Patrick Doreian

Linear Models with Spatially Distributed Data

This article deals with linear models for which data have been aggregated over well-defined geographic areas. Such data may be generated by spatial processes, and these may be represented in the form of spatial autocorrelation in the disturbance term or directly in the form of a spatial effect. This article details the derivation of Ords (1975) MLEprocedurefor the spatial disturbances model and contrasts it with this MLE procedure for the spatial effects model. These alternative model specifications and estimation procedures are then illustrated by a variety of examples. These MLEprocedures for the spatial models are also contrasted with conventional regression procedures (which ignored geographical space). If there is spatial autocorrelation present, an MLE procedure is preferable.

A partitioning approach to structural balance

Abstract The classic formulation of structural balance by Cartwright and Harary (Psychological Review, 63, 1956, 277–293) had the basic structural theorem that a balanced structure could be partitioned into two mutually antagonistic subgroups each having internal solidarity. Davis (Human Relations, 20, 1967, 181–187) extended this theorem for cases where there can be more than two such mutually antagonistic subgroups. We use these theorems to construct a criterion function for a local optimization partitioning procedure for signed digraphs. For any signed digraph, this procedure yields those partitions with the smallest number of errors, a measure of the imbalance in the graph, and an identification of those links inconsistent with both generalized and structural balance. These methods are applied to some artificial data and to the affect data from Sampson (A novitiate in a period of change: An experimental and case study of social relationships, Dissertation, Cornell University, 1968). The latter provides a positive test of a basic tenet of balance theory, that there is a tendency towards balance with signed relations in human groups. While these methods can be applied to all signed digraphs and signed graphs, the balance hypothesis is relevant only for affect ties.

Some dynamics of social balance processes: bringing Heider back into balance theory

Structural (or social) balance is regarded as a fundamental social process. It has been used to explain how the feelings, attitudes and beliefs, which the social actors have towards each other, promotes the formation of stable (but not necessarily conflict free) social groups. While balance theory has a rich and long history, it has lost favor in recent times. The empirical work has taken one of two forms. Most empirical work on social balance has focused on dyads and triples, and findings have been inconsistent. The remaining studies focus on the structure of the group as a whole. Results here have been inconsistent also. One major problem is that the first line of work is based only on the source ideas of Heider while the second has been based only on the ideas of Cartwright and Harary. Some of the inconsistencies may be due to this empirical split where the two streams of ideas do not inform each other. We propose a new theoretical model for social balance in the form of an agent-based simulation model. The results we present account for several of the inconsistencies found in the literature. The model simulates distinct but interdependent social actors making positive and negative selections of each other in efforts to reach balanced cognitive states. The design variables for the simulations are group size, degree of contentiousness of a group and the mode of communicating choices regarding the existence and sign of social ties. The group level balance mechanism used by the dynamic model is based on the idea of partition balance, as proposed by Doreian and Mrvar [Soc. Netw. 18 (1996) 149]. Actor selections, over time, generate networks that partition group members into stable, balanced subsets at equilibrium or near equilibrium. The design variables have complicated impacts on the number of actor choices made to reach balance, the level of group imbalance, the number of actors with balanced images and the number of plus-sets formed.

Generalized blockmodeling of two-mode network data

Abstract We extend the direct approach for blockmodeling one-mode data to two-mode data. The key idea in this development is that the rows and columns are partitioned simultaneously but in different ways. Many (but not all) of the generalized block types can be mobilized in blockmodeling two-mode network data. These methods were applied to some ‘voting’ data from the 2000–2001 term of the Supreme Court and to the classic Deep South data on women attending events. The obtained partitions are easy to interpret and compelling. The insight that rows and columns can be partitioned in different ways can be applied also to one-mode data. This is illustrated by a partition of a journal-to-journal citation network where journals are viewed simultaneously as both producers and consumers of scientific knowledge.

Estimating Linear Models with Spatially Distributed Data

Sociologists study a wide variety of social, political, and economic phenomena. Many of these phenomena-for example, urbanization, political mobilization, economic development, diffusion of innovations-take place in and are distributed across geographical space. It is reasonable, therefore, to argue that sociologists are interested, indeed have long been interested, in social phenomena distributed in geographical space. Yet, in the main, our theoretical frameworks and data-analytic capabilities do not include the geography of

Partitioning signed social networks

Structural balance theory has proven useful for delineating the blockmodel structure of signed social networks. Even so, most of the observed signed networks are not perfectly balanced. One possibility for this is that in examining the dynamics underlying the generation of signed social networks, insufficient attention has been given to other processes and features of signed networks. These include: actors who have positive ties to pairs of actors linked by a negative relation or who belong to two mutually hostile subgroups; some actors that are viewed positively across the network despite the presence of negative ties and subsets of actors with negative ties towards each other. We suggest that instead viewing these situations as violations of structural balance, they can be seen as belonging to other relevant processes we call mediation, differential popularity and internal subgroup hostility. Formalizing these ideas leads to the relaxed structural balance blockmodel as a proper generalization of structural balance blockmodels. Some formal properties concerning the relation between these two models are presented along with the properties of the fitting method proposed for the new blockmodel type. The new method is applied to four empirical data sets where improved fits with more nuanced interpretations are obtained.

Fixed list versus snowball selection of social networks

Abstract Two ways of collecting network data are discussed in the context of interorganizational networks among social service agencies. One method proceeds with a fixed agency list while the other uses a snowball selection procedure. We find that: 1. (i) the agencies included in the two selection procedures differ; 2. (ii) network-based indicators for agencies (such as centrality) differ; 3. (iii) the substantive contents of the included ties differ; and 4. (iv) the structure of the networks differ. The two methods are fundamentally different and cannot be used as surrogates for each other. When data are gathered at multiple points in time, the differences between the methods are more acute. Interagency networks change through time: agencies leave the network while other agencies join. Snowball selection can respond to these changes while fixed list selection does not.

Structural equivalence in a journal network

Concepts and techniques used in contemporary social network analysis are applied to a network of journals based on citation. By means of procedures drawing on the notion of structural equivalence, a set of blocks or positions, containing journals, are delineated. These blocks have a very close correspondence to a categorization of the journals based on their aims and objectives, supporting the idea of treating the journals of a discipline as a status‐role relational system. By means of the reduced image of the network, a highly centralized and hierarchical structure appears. Some hypotheses concerning the structure and operation of journal networks are advanced.

Direct and indirect methods for structural equivalence

Abstract Procedures for establishing a partition of a network in terms of structural equivalence can be divided into direct and indirect approaches. For the former, a new criterion function is proposed that reflects directly structural equivalence concerns. This criterion function can then be (locally) optimized to create a partition. For indirect approaches, measures of dissimilarity must be compatible with the definition of structural equivalence.

A brief history of balance through time

We present methods for establishing the amount of reciprocity, transitivity and group balance (a generalization of structural balance) in sociometric structures. These methods are applied to the second time series of sociometric data provided by the Newcomb (1961) study. The amount of reciprocity was above chance levels at the outset and showed no systematic variation thereafter. Transitivity has a very different time scale. It climbed steadily through the first nine weeks and remained stable thereafter. While consistent with chance at the beginning of the study period, it grew to above chance levels at week 3. Group imbalance declined throughout the entire period. The reasons for these different time scales are discussed.