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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]

To achieve scientific progress in terms of building a cumulative body of knowledge, careful attention to benchmarking is of the utmost importance, requiring that proposals of new methods are extensively and carefully compared with their best predecessors, and existing methods subjected to neutral comparison studies. Answers to benchmarking questions should be evidence‐based, with the relevant evidence being collected through well‐thought‐out procedures, in reproducible and replicable ways. In the present paper, we review good research practices in benchmarking from the perspective of the area of cluster analysis. Discussion is given to the theoretical, conceptual underpinnings of benchmarking based on simulated and empirical data in this context. Subsequently, the practicalities of how to address benchmarking questions in clustering are dealt with, and foundational recommendations are made based on existing literature. This article is categorized under:Fundamental Concepts of Data and Knowledge > Data ConceptsFundamental Concepts of Data and Knowledge > Key Design Issues in Data MiningTechnologies > Structure Discovery and Clustering [ABSTRACT FROM AUTHOR]

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This can lead to the overextraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study are (1) to explore the performance of the Bayesian information criterion, sample-adjusted BIC, and bootstrap likelihood ratio test in growth mixture modeling analysis with nonnormal distributed outcome variables and (2) to examine the effects of nonnormal time invariant covariates in the estimation of the number of latent classes when outcome variables are normally distributed. For both of these goals, we will include nonnormal conditions not considered previously in the literature. Two simulation studies were conducted. Results show that spurious classes may be selected and optimal solutions obtained in the data analysis when the population departs from normality even when the nonnormality is only present in time invariant covariates.

The modularity index (Q) is an important criterion for many community detection heuristics used in network psychometrics and its subareas (e.g., exploratory graph analysis). Some heuristics seek to directly maximize Q, whereas others, such as the walktrap algorithm, only use the modularity index post hoc to determine the number of communities. Researchers in network psychometrics have typically not employed methods that are guaranteed to find a partition that maximizes Q, perhaps because of the complexity of the underlying mathematical programming problem. In this paper, for networks of the size commonly encountered in network psychometrics, we explore the utility of finding the partition that maximizes Q via formulation and solution of a clique partitioning problem (CPP). A key benefit of the CPP is that the number of communities is naturally determined by its solution and, therefore, need not be prespecified in advance. The results of two simulation studies comparing maximization of Q to two other methods that seek to maximize modularity (fast greedy and Louvain), as well as one popular method that does not (walktrap algorithm), provide interesting insights as to the relative performances of the methods with respect to identification of the correct number of communities and the recovery of underlying community structure. [ABSTRACT FROM AUTHOR]

The Ising model has received significant attention in network psychometrics during the past decade. A popular estimation procedure is IsingFit, which uses nodewise l1-regularized logistic regression along with the extended Bayesian information criterion to establish the edge weights for the network. In this paper, we report the results of a simulation study comparing IsingFit to two alternative approaches: (1) a nonregularized nodewise stepwise logistic regression method, and (2) a recently proposed global l1-regularized logistic regression method that estimates all edge weights in a single stage, thus circumventing the need for nodewise estimation. MATLAB scripts for the methods are provided as supplemental material. The global l1-regularized logistic regression method generally provided greater accuracy and sensitivity than IsingFit, at the expense of lower specificity and much greater computation time. The stepwise approach showed considerable promise. Relative to the l1-regularized approaches, the stepwise method provided better average specificity for all experimental conditions, as well as comparable accuracy and sensitivity at the largest sample size. [ABSTRACT FROM AUTHOR]

A measure of "clusterability" serves as the basis of a new methodology designed to preserve cluster structure in a reduced dimensional space. Similar to principal component analysis, which finds the direction of maximal variance in multivariate space, principal cluster axes find the direction of maximum clusterability in multivariate space. Furthermore, the principal clustering approach falls into the class of projection pursuit techniques. Comparisons are made with existing methodologies both in a simulation study and analysis of real-world data sets. Furthermore, a demonstration of how to interpret the results of the principal cluster axes is provided on the analysis of Supreme Court voting data and similarities between the interpretation of competing procedures (e.g., factor analysis and principal component analysis) are provided. In addition to the Supreme Court analysis, we analyze several data sets often used to test cluster analysis procedures, including Fisher's Iris data, Agresti's Crab data, and a data set on glass fragments. Finally, discussion is provided to help determine when the proposed procedure will be the most beneficial to the researcher. (Contains 5 footnotes, 5 tables, and 8 figures.)