and Osgood and Tannenbaum (1955), Heider’s formulation is used here as the point of departure.