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Deterministic blockmodelling is a well-established clustering method for both exploratory and confirmatory social network analysis seeking partitions of a set of actors so that actors within each cluster are similar with respect to their patterns of ties to other actors (or, in some cases, other objects when considering two-mode networks). Even though some of the historical foundations for certain types of blockmodelling stem from the psychological literature, applications of deterministic blockmodelling in psychological research are relatively rare. This scarcity is potentially attributable to three factors: a general unfamiliarity with relevant blockmodelling methods and applications; a lack of awareness of the value of partitioning network data for understanding group structures and processes; and the unavailability of such methods on software platforms familiar to most psychological researchers. To tackle the first two items, we provide a tutorial presenting a general framework for blockmodelling and describe two of the most important types of deterministic blockmodelling applications relevant to psychological research: structural balance partitioning and two-mode partitioning based on structural equivalence. To address the third problem, we developed a suite of software programs that are available as both Fortran executable files and compiled Fortran dynamic-link libraries that can be implemented in the R software system. We demonstrate these software programs using networks from the literature., (© 2019 The British Psychological Society.)

Most partitioning methods used in psychological research seek to produce homogeneous groups (i.e., groups with low intra-group dissimilarity). However, there are also applications where the goal is to provide heterogeneous groups (i.e., groups with high intra-group dissimilarity). Examples of these anticlustering contexts include construction of stimulus sets, formation of student groups, assignment of employees to project work teams, and assembly of test forms from a bank of items. Unfortunately, most commercial software packages are not equipped to accommodate the objective criteria and constraints that commonly arise for anticlustering problems. Two important objective criteria for anticlustering based on information in a dissimilarity matrix are: a diversity measure based on within-cluster sums of dissimilarities; and a dispersion measure based on the within-cluster minimum dissimilarities. In many instances, it is possible to find a partition that provides a large improvement in one of these two criteria with little (or no) sacrifice in the other criterion. For this reason, it is of significant value to explore the trade-offs that arise between these two criteria. Accordingly, the key contribution of this paper is the formulation of a bicriterion optimization problem for anticlustering based on the diversity and dispersion criteria, along with heuristics to approximate the Pareto efficient set of partitions. A motivating example and computational study are provided within the framework of test assembly., (© 2019 The British Psychological Society.)

Affinity propagation is a message-passing-based clustering procedure that has received widespread attention in domains such as biological science, physics, and computer science. However, its implementation in psychology and related areas of social science is comparatively scant. In this paper, we describe the basic principles of affinity propagation, its relationship to other clustering problems, and the types of data for which it can be used for cluster analysis. More importantly, we identify the strengths and weaknesses of affinity propagation as a clustering tool in general and highlight potential opportunities for its use in psychological research. Numerical examples are provided to illustrate the method., (© 2018 The British Psychological Society.)

Two expectations of the adjusted Rand index (ARI) are compared. It is shown that the expectation derived by Morey and Agresti (1984, Educational and Psychological Measurement, 44, 33) under the multinomial distribution to approximate the exact expectation from the hypergeometric distribution (Hubert & Arabie, 1985, Journal of Classification, 2, 193) provides a poor approximation, and, in some cases, the difference between the two expectations can increase with the sample size. Proofs concerning the minimum and maximum difference between the two expectations are provided, and it is shown through simulation that the ARI can differ significantly depending on which expectation is used. Furthermore, when compared in a hypothesis testing framework, multinomial approximation overly favours the null hypothesis., (© 2017 The British Psychological Society.)

There are a number of important problems in quantitative psychology that require the identification of a permutation of the n rows and columns of an n × n proximity matrix. These problems encompass applications such as unidimensional scaling, paired-comparison ranking, and anti-Robinson forms. The importance of simultaneously incorporating multiple objective criteria in matrix permutation applications is well recognized in the literature; however, to date, there has been a reliance on weighted-sum approaches that transform the multiobjective problem into a single-objective optimization problem. Although exact solutions to these single-objective problems produce supported Pareto efficient solutions to the multiobjective problem, many interesting unsupported Pareto efficient solutions may be missed. We illustrate the limitation of the weighted-sum approach with an example from the psychological literature and devise an effective heuristic algorithm for estimating both the supported and unsupported solutions of the Pareto efficient set., (© 2011 The British Psychological Society.)