A multiple indicator approach to blockmodeling signed networks

Regardless of whether the focus is on algebraic structures, elaborating role structures or the simple delineation of concrete social structures, generalized blockmodeling faces a pair of vulnerabilities. One is sensitivity to poor quality of the relational data and the other is a risk of over fitting blockmodels to the details of specific networks. Over fitting blockmodels can lead to multiple equally well fitting partitions where choices cannot be made between them on a principled basis. This paper presents a method of tackling these problems by viewing (when possible) observed social relations as multiple indicators of an underlying affect dimension. Quadratic assignment methods using matching coefficients, product moment correlations and Goodman and Kruskal's gamma are used to assess the appropriateness of using the sum of observed relations as input for applying generalized blockmodeling. Data for four groups are used to show the value of this approach within which multiple equally well fitting blockmodels for single relations are replaced by unique (or near-unique) partitions of the summed data. This strategy is located also within a broader problem of blockmodeling three-dimensional networks data and suggestions are made for future work.