Using Additive Conjoint Measurement Analysis of Social Network Data
A procedure for analyzing social network data is introduced. The procedure can analyze social networkdata which are (a) not binary but discrete or continuously valued, and (b) asymmetric. The procedure utilizes the additive conjoint measurement by regardi
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Introduction
Social networks represent relationships among a set of actors which are called one-mode two-way (Carroll, Arabie (1980)) social network. Researchers on social networks have focused their attention mainly on onemode two-way social network data which are represented by a square symmetric matrix. Usually a social network data matrix consists of 01 or binary elements (Wasserman, Faust (1994, p.169)). When social network data are binary, either the presence or the absence of a relationship is shown. But relationships among actors are not necessarily binary (Wasserman, Iacobucci (1986)). When social network data are discrete (not binary) or continuously valued, relationships among actors can more fully be described than when they are binary. Although some social networks are inevitably asymmetric, relationships among actors would have been basically regarded to be symmetric (Bonacich (1972)). But several researchers have paid attention to asymmetric social networks (Carley, Krackhart (1996)). In the case of the asymmetric social network, the relationship from actors j to k and that from actors k to j can be differentiated. The two relationships are not necessarily equal to each other, nor they are not necessarily symmetric.
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The Procedure
Let n be the number of actors. The social network data matrix among n actors has n rows and n columns. Actor j is represented by row j as well as by column j. The (j, k) element of the matrix represents the relationship from actors j to k. As mentioned earlier, the (j, k) element M. Schwaiger et al. (eds.), Exploratory Data Analysis in Empirical Research © Springer-Verlag Berlin Heidelberg 2003
150 of the matrix is not necessarily equal to the (k,j) element of the matrix, which represents the relationship from actors k to j. The procedure is based on additive conjoint measurement. A set of n rows of the matrix is regarded as one attribute, and a set of n columns of the matrix is regarded as the other attribute. Each row or actor represented by a row is regarded as a level of the attribute corresponding to the rows. And each column or actor represented by a column is regarded as a level of the other attribute corresponding to the columns. The (j, k) element of the matrix, which represents the relationship from actors j to k, is regarded to be the degree of the preference toward or the worth of the 'product' made by combining level j of the attribute corresponding to rows and level k of the attribute corresponding to columns. An analysis of a social network data matrix among actors by the procedure using additive conjoint measurement results in two sets of partworths; one consists of part-worths assigned to levels of an attribute corresponding to rows of the matrix, and the other consists of part-worths assigned to levels of the other attribute corresponding to columns. Thus two terms are assigned to each of n actors. One is the part-worth assigned to an actor represented by a row. The other is the part-worth assigned to an actor represented by a column. The part-wo
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