Networks of several distinct types of social tie are aggregated by a dual model that partitions a population while simultaneously identifying patterns of relations. Concepts and algorithms are demonstrated in five case studies involving up to 100 persons and up to eight types of tie, over as many as 15 time periods. In each case the model identifies a concrete social structure. Role and position concepts are then identified and interpreted in terms of these new models of concrete social structure. Part II, to be published in the May issue of this Journal (Boorman and White 1976), will show how the operational meaning of role structures in small populations can be generated from the sociometric blockmodels of Part I.

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Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions

An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

Holland and Leinhardt (1981) proposed the p 1 model for the analysis of binary directed graph data in network studies. Such a model provides information about the “attractiveness” and “expansiveness” of the individual nodes in the network, as well as the tendency of a pair of nodes to reciprocate relational ties. When the nodes are a priori partitioned into subgroups based on attributes such as race and sex, the density of ties from one subgroup to another can differ considerably from that relating another pair of subgroups, thus creating a situation called blocking in social networks. The p 1 model completely ignores this extra piece of information and is, therefore, unable to explain the block structure. Blockmodels that are simple extensions of the p 1 model are proposed specifically for such data. An iterative scaling algorithm is presented for fitting the model parameters by maximum likelihood. The methodology is illustrated in detail on two empirical examples.

https://www.jstor.org/stable/info/2289119

Stochastic Blockmodels for Directed Graphs

Social structure from multiple networks: I

Constructing blockmodels: How and why

The revised matrix is called an intercolumnar matrix; it reports the intercorrelations of every column of the original matrix with every other column of the original matrix. In the example to which the above approach was applied, the intercolumnar matrix portrayed clusters more clearly than did the original matrix. More specifically, in comparing the intercolumnar matrix with the original matrix, the indices of association between members of a cluster moved toward plus one, and those between variables not belonging to the same clusters moved to minus val-

Clusters from Iterative, Intercolumnar Correlational Analysis:

ONE of the values of Hierarchical Classification by Reciprocal Pairs and similar methods (McQuitty, 1966), is their ability to classify data without superimposing or forcing the kind of hierarchical classification which will emerge. Another is their ability to classify almost any set of data without encountering circumstances that necessitate arbitrary decisions. There is, however, one special condition which does require an improvement in order to avoid an arbitrary decision which might affect the resulting hierarchical structure. This condition pertains to one type of tie in the degree of association between objects t o be classified into a hierarchical structure. The effects of an arbitrary resolution of the tie can be extensive in certain unusual cases, i.e., when the tie is for the highest entry in the matrix, and for certain other pairs, when the mechanics of the solution provide that two or more pairs can be classified simultaneously.

The Problem of Ties in a Pattern Analytic Method

This paper illustrakes Iterative, Intercolumnar Correlational Analysis, both single and multiple methods (McQuitty, 1967, 1968; McQuitty and Clark, 1968). It is applied to a test designed to assess psychological well-being. The test is derived from the same general theory as the method of analysis. The method is applied in the paktern analysis of both composite matrices of interassociation land matrices genemted from results by the single individual. The test and method investigate intra-individual personality structure as well as composite personality structure.

James A. Clark

Papers

Clusters from Iterative, Intercolumnar Correlational Analysis:

The Problem of Ties in a Pattern Analytic Method

A study of the reliability of by iterative, intercolumnar correlational analysis intra-individual personality structure.

Hierarchical Classification by Reciprocal Pairs of Course Selections in Psychology