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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]

During the past 5 to 10 years, an estimation method known as eLasso has been used extensively to produce symptom networks (or, more precisely, symptom dependence graphs) from binary data in psychopathological research. The eLasso method is based on a particular type of Ising model that corresponds to binary pairwise Markov random fields, and its popularity is due, in part, to an efficient estimation process that is based on a series of l1-regularized logistic regressions. In this article, we offer an unprecedented critique of the Ising model and eLasso. We provide a careful assessment of the conditions that underlie the Ising model as well as specific limitations associated with the eLasso estimation algorithm. This assessment leads to serious concerns regarding the implementation of eLasso in psychopathological research. Some potential strategies for eliminating or, at least, mitigating these concerns include (a) the use of partitioning or mixture modeling to account for unobserved heterogeneity in the sample of respondents, and (b) the use of co-occurrence measures for symptom similarity to either replace or supplement the covariance/correlation measure associated with eLasso. Two psychopathological data sets are used to highlight the concerns that are raised in the critique. We present the first principled critique of the Ising model and the associated eLasso method. The Ising model is a form of a pairwise Markov random field that is used to model binary data. The current approach utilizes a set of logistic regressions to obtain parameter estimates, with the final model being chosen with the so-called eLasso method to mitigate against overfitting. Throughout, we highlight why application of this model to data with traits that are commonly found in psychopathological data may be problematic due to issues such as sample size, density, asymmetric parameter weights, and so on. Specifically, the necessary sample size for fitting these models is dependent on the density (e.g., the number of connections) of the network, with a strong preference being given to networks that are not dense. Unfortunately, several (if not the vast majority of) psychopathology disorders have been conceptualized as cohesive traits, and as such, methods used to measure them assume that all of the items arise from a common factor. This standard assumption leads to items that are highly intercorrelated, resulting in networks that are dense—exactly the situation that is not desired for the predominant estimation techniques of the Ising model. In turn, we recommend a partitioning approach that may help address some of these issues. Beyond this issue, we assess the appropriateness of averaging parameter asymmetric parameter estimates to achieve symmetric parameter estimates—a practice that could result in the loss of information. Finally, we show that it is likely that much of the data analyzed with these methods do not arise from the same homogeneous population; as such, we introduce a partitioning method to aid in determining if several "subnetworks" are being averaged together when they are fit together as one big network, resulting in global findings that are not consistent with any local structures. [ABSTRACT FROM AUTHOR]

The problem of partitioning a collection of objects based on their measurements on a set of dichotomous variables is a well-established problem in psychological research, with applications including clinical diagnosis, educational testing, cognitive categorization, and choice analysis. Latent class analysis and K-means clustering are popular methods for partitioning objects based on dichotomous measures in the psychological literature. The K-median clustering method has recently been touted as a potentially useful tool for psychological data and might be preferable to its close neighbor, K-means, when the variable measures are dichotomous. We conducted simulation-based comparisons of the latent class, K-means, and K-median approaches for partitioning dichotomous data. Although all 3 methods proved capable of recovering cluster structure, K-median clustering yielded the best average performance, followed closely by latent class analysis. We also report results for the 3 methods within the context of an application to transitive reasoning data, in which it was found that the 3 approaches can exhibit profound differences when applied to real data. [ABSTRACT FROM AUTHOR]

Objective: Medical over- and underutilization are central problems that stand in the way of delivering optimal health care. As a result, one important question is how people decide to take action, versus not, when it comes to their health. The present article proposes and validates a new measure that captures the extent to which individuals are "medical maximizers" who are predisposed to seek health care even for minor problems, versus "medical minimizers" who prefer to avoid medical intervention unless it is necessary. Method: Studies 1-3 recruited participants using Amazon's Mechanical Turk. Study 1 conducted exploratory factor analysis (EFA) to identify items relevant to the proposed construct. In Study 2 confirmatory factor analysis (CFA) was conducted on the identified items, as well as tests of internal, discriminant, and convergent validity. Study 3 examined test-retest reliability of the scale. Study 4 validated the scale in a non-Internet sample. Results: EFA identified 10 items consistent with the proposed construct, and subsequent CFA showed that the 10 items were best understood with a bifactor model that assessed a single underlying construct consistent with medical maximizing-minimizing, with 3 of the 10 items cross-loading on another independent factor. The scale was distinct from hypochondriasis, distrust in medicine, health care access, and health status, and predicted self-reported health care utilization and a variety of treatment preferences. Conclusions: Individuals have general preferences to maximize versus minimize their use of health care, and these preferences are predictive of health care utilization and treatment preferences across a range of health care contexts. [ABSTRACT FROM AUTHOR]

For 30 years, the adjusted Rand index has been the preferred method for comparing 2 partitions (e.g., clusterings) of a set of observations. Although the index is widely used, little is known about its variability. Herein, the variance of the adjusted Rand index (Hubert & Arabie, 1985) is provided and its properties are explored. It is shown that a normal approximation is appropriate across a wide range of sample sizes and varying numbers of clusters. Further, it is shown that confidence intervals based on the normal distribution have desirable levels of coverage and accuracy. Finally, the first power analysis evaluating the ability to detect differences between 2, different adjusted Rand indices is provided. [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]

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 outperlbrm several other commonly used procedures for determining both the presence of clusters and their number. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [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]

This article provides an investigation of cluster validation indices that relates 4 of the indices to the L. Hubert and P. Arabie (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. [ABSTRACT FROM AUTHOR]

The popular K-means clustering method, as implemented in 3 commercial software packages (SPSS, SYSTAT, and SAS), generally provides solutions that are only locally optimal for a given set of data. Because none of these commercial implementations offer a reasonable mechanism to begin the K-means method at alternative starting points, separate routines were written within the MATLAB (Math-Works, 1999) environment that can be initialized randomly (these routines are provided at the end of the online version of this article in the PsycARTICLES database). Through the analysis of 2 empirical data sets and 810 simulated data sets, it is shown that the results provided by commercial packages are most likely locally optimal. These results suggest the need for some strategy to study the local optima problem for a specific data set or to identify methods for finding "good" starting values that might lead to the best solutions possible. [ABSTRACT FROM AUTHOR]