Optimal Partitioning of a Data Set Based on the p-Median Model

Although the K-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The p-median model is an especially well-studied clustering problem that requires the selection of p objects to serve as cluster centers. The objective is to choose the cluster centers such that the sum of the Euclidean distances (or some other dissimilarity measure) of objects assigned to each center is minimized. Using 12 data sets from the literature, we demonstrate that a three-stage procedure consisting of a greedy heuristic, Lagrangian relaxation, and a branch-and-bound algorithm can produce globally optimal solutions for p-median problems of nontrivial size (several hundred objects, five or more variables, and up to 10 clusters). We also report the results of an application of the p-median model to an empirical data set from the telecommunications industry.     

A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.     

Dissimilarity cumulation as a procedure correcting for violations of triangle inequality

Dissimilarity on a finite set is a function that assigns to every pair of points (stimuli) a nonnengative number vanishing if and only if the two points are identical. For any two points in a finite set, the minimum of the length of all finite chains connecting these points is a quasimetric (i.e., it satisfies all metric axioms except for symmetry). The computation of the quasimetric from a dissimilarity can be viewed as a data-analytic procedure of “correcting” dissimilarities into (quasi)distances, an alternative to nonmetric Multidimensional Scaling: the procedure simply replaces the dissimilarity between any two points with the shortest length across all chains of points connecting them. It is shown in this paper that this procedure can be equivalently described as a series of recursive corrections for violations of the triangle inequality across all triples of points considered in an arbitrary order.     

Sticking Out Like a Sore Thumb: Employee Dissimilarity and Deviance at Work*

This study examined demographic‐ and personality‐based employee dissimilarities in relation to organizational and interpersonal deviant behaviors. Perceived organizational support (POS), organizational commitment, perceived coworker support, and coworker satisfaction were proposed as mediators. The results revealed that dissimilarities in ethnicity, Agreeableness, and Openness to Experience were significantly related to organizational deviance; dissimilarities in gender, Conscientiousness, and Extraversion were significantly related to interpersonal deviance. In addition, ethnic dissimilarity negatively predicted POS and organizational commitment, age dissimilarity positively predicted perceived coworker support, Extraversion dissimilarity positively predicted coworker satisfaction, Agreeableness dissimilarity negatively predicted POS, and Openness to Experience dissimilarity negatively predicted POS, organizational commitment, perceived coworker support, and coworker satisfaction. Finally, POS partially mediated the relationship between Agreeableness dissimilarity and organizational deviance. Interpretations of results, implications for management, and future research are discussed.     

The force of dissimilar analogies in bioethics

Although analogical reasoning has long been a popular method of reasoning in bioethics, current literature does not sufficiently grasp its variety. We assert that the main shortcoming is the fact that an analogy’s value is often judged on the extent of similarity between the source situation and the target situation, while in (bio)ethics, analogies are often used because of certain dissimilarities rather than in spite of them. We make a clear distinction between dissimilarities that aim to reinforce a similar approach in the source situation and the target situation and dissimilarities that aim to undermine or denounce a similar approach. The former kind of dissimilarity offers the analogy more normative force than if there were no dissimilarities present; this is often overlooked by authors who regard all relevant dissimilarities as detrimental to the analogy’s strength. Another observation is that an evaluation of the normative force of an analogy cannot be made independently of moral principles or theories. Without these, one cannot select which elements in an analogy are morally relevant nor determine how they should be interpreted.     

Comparison of Methods for Collecting and Modeling Dissimilarity Data: Applications to Complex Sound Stimuli

Sorting procedures are frequently adopted as an alternative to dissimilarity ratings to measure the dissimilarity of large sets of stimuli in a comparatively short time. However, systematic empirical research on the consequences of this experiment-design choice is lacking. We carried out a behavioral experiment to assess the extent to which sorting procedures compare to dissimilarity ratings in terms of efficiency, reliability, and accuracy, and the extent to which data from different data-collection methods are redundant and are better fit by different distance models. Participants estimated the dissimilarity of either semantically charged environmental sounds or semantically neutral synthetic sounds. We considered free and hierarchical sorting and derived indications concerning the properties of constrained and truncated hierarchical sorting methods from hierarchical sorting data. Results show that the higher efficiency of sorting methods comes at a considerable cost in terms of data reliability and accuracy. This loss appears to be minimized with truncated hierarchical sorting methods that start from a relatively low number of groups of stimuli. Finally, variations in data-collection method differentially affect the fit of various distance models at the group-average and individual levels. On the basis of these results, we suggest adopting sorting as an alternative to dissimilarity-rating methods only when strictly necessary. We also suggest analyzing the raw behavioral dissimilarities, and avoiding modeling them with one single distance model.     

Surface‐ and deep‐level dissimilarity effects on social integration and individual effectiveness related outcomes in work groups: A meta‐analytic integration

Prior research linking demographic (e.g., age, ethnicity/race, gender, and tenure) and underlying psychological (e.g., personality, attitudes, and values) dissimilarity variables to individual group member's work‐related outcomes produced mixed and contradictory results. To account for these findings, this study develops a contingency framework and tests it using meta‐analytic and structural equation modelling techniques. In line with this framework, results showed different effects of surface‐level (i.e., demographic) dissimilarity and deep‐level (i.e., underlying psychological) dissimilarity on social integration, and ultimately on individual effectiveness related outcomes (i.e., turnover, task, and contextual performance). Specifically, surface‐level dissimilarity had a negative effect on social integration under low but not under high team interdependence. In return, social integration fully mediated the negative relationship between surface‐level dissimilarity and individual effectiveness related outcomes under low interdependence. In contrast, deep‐level dissimilarity had a negative effect on social integration, which was stronger under high and weaker under low team interdependence. Contrary to our predictions, social integration did not mediate the negative relationship between deep‐level dissimilarity and individual effectiveness related outcomes but suppressed positive direct effects of deep‐level dissimilarity on individual effectiveness related outcomes. Possible explanations for these counterintuitive findings are discussed.     

An enhanced branch‐and‐bound algorithm for a partitioning problem

This paper focuses on the problem of developing a partition of n objects based on the information in a symmetric, non‐negative dissimilarity matrix. The goal is to partition the objects into a set of non‐overlapping subsets with the objective of minimizing the sum of the within‐subset dissimilarities. Optimal solutions to this problem can be obtained using dynamic programming, branch‐and‐bound and other mathematical programming methods. An improved branch‐and‐bound algorithm is shown to be particularly efficient. The improvements include better upper bounds that are obtained via a fast exchange algorithm and, more importantly, sharper lower bounds obtained through sequential solution of submatrices. A modified version of the branch‐and‐bound algorithm for minimizing the diameter of a partition is also presented. Computational results for both synthetic and empirical dissimilarity matrices reveal the effectiveness of the branch‐and‐bound methodology.     

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.     

Examining the effects of work externalization through the lens of social identity theory

This study examines whether dissimilarity among employees that is based on their work status (i.e., whether they are temporary or internal workers) influences their organization-based self-esteem, their trust in and attraction toward their peers, and their altruism. A model that is based on social identity theory posits that work-status dissimilarity negatively influences each outcome variable and that the strength of this relationship varies depending on whether employees have temporary or internal status and the composition of their work groups. Results that are based on a survey of 326 employees (189 internal and 137 temporary) from 34 work groups, belonging to 2 organizations, indicate that work-status dissimilarity has a systematic negative effect only on outcomes related to internal workers when they work in temporary-worker-dominated groups.     

Robustness of parameter and standard error estimates against ignoring a contextual effect of a subject-level covariate in cluster-randomized trials

In experimental research, it is not uncommon to assign clusters to conditions. When analysing the data of such cluster-randomized trials, a multilevel analysis should be applied in order to take into account the dependency of first-level units (i.e., subjects) within a second-level unit (i.e., a cluster). Moreover, the multilevel analysis can handle covariates on both levels. If a first-level covariate is involved, usually the within-cluster effect of this covariate will be estimated, implicitly assuming the contextual effect to be equal. However, this assumption may be violated. The focus of the present simulation study is the effects of ignoring the inequality of the within-cluster and contextual covariate effects on parameter and standard error estimates of the treatment effect, which is the parameter of main interest in experimental research. We found that ignoring the inequality of the within-cluster and contextual effects does not affect the estimation of the treatment effect or its standard errors. However, estimates of the variance components, as well as standard errors of the constant, were found to be biased.     

Target Meaning-Making of Workplace Incivility Based on Perceived Personality Similarity with Perpetrators

Abstract

Target meaning-making of incivility (i.e., the ways targets assess uncivil events) has received attention as an important mediating mechanism in explaining the varied outcomes of incivility. The present study draws on person-environment (PE) fit theory, as well as the similarity-attraction paradigm and repulsion hypothesis, to uncover how perceived personality (dis)similarity affects both cognitive (i.e., attribution, negative appraisal) and emotional reactions (i.e., hostility) to incivility. Specifically, we examine whether incongruence between target personality and perceived perpetrator personality worsens target meaning-making (vice versa for personality congruence). Study 1 (N?=?479 employees) addressed (dis)similarity in agreeableness, while Study 2 (N?=?296 working adults) addressed (dis)similarity in neuroticism. Based on polynomial regressions with response surface modeling, the results generally supported the hypotheses. Along the line of dissimilarity, targets often assessed (i.e., attributed intent to, appraised, reacted emotionally to) uncivil events more negatively when they perceived personality dissimilarity with perpetrators. However, similarity in personality did not always have the opposite effect by buffering against negative assessments; meaning-making was worse when both parties scored high on neuroticism. Implications for workplace incivility and PE fit literatures are discussed, along with practical implications that highlight information elaboration and perspective taking.     

Bicriterion methods for partitioning dissimilarity matrices

Partitioning indices associated with the within‐cluster sums of pairwise dissimilarities often exhibit a systematic bias towards clusters of a particular size, whereas minimization of the partition diameter (i.e. the maximum dissimilarity element across all pairs of objects within the same cluster) does not typically have this problem. However, when the partition‐diameter criterion is used, there is often a myriad of alternative optimal solutions that can vary significantly with respect to their substantive interpretation. We propose a bicriterion partitioning approach that considers both diameter and within‐cluster sums in the optimization problem and facilitates selection from among the alternative optima. We developed several MATLAB‐based exchange algorithms that rapidly provide excellent solutions to bicriterion partitioning problems. These algorithms were evaluated using synthetic data sets, as well as an empirical dissimilarity matrix.     

Comparison of perceptual and motor latencies via anticipatory and reactive response times

To compare the timing of perceptual and motor decisions, distinct tasks have been designed, all of which have yielded systematic differences between these two moments. These observations have been taken as evidence of a sensorimotor dissociation. Inasmuch as the distinction between perceptual and motor decision moments is conceptually warranted, this conclusion remains debatable, since the observed differences may reflect the dissimilarity between the stimulations/tasks used to assess them. Here, we minimize such dissimilarities by comparing response time (RT) and anticipatory RT (ART), an alternative technique with which to infer the relative perceptual decision moments. Observers pressed a key either in synchrony with the third of a sequence of three stimuli appearing at a constant pace (ART) or in response to the onset of this third stimulus presented at a random interval after the second (RT). Hence, the two stimulation sequences were virtually identical. Both the mean and the variance of RT were affected by stimulus intensity about 1.5 times more than were the mean and the variance of ART. Within the framework of two simple integration-to-bound models, these findings are compatible with the hypothesis that perceptual and motor decisions operate on the same internal signal but are based on distinct criteria, with the perceptual criterion lower than the motor one.     

The Relationship Between Perceived and Actual Physical Fitness: A Meta-Analysis

The purpose of our study was to meta-analytically estimate the relationship between actual and perceived fitness, and variables that may moderate this relationship (i.e., gender, age, and perceived fitness measure). Computer, hand, and journal literature searches identified 53 potential studies. On review, 28 of these studies met the inclusion criteria of having a perceived and actual (i.e., objective) measure of physical fitness. Using random effects modeling procedures, we found a medium mean effect size of .38 (N = 33 independent effect sizes, p < .001, Fail-Safe N = 4,654). Moderator analyses revealed that younger people had more accurate estimates of their fitness, and standardized perceived fitness measures had significantly larger effect sizes than unstandardized perceived fitness measures. In summary, men and women of all ages accurately perceived their fitness level, with larger effects evidenced for younger people and for studies that used standardized perceived fitness measures. Unfortunately, because most Americans are either low active or sedentary, their perceptions reveal that they are not fit. Research limitations and future directions are discussed.     

Dissimilarities as indices of individual perceptual structure

The generality of dissimilarity judgments and of configurations obtained by multidimensional scaling (MDS) as indices of perceptual structure was examined. The Ss made magnitude estimates of dissimilarity of pairs of photos, and MDS configurations were constructed separately for each S. The compatability of dissimilarities (judgments or distances in MDS configurations) with two other tasks Ss performed was then examined. These additional tasks, an “encoding” and a “decoding” task, required the S to first construct a message by making use of a set of four photos and, a week later, to decode the messages. Results obtained were interpreted as indicating a degree of generality of the dissimilarities and supporting a hypothesis of individual differences in perceptual structure for the stimulus set. A “data-purification” hypothesis for MDS was discussed and examined.

     

Fast similarities: efficiency advantages of similarity-focused comparisons

People constantly have to make efficient use of their limited cognitive resources. Recently, T. Mussweiler and K. Epstude (2009) demonstrated that comparative thinking simplifies information processing and increases the efficiency of judgment. However, there are different types of comparative thinking. While comparing 2 entities, people may focus on either similarities or dissimilarities between target and standard. The authors propose that these 2 comparative thinking styles differ in their efficiency. Specifically, the authors hypothesize that comparisons with a focus on similarities lead to more focused information processing and faster judgments than comparisons with a dissimilarity focus. In line with these hypotheses, the authors demonstrate that participants are indeed faster at judging the similarity of 2 stimuli (Study 1) and that they search for less target information in a comparative judgment task (Study 2) if they focus on similarities rather than dissimilarities. Focusing on similarities thus appears to be the more efficient comparative thinking style.     

Experimental comparison of physical activity self-efficacy measurement: Do vignettes reduce motivational confounding?

ObjectivesSelf-efficacy is one of the most reliable correlates of physical activity, yet a growing body of literature has demonstrated that traditional self-efficacy measures may be flawed because they measure perceived capability and other constructs such as motivation. This study adds to this evidence base by comparing a standard self-efficacy measurement group and two measurement conditions that may provide greater validity: motivation held constant (i.e., adding “If you really wanted to” at the beginning of the item) and vignette (i.e., adding a clarifying vignette before the item). The first objective of this study was to compare these groups regarding self-efficacy scores. The second objective was to examine whether physical activity level (i.e., adhering to physical activity guidelines or not) interacted with measurement condition.DesignRandomized cross-sectional design with three independent groups.MethodParticipants were 444 undergraduate students (M age in years = 21.10, SD = 3.73) who completed an online survey measuring physical activity self-efficacy and behaviour.ResultsThe vignette group had higher self-efficacy scores than the standard and motivation held constant groups. Scores were also higher among those adhering to guidelines and there were no differences between the groups for physically active individuals. Finally, among those not adhering to the guidelines, the vignette group had especially high scores compared to the other groups.ConclusionsThis study demonstrated that reading a vignette prior to completing a self-efficacy item clarifies the meaning of the item thereby improving validity of the measure.     

Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures

Eight different variable selection techniques for model-based and non-model-based clustering are evaluated across a wide range of cluster structures. It is shown that several methods have difficulties when non-informative variables (i.e., random noise) are included in the model. Furthermore, the distribution of the random noise greatly impacts the performance of nearly all of the variable selection procedures. Overall, a variable selection technique based on a variance-to-range weighting procedure coupled with the largest decreases in within-cluster sums of squares error performed the best. On the other hand, variable selection methods used in conjunction with finite mixture models performed the worst.