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Two-mode binary data matrices arise in a variety of social network contexts, such as the attendance or non-attendance of individuals at events, the participation or lack of participation of groups in projects, and the votes of judges on cases. A popular method for analyzing such data is two-mode blockmodeling based on structural equivalence, where the goal is to identify partitions for the row and column objects such that the clusters of the row and column objects form blocks that are either complete (all 1s) or null (all 0s) to the greatest extent possible. Multiple restarts of an object relocation heuristic that seeks to minimize the number of inconsistencies (i.e., 1s in null blocks and 0s in complete blocks) with ideal block structure is the predominant approach for tackling this problem. As an alternative, we propose a fast and effective implementation of tabu search. Computational comparisons across a set of 48 large network matrices revealed that the new tabu-search heuristic always provided objective function values that were better than those of the relocation heuristic when the two methods were constrained to the same amount of computation time. (Contains 4 tables.)

The "p"-median clustering model represents a combinatorial approach to partition data sets into disjoint, nonhierarchical groups. Object classes are constructed around "exemplars", that is, manifest objects in the data set, with the remaining instances assigned to their closest cluster centers. Effective, state-of-the-art implementations of "p"-median clustering are virtually unavailable in the popular social and behavioral science statistical software packages. We present "p"-median clustering, including a detailed description of its mechanics and a discussion of available software programs and their capabilities. Application to a complex structured data set on the perception of food items illustrates "p"-median clustering. (Contains 2 figures and 2 tables.)

A variance-to-range ratio variable weighting procedure is proposed. We show how this weighting method is theoretically grounded in the inherent variability found in data exhibiting cluster structure. In addition, a variable selection procedure is proposed to operate in conjunction with the variable weighting technique. The performances of these procedures are demonstrated in a simulation study, showing favorable results when compared with existing standardization methods. A detailed demonstration of the weighting and selection procedure is provided for the well-known Fisher Iris data and several synthetic data sets. (Contains 6 figures, 9 tables, and 3 footnotes.)

Using the cluster generation procedure proposed by D. Steinley and R. Henson (2005), the author investigated the performance of K-means clustering under the following scenarios: (a) different probabilities of cluster overlap; (b) different types of cluster overlap; (c) varying samples sizes, clusters, and dimensions; (d) different multivariate distributions of clusters; and (e) various multidimensional data structures. The results are evaluated in terms of the Hubert-Arabie adjusted Rand index, and several observations concerning the performance of K-means clustering are made. Finally, the article concludes with the proposal of a diagnostic technique indicating when the partitioning given by a K-means cluster analysis can be trusted. By combining the information from several observable characteristics of the data (number of clusters, number of variables, sample size, etc.) with the prevalence of unique local optima in several thousand implementations of the K-means algorithm, the author provides a method capable of guiding key data-analysis decisions.

This reply addresses the commentary by Epskamp et al. (in press) on our prior work, of using fixed marginals for sampling the data for testing hypothesis in psychometric network application. Mathematical results are presented for expected column (e.g., item prevalence) and row (e.g., subject severity) probabilities under three classical sampling schemes in categorical data analysis: (i) fixing the density, (ii) fixing either the row or column marginal, or (iii) fixing both the row and column marginal. It is argued that, while a unidimensional structure may not be the model we want, it is the structure we are confronted with given the binary nature of the data. Interpreting network models in the context of this artifactual structure is necessary, with preferred solutions to be expanding the item sets of disorders and moving away from the use of binary data and their associated constraints. [ABSTRACT FROM AUTHOR]

We present a procedure (RAUS) for residual analysis of a dissimilarity matrix whereby unidimensional scaling is successively applied to the absolute value of residuals. A key advantage of RAUS is that the efficient Defays formulation of unidimensional scaling can be used for the fitting of each scale. An example using U.S. Supreme Court voting data is provided to illustrate the interpretation of successive scales. A simulation study was performed to evaluate RAUS. [ABSTRACT FROM AUTHOR]

The emergence of Gaussian model-based partitioning as a viable alternative to K-means clustering fosters a need for discrete optimization methods that can be efficiently implemented using model-based criteria. A variety of alternative partitioning criteria have been proposed for more general data conditions that permit elliptical clusters, different spatial orientations for the clusters, and unequal cluster sizes. Unfortunately, many of these partitioning criteria are computationally demanding, which makes the multiple-restart (multistart) approach commonly used for K-means partitioning less effective as a heuristic solution strategy. As an alternative, we propose an approach based on iterated local search (ILS), which has proved effective in previous combinatorial data analysis contexts. We compared multistart, ILS and hybrid multistart-ILS procedures for minimizing a very general model-based criterion that assumes no restrictions on cluster size or within-group covariance structure. This comparison, which used 23 data sets from the classification literature, revealed that the ILS and hybrid heuristics generally provided better criterion function values than the multistart approach when all three methods were constrained to the same 10-min time limit. In many instances, these differences in criterion function values reflected profound differences in the partitions obtained. [ABSTRACT FROM AUTHOR]

Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to "right-size" the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting, overly parsimonious models to more complex, better-fitting alternatives and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically underidentified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A 3-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation-covariation patterns. The orthogonal free curve slope intercept (FCSI) growth model is considered a general model that includes, as special cases, many models, including the factor mean (FM) model (McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, hierarchical linear models (HLMs), repeatedmeasures multivariate analysis of variance (MANOVA), and the linear slope intercept (linearSI) growth model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparing several candidate parametric growth and chronometric models in a Monte Carlo study. [ABSTRACT FROM AUTHOR]

As network data gains popularity for research in various fields, the need for methods to predict future links or find missing links in the data increases. One subset of the methodology used to solve this problem involves creating a similarity measure between each pair of nodes in the network; unfortunately, these methods can be shown to have arbitrary cutoffs and poor performance. To address these shortcomings, we use the adjusted Rand index to create a similarity measure between nodes that has a natural threshold of zero. The effectiveness of this method is then compared to a number of other similarity measures and assessed on a variety of simulated data sets with block model structure and three real network data sets. Under this particular formulation of the adjusted Rand index, information is also provided on dissimilarity. As such, we then go on to test its use for detecting incorrect links in network data, highlighting the dual use of the approach. [ABSTRACT FROM AUTHOR]

To date, most methods for direct blockmodeling of social network data have focused on the optimization of a single objective function. However, there are a variety of social network applications where it is advantageous to consider two or more objectives simultaneously. These applications can broadly be placed into two categories: (1) simultaneous optimization of multiple criteria for fitting a blockmodel based on a single network matrix and (2) simultaneous optimization of multiple criteria for fitting a blockmodel based on two or more network matrices, where the matrices being fit can take the form of multiple indicators for an underlying relationship, or multiple matrices for a set of objects measured at two or more different points in time. A multiobjective tabu search procedure is proposed for estimating the set of Pareto efficient blockmodels. This procedure is used in three examples that demonstrate possible applications of the multiobjective blockmodeling paradigm. [ABSTRACT FROM AUTHOR]

Objective: How to best classify concerns related to eating, weight, and shape (CREWS) in men remains an open question. Research on men considering CREWS during different developmental periods could be particularly informative. Method: Focusing on one potentially dynamic developmental period, this study charts the course of CREWS in men over the college years. Latent class/latent transition analysis identified typologies of weight- and shape-influenced self judgment, limiting attempts, fasting, overeating, binge eating, self-induced vomiting, and laxative or diuretic abuse for 1,025 men over the four traditional college years. Results: Three classes emerged: (1) no obvious pathological eating-related concerns (61-65%); (2) a high likelihood of limiting attempts and a moderately high likelihood of overeating (31-34%); (3) pervasive bulimic-like concerns (4-6%). Class membership was highly stable across assessment occasions. Discussion: The results contribute to the growing literature on empirically derived classifications of CREWS and indicate that for many men CREWS are a chronic presence during the college years. © 2011 by Wiley Periodicals, Inc. (Int J Eat Disord 2012; 45:768-775) [ABSTRACT FROM AUTHOR]

Understanding social phenomena with the help of mathematical models requires a coherent combination of theory, models, and data together with using valid data analytic methods. The study of social networks through the use of mathematical models is no exception. The intuitions of structural balance were formalized and led to a pair of remarkable theorems giving the nature of partition structures for balanced signed networks. Algorithms for partitioning signed networks, informed by these formal results, were developed and applied empirically. More recently, ‘‘structural balance’’ was generalized to ‘‘relaxed structural balance,’’ and a modified partitioning algorithm was proposed. Given the critical interplay of theory, models, and data, it is important that methods for the partitioning of signed networks in terms of relaxed structural balance model are appropriate. The authors consider two algorithms for establishing partitions of signed networks in terms of relaxed structural balance. One is an older heuristic relocation algorithm, and the other is a new exact solution procedure. The former can be used both inductively and deductively. When used deductively, this requires some prespecification incorporating substantive insights. The new branch-and-bound algorithm is used inductively and requires no prespecification of an image matrix in terms of ideal blocks. Both procedures are demonstrated using several examples from the literature, and their contributions are discussed. Together, the two algorithms provide a sound foundation for partitioning signed networks and yield optimal partitions. Issues of network size and density are considered in terms of their consequences for algorithm performance. [ABSTRACT FROM PUBLISHER]

A variance-to-range ratio variable weighting procedure is proposed. We show how this weighting method is theoretically grounded in the inherent variability found in data exhibiting cluster structure. In addition, a variable selection procedure is proposed to operate in conjunction with the variable weighting technique. The performances of these procedures are demonstrated in a simulation study, showing favorable results when compared with existing standardization methods. A detailed demonstration of the weighting and selection procedure is provided for the well-known Fisher Iris data and several synthetic data sets. [ABSTRACT FROM AUTHOR]

Clusterwise linear regression is a multivariate statistical procedure that attempts to cluster objects with the objective of minimizing the sum of the error sums of squares for the within-cluster regression models. In this article, we show that the minimization of this criterion makes no effort to distinguish the error explained by the within-cluster regression models from the error explained by the clustering process. In some cases, most of the variation in the response variable is explained by clustering the objects, with little additional benefit provided by the within-cluster regression models. Accordingly, there is tremendous potential for overfitting with clusterwise regression, which is demonstrated with numerical examples and simulation experiments. To guard against the misuse of clusterwise regression, we recommend a benchmarking procedure that compares the results for the observed empirical data with those obtained across a set of random permutations of the response measures. We also demonstrate the potential for overfitting via an empirical application related to the prediction of reflective judgment using high school and college performance measures. [ABSTRACT FROM AUTHOR]

Using the cluster generation procedure proposed by D. Steinley and R. Henson (2005), the author investigated the performance of K-means clustering under the following scenarios: (a) different probabilities of cluster overlap; (b) different types of cluster overlap; (c) varying samples sizes, clusters, and dimensions; (d) different multivariate distributions of clusters; and (e) various multidimensional data structures. The results are evaluated in terms of the Hubert--Arabie adjusted Rand index, and several observations concerning the performance of K-means clustering are made. Finally, the article concludes with the proposal of a diagnostic technique indicating when the partitioning given by a K-means cluster analysis can be trusted. By combining the information from several observable characteristics of the data (number of clusters, number of variables, sample size, etc.) with the prevalence of unique local optima in several thousand implementations of the K-means algorithm, the author provides a method capable of guiding key data-analysis decisions. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including K-means clustering, effect of model misspecification on determining the number of classes in growth mixture modeling and clustering functional data.