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Most researchers have estimated the edge weights for relative importance networks using a well-established measure of general dominance for multiple regression. This approach has several desirable properties including edge weights that represent R2 contributions, in-degree centralities that correspond to R2 for each item when using other items as predictors, and strong replicability. We endorse the continued use of relative importance networks and believe they have a valuable role in network psychometrics. However, to improve their utility, we introduce a modified approach that uses best-subsets regression as a preceding step to select an appropriate subset of predictors for each item. The benefits of this modification include: (a) computation time savings that can enable larger relative importance networks to be estimated, (b) a principled approach to edge selection that can significantly improve specificity, (c) the provision of a signed network if desired, (d) the potential use of the best-subsets regression approach for estimating Gaussian graphical models, and (e) possible generalization to best-subsets logistic regression for Ising models. We describe, evaluate, and demonstrate the proposed approach and discuss its strengths and limitations. The standard approach for fitting a relative importance network is to take each node of the network in turn as the dependent variable and run an all-possible-subsets regression using all of the other nodes as independent variables. With this approach, nodes are included as variables in the regression models even if they have little or no explanatory value. We propose a modification of the standard approach whereby best-subsets regression is used to select subsets of independent variables prior to running the all-possible-subsets regressions that estimate the relative importance network. The results of a simulation study showed that this modified approach leads to better recovery of the population-model relative importance network structure. The practical value of the modified approach is that a more parsimonious and interpretable network is obtained [ABSTRACT FROM AUTHOR]

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple clusters, the procedure is extended to determine the number of clusters. Through a series of simulations, the proposed methodology is shown to outperform several other commonly used procedures for determining both the presence of clusters and their number. (Contains 3 figures, 4 tables and 5 footnotes.)

McLachlan (2011) and Vermunt (2011) each provided thoughtful replies to our original article (Steinley & Brusco, 2011). This response serves to incorporate some of their comments while simultaneously clarifying our position. We argue that greater caution against overparamaterization must be taken when assuming that clusters are highly elliptical in nature. Specifically, users of mixture model clustering techniques should be wary of overreliance on fit indices, and the importance of cross-validation is highlighted. Additionally, we note that "K"-means clustering is part of a larger family of discrete partitioning algorithms, many of which are designed to solve problems identical to those for which mixture modeling approaches are often touted. (Contains 3 footnotes.)

This article provides a large-scale investigation into several of the properties of mixture-model clustering techniques (also referred to as latent class cluster analysis, latent profile analysis, model-based clustering, probabilistic clustering, Bayesian classification, unsupervised learning, and finite mixture models; see Vermunt & Magdison, 2002). Focus is given to the multivariate normal distribution, and 9 separate decompositions (i.e., class structures) of the covariance matrix are investigated. To provide a link to the current literature, comparisons are made with K-means clustering in 3 detailed Monte Carlo studies. The findings have implications for applied researchers in that mixture-model clustering techniques performed best when the covariance structure and number of clusters were known. However, as the information about the shape and number of clusters became unknown, degraded performance was observed for both K-means clustering and mixture-model clustering. (Contains 5 figures, 5 tables and 8 footnotes.)

Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into "K" clusters. This "K"-balance partitioning problem also has more general psychological applications associated with the analysis of similarity/dissimilarity relationships among stimuli. Accordingly, "K"-balance partitioning can be gainfully used in a wide variety of SBT applications, such as attraction and child development, evaluation of group membership, marketing and consumer issues, and other psychological contexts not necessarily related to SBT. We present a branch-and-bound algorithm for the "K"-balance partitioning problem. This new algorithm is applied to 2 synthetic numerical examples as well as to several real-world data sets from the behavioral sciences literature. (Contains 6 tables and 4 figures.)

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.)

The study of confusion data is a well established practice in psychology. Although many types of analytical approaches for confusion data are available, among the most common methods are the extraction of 1 or more subsets of stimuli, the partitioning of the complete stimulus set into distinct groups, and the ordering of the stimulus set. Although standard commercial software packages can sometimes facilitate these types of analyses, they are not guaranteed to produce optimal solutions. The authors present a MATLAB *.m file for preprocessing confusion matrices, which includes fitting of the similarity-choice model. Two additional MATLAB programs are available for optimally clustering stimuli on the basis of confusion data. The authors also developed programs for optimally ordering stimuli and extracting subsets of stimuli using information from confusion matrices. Together, these programs provide several pragmatic alternatives for the applied researcher when analyzing confusion data. Although the programs are described within the context of confusion data, they are also amenable to other types of proximity data.

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 article provides an investigation of cluster validation indices that relates 4 of the indices to the L. Hubert and P. Arable (1985) adjusted Rand index--the cluster validation measure of choice (G. W. Milligan & M. C. Cooper, 1986). It is shown how these other indices can be "roughly" transformed into the same scale as the adjusted Rand index. Furthermore, in-depth explanations are given of why classification rates should not be used in cluster validation research. The article concludes by summarizing several properties of the adjusted Rand index across many conditions and provides a method for testing the significance of observed adjusted Rand indices.