Hierarchical classes: Model and data analysis

A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft.     

Fragile promise: The role of justification in promise-breaking

People who consider themselves moral sometimes use self-serving justifications to rationalize their selfish behaviours. Previous studies have tested the role of ambiguity in justifying wrongdoings, but it remains unclear whether ambiguity also plays a role in justifying promise-breaking behaviour and whether heterogeneity exists. To investigate justification in promise-breaking, we introduced a new experimental paradigm called the card-guessing task and used hierarchical cluster analysis to classify participants based on their promise-breaking decisions in unambiguous and ambiguous conditions. Experiment 1 revealed three clusters of solutions: Cluster 1 always kept their promises (i.e., keepers); Cluster 2 only exploited the vague promises and broke their promises in the ambiguous condition (i.e., intermediates); Cluster 3 tended to take advantage of vague promises and broke their promises irrespective of ambiguity (i.e., breakers). Experiment 2 confirmed that participants in the three clusters differed in their norm-abiding preferences and social value orientations. Keepers were more altruistic and had a stronger sense of norm compliance than intermediates and breakers. In conclusion, our study demonstrates that self-serving justifications were more likely to be employed by people who are moderately sensitive to deviation from social norms, which has implications for strategic interventions and policy formulation concerning unethical behaviour.     

“均”与“寡”阶段性变动下中国居民公平感的变迁

利用中国综合社会调查和中国社会状况综合调查重复截面数据,通过年龄-时期-队列模型对居民公平感的时代变化进行分析。研究发现公平感在年龄上呈“J”型趋势;从时期效应看, 2008年公平感较高, 2010～2013年在低谷徘徊,2015年以后又开始回升;从队列视角看,建国前出生队列公平感偏低,建国后初期的队列相对较高,“50”后有所下滑,从“60”后开始公平感持续走低,到“80”后跌入低谷,但“90”后又开始升高。从1949年前后“寡且不均”到建国初期阶段的“寡且均”,再到改革开放40年快速经济增长下“不寡但不均”的社会变迁过程影响了居民的公平感。     

Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. The number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping-rule validity. Equal and unequal population base rates were also considered. Both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space. The replication criterion, which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set, was superior as the degree of overlap in population distributions increased. Neither method performed adequately when overlap obliterated visually discernible density nodes.This research was supported in part by NIMH grant 5R01 MH 32457 14.     

学业不良学生类型与特点的聚类分析

该研究运用Ｑ聚类分析对上海市区１４８０名初中预备班学生的能力和个性特征进行分类研究。结果发现１４８０名被试中存有心理发展水平不同的六个主要类别,这些类别与学生学业成绩的优劣关系密切。同时,３５３名差生可分为四个主要类型：即,暂时性困难学生、能力型困难学生、动力型困难学生和整体性困难学生,不同类型的差生具有不同的特点。这为针对不同类型学生的特点制定有效的教育措施提供了依据。     

U-statistic hierarchical clustering

A monotone invariant method of hierarchical clustering based on the Mann-Whitney U-statistic is presented. The effectiveness of the complete-link, single-link, and U-statistic methods in recovering tree structures from error perturbed data are evaluated. The U-statistic method is found to be consistently more effective in recovering the original tree structures than either the single-link or complete-link methods.     

An examination of the effect of six types of error perturbation on fifteen clustering algorithms

An evaluation of several clustering methods was conducted. Artificial clusters which exhibited the properties of internal cohesion and external isolation were constructed. The true cluster structure was subsequently hidden by six types of error-perturbation. The results indicated that the hierarchical methods were differentially sensitive to the type of error perturbation. In addition, generally poor recovery performance was obtained when random seed points were used to start theK-means algorithms. However, two alternative starting procedures for the nonhierarchical methods produced greatly enhanced cluster recovery and were found to be robust with respect to all of the types of error examined.     

Indclus: An individual differences generalization of the adclus model and the mapclus algorithm

We present a new model and associated algorithm, INDCLUS, that generalizes the Shepard-Arabie ADCLUS (ADditive CLUStering) model and the MAPCLUS algorithm, so as to represent in a clustering solution individual differences among subjects or other sources of data. Like MAPCLUS, the INDCLUS generalization utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach to impose discrete (0,1) constraints on parameters defining cluster membership. All subjects in an INDCLUS analysis are assumed to have a common set of clusters, which are differentially weighted by subjects in order to portray individual differences. As such, INDCLUS provides a (discrete) clustering counterpart to the Carroll-Chang INDSCAL model for (continuous) spatial representations. Finally, we consider possible generalizations of the INDCLUS model and algorithm.We are indebted to Seymour Rosenberg for making available the data from Rosenberg and Kim [1975]. Also, this work has benefited from the observations of S. A. Boorman, W. S. DeSarbo, G. Furnas, P. E. Green, L. J. Hubert, L. E. Jones, J. B. Kruskal, S. Pruzansky, D. Schmittlein, E. J. Shoben, S. D. Soli, and anonymous referees.This research was supported in part by NSF Grant SES82 00441, LEAA Grant 78-NI-AX-0142, and NSF Grant SES80 04815.     

Gennclus: New models for general nonhierarchical clustering analysis

A general class of nonhierarchical clustering models and associated algorithms for fitting them are presented. These (metric) clustering models generalize the Shepard-Arabie Additive Clusters model in allowing for: (1). either overlapping or nonoverlapping clusters; (2). either symmetric (one-way clustering) or nonsymmetric (two-way clustering) proximities (input data); and, (3). either symmetric or diagonal weights. The GENNCLUS algorithms utilize alternating least-squares methods combining ordinary and constrained least-squares, nonlinear constrained mathematical programming, and combinatorial optimization techniques in estimating model parameters. In addition to developing the mathematical bases of these models, a comprehensive set of Monte Carlo simulations of the different models is reported. Two applications concerning brand-switching data and celebrity-brand proximities are discussed. Finally, extensions to three-way models, nonmetric analyses, and other model specifications are provided.Wayne S. DeSarbo is a Member of Technical Staff in the Mathematics and Statistics Research Center at Bell Laboratories in Murray Hill, N.J. I wish to thank R. Gnanadesikan, J. D. Carroll, and P. Arabie for their comments on a previous draft of this paper. I also wish to acknowledge the computer assistance provided by Linda Clark. Finally, I wish to thank the reviewers and editor for their very complete reviews and comments.     

The use of latent class models for assessing prerequisite relations and transference among traits

This paper presents a strategy for pairwise assessment which may be used to evaluate the nature of both prerequisite and transference relations existing among a set of traits. This strategy is appropriate for use both within a confirmatory context, in which an attempt is made to establish the validity of some specified set of relations among traits, as well as within an exploratory context, in which a search is made for unconjectured prerequisite and transference relations existing between pairs of traits. Both uses of this strategy are based on a variety of latent class models which are representative of various possible relational states existing between pairs of traits. Thus, the nature of trait relations may be investigated through the use of statistical assessments of both absolute and relative fit attained by these models. An application is presented to exemplify how this strategy may be used within the exploratory context.The author is obliged to Clifford Clogg, C. Mitchell, Dayton, and William Schafer for helpful comments made regarding a previous draft of this paper as well as to Mary Papageorgiou who provided access to the data which was considered in this study.