Improving the Walktrap Algorithm Using K-Means Clustering.

The walktrap algorithm is one of the most popular community-detection methods in psychological research. Several simulation studies have shown that it is often effective at determining the correct number of communities and assigning items to their proper community. Nevertheless, it is important to recognize that the walktrap algorithm relies on hierarchical clustering because it was originally developed for networks much larger than those encountered in psychological research. In this paper, we present and demonstrate a computational alternative to the hierarchical algorithm that is conceptually easier to understand. More importantly, we show that better solutions to the sum-of-squares optimization problem that is heuristically tackled by hierarchical clustering in the walktrap algorithm can often be obtained using exact or approximate methods for K-means clustering. Three simulation studies and analyses of empirical networks were completed to assess the impact of better sum-of-squares solutions.

Predictors of symptom course in alcohol use disorder.

BACKGROUND: Symptoms often play an important role in the scientific inquiry of psychological disorders and have been theorized to play a functional role in the disorders themselves. However, little is known about the course of specific symptoms and individual differences in course. Understanding the course of specific symptoms and factors influencing symptom course can inform psychological theory and future research on course and treatment. METHODS: The current study examined alcohol use disorder (AUD) criteria to explore how etiologically relevant covariates differentially affected the course of individual criteria. The study examined 34,653 participants from Wave 1 (2001-2002) and Wave 2 (2003-2004) of the National Epidemiological Survey on Alcohol and Related Conditions (NESARC), to analyze the extent to which AUD symptom course is predicted by alcohol consumption patterns, family history of alcoholism, the presence of internalizing and externalizing disorders, and race. RESULTS: The course of all AUD criteria was significantly influenced by these predictors, with the magnitude of the influence varying across different criteria and different aspects of the course (i.e., onset, persistence, recurrence). The strength of the relationship is partially related to the theoretical proximity of a given covariate to AUD symptomatology, with heavy drinking being the strongest and family history of AUD being the weakest. The course of all criteria was strongly associated with the prevalence of the criterion in the overall sample. CONCLUSIONS: The course of AUD criteria is heterogeneous, appearing to be influenced by conceptually proximal predictors, the prevalence of the criterion, and perhaps an underlying common factor. Diagnostic accuracy may be improved by including a criterion related to alcohol consumption. Future work should include exploring the interchangeability of criteria and alternative operationalization of them.

A comparison of logistic regression methods for Ising model estimation.

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.

On maximization of the modularity index in network psychometrics.

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.

A brief young adult alcohol problems screening test: Short form development using combinatorics.

Objective: To develop a shortened form of the Young Adult Alcohol Problems Screening Test1 (YAAPST; original length = 27 items) using a novel combinatorial approach. Participants: 489 college freshmen, half of whom were above average risk for alcohol use disorder based upon family history, attending a large, Midwestern University followed prospectively for 16-17 years across 7 measurement occasions (waves). Methods: Using an exhaustive combinatorial approach, we evaluated all possible combinations of questions and questionnaire length. Each candidate short-form was evaluated using part-whole correlations, alpha coefficients, and polyserial correlations with DSM-III criteria. Results: The 12-item scale, the Brief-YAAPST, was chosen as the best candidate short-form as this scale had the fewest items while maintaining strong reliability and validity. Conclusions: Complete enumeration optimization effectively produced a 12-item short form with minimal loss of reliability and validity making the Brief-YAAPST a desirable assessment alternative when there are concerns about participant or client burden.

A comparison of spectral clustering and the walktrap algorithm for community detection in network psychometrics.

Spectral clustering is a well-known method for clustering the vertices of an undirected network. Although its use in network psychometrics has been limited, spectral clustering has a close relationship to the commonly used walktrap algorithm. In this article, we report results from simulation experiments designed to evaluate the ability of spectral clustering and the walktrap algorithm to recover underlying cluster (or community) structure in networks. The salient findings include: (a) the recovery performance of the walktrap algorithm can be improved by using K-means clustering instead of hierarchical clustering; (b) K-means and K-median clustering led to comparable recovery performance when used to cluster vertices based on the eigenvectors of Laplacian matrices in spectral clustering; (c) spectral clustering using the unnormalized Laplacian matrix generally yielded inferior cluster recovery in comparison to the other methods; (d) when the correct number of clusters was provided for the methods, spectral clustering using the normalized Laplacian matrix led to better recovery than the walktrap algorithm; and (e) when the correct number of clusters was not provided, the walktrap algorithm using the Qw modularity index was better than spectral clustering using the eigengap heuristic at determining the appropriate number of clusters. Overall, both the walktrap algorithm and spectral clustering of the normalized Laplacian matrix are effective for partitioning the vertices of undirected networks, with the latter performing better in most instances. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

A modified approach to fitting relative importance networks.

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. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Cross-sectional and longitudinal AUD symptom networks: They tell different stories.

Modern theoretical models of Alcohol Use Disorder (AUD) highlight the different functional roles played by various mechanisms associated with different symptoms. Symptom network models (SNMs) offer one approach to modeling AUD symptomatology in a way that could reflect these processes and provide important information on the progression and persistence of disorder. However, much of the research conducted using SNMs relies on cross-sectional data, which has raised questions regarding the extent they reflect dynamic processes. The current study aimed to (a) examine symptom networks of AUD and (b) compare the extent to which cross-sectional network models had similar structures and interpretations as longitudinal network models. 17,360 participants from Wave 1 (2001-2002) and Wave 2 (2003-2004) of the National Epidemiological Survey on Alcohol and Related Conditions (NESARC) were used to model cross-sectional and longitudinal AUD symptom networks. The cross-sectional analyses demonstrate high replicability across waves and central symptoms consistent with other cross-sectional studies on addiction networks. The longitudinal network shared much less similarity than the cross-sectional networks and had a substantially different structure. Given the increasing attention given to the network perspective in psychopathology research, the results of this study raise concerns about interpreting cross-sectional symptom networks as representative of temporal changes occurring within a psychological disorder. We conclude that the psychological symptom network literature should be bolstered with additional research on longitudinal network models.

Disentangling relationships in symptom networks using matrix permutation methods.

Common outputs of software programs for network estimation include association matrices containing the edge weights between pairs of symptoms and a plot of the symptom network. Although such outputs are useful, it is sometimes difficult to ascertain structural relationships among symptoms from these types of output alone. We propose that matrix permutation provides a simple, yet effective, approach for clarifying the order relationships among the symptoms based on the edge weights of the network. For directed symptom networks, we use a permutation criterion that has classic applications in electrical circuit theory and economics. This criterion can be used to place symptoms that strongly predict other symptoms at the beginning of the ordering, and symptoms that are strongly predicted by other symptoms at the end. For undirected symptom networks, we recommend a permutation criterion that is based on location theory in the field of operations research. When using this criterion, symptoms with many strong ties tend to be placed centrally in the ordering, whereas weakly-tied symptoms are placed at the ends. The permutation optimization problems are solved using dynamic programming. We also make use of branch-search algorithms for extracting maximum cardinality subsets of symptoms that have perfect structure with respect to a selected criterion. Software for implementing the dynamic programming algorithms is available in MATLAB and R. Two networks from the literature are used to demonstrate the matrix permutation algorithms.

Does crude measurement contribute to observed unidimensionality of psychological constructs? A demonstration with DSM-5 alcohol use disorder.

Mental disorders are complex, multifaceted phenomena that are associated with profound heterogeneity and comorbidity. Despite the heterogeneity of mental disorders, most are generally considered unitary dimensions. We argue that certain measurement practices, especially using too few indicators per construct, preclude the detection of meaningful multidimensionality. We demonstrate the implications of crude measurement for detecting construct multidimensionality with alcohol use disorder (AUD). To do so, we used a large sample of college heavy drinkers (N = 909) for whom AUD symptomology was thoroughly assessed (87 items) and a blend of confirmatory factor analysis, exploratory factor analysis, and hierarchical clustering. A unidimensional AUD model with one item per symptom criterion fit the data well, whereas a unidimensional model with all items fit the data poorly. Starting with an 11-item AUD model, model fit decreased and the variability in factor loadings increased as additional items were added to the model. Additionally, multidimensional models outperformed unidimensional ones in terms of variance explained in theoretically relevant external criteria. All told, we converged on a hierarchically organized model of AUD with three broad, transcriterial dimensions that reflected tolerance, withdrawal, and loss of control. In addition to introducing a hierarchical model of AUD, we propose that thorough assessment of psychological constructs paired with serious consideration of alternative, multidimensional structures can move past the deadlock of their unidimensional representations. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

On Fixed Marginal Distributions and Psychometric Network Models.

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.

Recent Advances in (Graphical) Network Models.

Recently, (as measured by advances in quantitative methodology) Borsboom (2008) has proposed network analysis as an alternative to the latent variable model as a method for understanding the potentially complex relationships among a system of variables. Over the past five to eight years, there has been a veritable explosion in methodology and its application in social, behavioral, and health sciences (citation). This current issue contains nine articles and three commentaries on new methodology, critiques, and the evaluation of current techniques surrounding psychometric network models. In this introduction, I provide a brief overview of these papers and some suggestions on potential ways in which to move the field forward.

A comparison of 71 binary similarity coefficients: The effect of base rates.

There are many psychological applications that require collapsing the information in a two-mode (e.g., respondents-by-attributes) binary matrix into a one-mode (e.g., attributes-by-attributes) similarity matrix. This process requires the selection of a measure of similarity between binary attributes. A vast number of binary similarity coefficients have been proposed in fields such as biology, geology, and ecology. Although previous studies have reported cluster analyses of binary similarity coefficients, there has been little exploration of how cluster memberships are affected by the base rates (percentage of ones) for the binary attributes. We conducted a simulation experiment that compared two-cluster K-median partitions of 71 binary similarity coefficients based on their pairwise correlations obtained under 15 different base-rate configurations. The results reveal that some subsets of coefficients consistently group together regardless of the base rates. However, there are other subsets of coefficients that group together for some base rates, but not for others.

Deterministic blockmodelling of signed and two-mode networks: A tutorial with software and psychological examples.

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.

Combinatorial Optimization of Clustering Decisions: An Approach to Refine Psychiatric Diagnoses.

Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the "diagnosis" group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the "diagnosis" to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.

Using Complete Enumeration to Derive "One-Size-Fits-All" Versus "Subgroup-Specific" Diagnostic Rules for Substance Use Disorder.

The use of fixed diagnostic rules, whereby the same diagnostic algorithms are applied across all individuals regardless of personal attributes, has been the tradition in the Diagnostic and Statistical Manual of Mental Disorders. This practice of "averaging" across individuals inevitably introduces diagnostic error. Furthermore, these average rules are typically derived through expert consensus rather than through data-driven approaches. Utilizing National Survey on Drug Use and Health 2013 (N = 23, 889), we examined whether subgroup-specific, "customized" alcohol use disorder diagnostic rules, derived using deterministic optimization, perform better than an average, "one-size-fits-all" diagnostic rule. The average solution for the full sample included a set size of six and diagnostic threshold of three. Subgroups had widely varying set sizes (M = 6.870; range = 5-10) with less varying thresholds (M = 2.70; range = 2-4). External validation verified that the customized algorithms performed as well, and sometimes better than, the average solution in the prediction of relevant correlates. However, the average solution still performed adequately with respect to external validators.

Item Responses in Quantity-Frequency Questionnaires: Implications for Data Generalizability.

Alcohol consumption is an important predictor of a variety of negative outcomes. There is an extensive literature that examines the differences in the estimated level of alcohol consumption between types of assessments (e.g., quantity-frequency [QF] questionnaires, daily diaries). However, it is typically assumed that all QF-based measures are nearly identical in their assessment of the volume of alcohol consumption in a population. Using timeline follow-back data and constructing common QF consumption measures, we examined differences among survey instruments to assess alcohol consumption and heavy drinking. Using three data sets, including clinical to community samples, we demonstrate how scale-specific item characteristics (i.e., number of response options and ranges of consumption assessed by each option) can substantially affect the estimated mean level of consumption and estimated prevalence of binge drinking. Our analyses suggest that problems can be mitigated by employing more resolved measures of quantity and frequency in consumption questionnaires.

Modeling Heterogeneous Peer Assortment Effects Using Finite Mixture Exponential Random Graph Models.

This article develops a class of models called sender/receiver finite mixture exponential random graph models (SRFM-ERGMs). This class of models extends the existing exponential random graph modeling framework to allow analysts to model unobserved heterogeneity in the effects of nodal covariates and network features without a block structure. An empirical example regarding substance use among adolescents is presented. Simulations across a variety of conditions are used to evaluate the performance of this technique. We conclude that unobserved heterogeneity in effects of nodal covariates can be a major cause of misfit in network models, and the SRFM-ERGM approach can alleviate this misfit. Implications for the analysis of social networks in psychological science are discussed.

Combining diversity and dispersion criteria for anticlustering: A bicriterion approach.

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.