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.
The Variance of the Adjusted Rand Index Steinley, Douglas; Brusco, Michael J; Hubert, Lawrence
Psychological methods,
06/2016, Letnik:
21, Številka:
2
Journal Article
Recenzirano
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.
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.
Mixture modeling is a popular technique for identifying unobserved subpopulations (e.g., components) within a data set, with Gaussian (normal) mixture modeling being the form most widely used. ...Generally, the parameters of these Gaussian mixtures cannot be estimated in closed form, so estimates are typically obtained via an iterative process. The most common estimation procedure is maximum likelihood via the expectation-maximization (EM) algorithm. Like many approaches for identifying subpopulations, finite mixture modeling can suffer from locally optimal solutions, and the final parameter estimates are dependent on the initial starting values of the EM algorithm. Initial values have been shown to significantly impact the quality of the solution, and researchers have proposed several approaches for selecting the set of starting values. Five techniques for obtaining starting values that are implemented in popular software packages are compared. Their performances are assessed in terms of the following four measures: (1) the ability to find the best observed solution, (2) settling on a solution that classifies observations correctly, (3) the number of local solutions found by each technique, and (4) the speed at which the start values are obtained. On the basis of these results, a set of recommendations is provided to the user.
Variable selection is a venerable problem in multivariate statistics. Simulated annealing is one of a variety of metaheuristics that can be gainfully employed for variable selection; however, its ...effectiveness is influenced by algorithm design features such as the construction of the initial subset, the maximum and minimum temperatures, the cooling scheme, and the process for generating trial subsets in the neighborhood of the incumbent subset. These design features were manipulated to produce 24 versions of a simulated annealing algorithm for the problem of selecting exactly p out of m candidate variables. The versions were then compared within the contexts of principal component analysis and discriminant analysis. The results suggest some complex and interesting interactions among the design features, yet some robust versions across the two studies were established.
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.
•Allocation of a cross-trained workforce is posed as a multiobjective optimization problem.•Variance-to-range normalization of the objective function is recommended.•Four partitioning approaches for ...Pareto set reduction (PSR) are compared.•p-median partitioning has several advantages as a method for PSR.•Maximum split partitioning can effectively augment p-median partitioning for PSR.
The Pareto (or nondominated set) for a multiobjective optimization problem is often of nontrivial size, and the decision maker may have a difficult time establishing objective criterion weights to select a solution. In light of these issues, clustering or partitioning methods can be of considerable value for pruning the Pareto set and limiting the decision to a few choice exemplars. A three-stage approach is proposed. In stage one, a variance-to-range measure is used to normalize the criterion function values. In stage two, maximum split partitioning and p-median partitioning are each applied to the normalized measures, thus producing two partitions of the Pareto set and two sets of exemplars. Finally, in stage three, the union of the exemplars obtained by the two partitioning methods is accepted as the final set of exemplars. The partitioning methods are compared within the context of multiobjective allocation of a cross-trained workforce to achieve both operational and human resource objectives.
The Ising model has received significant attention in network psychometrics during the past decade. A popular estimation procedure is IsingFit, which uses nodewise
l
1
-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
l
1
-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
l
1
-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
l
1
-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.
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.
Translational Abstract
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.
Purpose
The purpose of this paper is twofold. First, the authors provide a survey of operations management (OM) research applications of traditional hierarchical and nonhierarchical clustering ...methods with respect to key decisions that are central to a valid analysis. Second, the authors offer recommendations for practice with respect to these decisions.
Design/methodology/approach
A coding study was conducted for 97 cluster analyses reported in six OM journals during the period spanning 1994-2015. Data were collected with respect to: variable selection, variable standardization, method, selection of the number of clusters, consistency/stability of the clustering solution, and profiling of the clusters based on exogenous variables. Recommended practices for validation of clustering solutions are provided within the context of this framework.
Findings
There is considerable variability across clustering applications with respect to the components of validation, as well as a mix of productive and undesirable practices. This justifies the importance of the authors’ provision of a schema for conducting a cluster analysis.
Research limitations/implications
Certain aspects of the coding study required some degree of subjectivity with respect to interpretation or classification. However, in light of the sheer magnitude of the coding study (97 articles), the authors are confident that an accurate picture of empirical OM clustering applications has been presented.
Practical implications
The paper provides a critique and synthesis of the practice of cluster analysis in OM research. The coding study provides a thorough foundation for how the key decisions of a cluster analysis have been previously handled in the literature. Both researchers and practitioners are provided with guidelines for performing a valid cluster analysis.
Originality/value
To the best of the authors’ knowledge, no study of this type has been reported in the OM literature. The authors’ recommendations for cluster validation draw from recent studies in other disciplines that are apt to be unfamiliar to many OM researchers.
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