An Extension of Multiple Correspondence Analysis for Identifying Heterogeneous Subgroups of Respondents

An extension of multiple correspondence analysis is proposed that takes into account cluster-level heterogeneity in respondents’ preferences/choices. The method involves combining multiple correspondence analysis and k-means in a unified framework. The former is used for uncovering a low-dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents. The proposed method offers an integrated graphical display that provides information on cluster-based structures inherent in multivariate categorical data as well as the interdependencies among the data. An empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches. The work reported in this paper was supported by Grant 290439 and Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the first and third authors, respectively. We wish to thank Ulf B?ckenholt, Paul Green, and Marc Tomiuk for their insightful comments on an earlier version of this paper. We also wish to thank Byunghwa Yang for generously providing us with his data.     

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.     

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.     

Cross‐cultural validation of the Resilience Scale for Adults (RSA) in Iran

Jowkar, B., Friborg, O. & Hjemdal, O. (2010). Cross‐cultural validation of the Resilience Scale for Adults (RSA) in Iran. Scandinavian Journal of Psychology, 51, 418–425. Resilience, as an ability to withstand and rebound from crisis and adversity, is becoming an increasingly popular concept in research on intervention and prevention of mental health. The present study examined psychometric properties of a Persian version of the Resilience Scale for Adults (RSA), a scale intended to measure protective factors presumed to enhance resilience. The participants were 373 university undergraduate students, as well as 30 pairs of run‐away girls and a matched control group. A confirmatory factor analysis verified the Norwegian five‐factor structure. All subscale scores, personal competence, social competence, family cohesion, social resources and structured style, had good reliability. The convergent validity of the RSA was supported by showing positive associations with another resilience scale, i.e., a Persian version of the Connor‐Davidson Resilience Scale (CD‐RISC). Predictive validity of the RSA was supported, as well, by significantly differentiating between girls who had run away from home and a matched control group. The results indicate that the RSA may be a valid and reliable scale for the assessment of resilience protective resources in an Iranian population.     

Cross‐cultural validation of the counselor burnout inventory in hong kong

This study investigated the cross‐cultural validation of the Chinese translation of the Counselor Burnout Inventory (CBI) with a sample of school counselors in Hong Kong. Specifically, this study examined the CBI's factor structure using confirmatory factor analysis and calculated the effect size, to compare burnout scores among the counselors of 4 countries (Hong Kong, Japan, South Korea, and the United States). Results indicated that a 5‐factor model was the most appropriate to accommodate the data. In addition, the results showed that the levels of Hong Kong counselors’ burnout were similar to those of U.S. counselors, but differed from counselors in Japan and South Korea.     

The conjunctive model of hierarchical classes

This paper describes the conjunctive counterpart of De Boeck and Rosenberg's hierarchical classes model. Both the original model and its conjunctive counterpart represent the set-theoretical structure of a two-way two-mode binary matrix. However, unlike the original model, the new model represents the row-column association as a conjunctive function of a set of hypothetical binary variables. The conjunctive nature of the new model further implies that it may represent some conjunctive higher order dependencies among rows and columns. The substantive significance of the conjunctive model is illustrated with empirical applications. Finally, it is shown how conjunctive and disjunctive hierarchical classes models relate to Galois lattices, and how hierarchical classes analysis can be useful to construct lattice models of empirical data.The research reported in this paper was supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg) and by the Research Fund of Katholieke Universiteit Leuven (Grants PDM92/19 and POR93/3 to Iven Van Mechelen; Grants OT89/9 and F91/56 to Paul De Boeck).     

Out-of-bag Prediction Error: A Cross Validation Index for Generalized Structured Component Analysis

Cross validation is a useful way of comparing predictive generalizability of theoretically plausible a priori models in structural equation modeling (SEM). A number of overall or local cross validation indices have been proposed for existing factor-based and component-based approaches to SEM, including covariance structure analysis and partial least squares path modeling. However, there is no such cross validation index available for generalized structured component analysis (GSCA) which is another component-based approach. We thus propose a cross validation index for GSCA, called Out-of-bag Prediction Error (OPE), which estimates the expected prediction error of a model over replications of so-called in-bag and out-of-bag samples constructed through the implementation of the bootstrap method. The calculation of this index is well-suited to the estimation procedure of GSCA, which uses the bootstrap method to obtain the standard errors or confidence intervals of parameter estimates. We empirically evaluate the performance of the proposed index through the analyses of both simulated and real data.     

情绪形容词词义的模糊赋值

353名大学生被试用模糊赋值方法对表示喜、怒、哀、惧四种基本情绪的48个形容词的强度和复杂度作语义经验赋值。结果表明：①强度和复杂度是两个不同的情绪评定维度,两者间的情绪形容词模糊语义赋值结果没有必然联系。②在强度和复杂度赋值上,各词的取值基本符合人们日常对这些词所表达情绪体验的理解,性别的量表值存在较大一致性。③男、女生在赋值上的差异主要表现在各词位次和把握度的不同,这种差异可能与性别差异的情绪经验及个体差异有关。④大学生情绪形容词模糊语义赋值的把握度总体上都较高,各词的语义在两个维度上都存在一定的模糊性。⑤根据各词强度赋值隶属度数据计算的模糊距离测度和Phi方关联测度得到了四类形容词相似的聚类分析结果。     

Taxicab Correspondence Analysis of Contingency Tables with One Heavyweight Column

The aim of this paper is to study the analysis of contingency tables with one heavyweight column or one heavyweight entry by taxicab correspondence analysis (TCA). Given that the mathematics of TCA is simpler than the mathematics of correspondence analysis (CA), the influence of one heavyweight column on the outputs of TCA is studied explicitly without recourse to asymptotics as done by Benzécri (Les Cahiers de L’Analyse des Données 4:413–16, 1979). A reweighting of the heavyweight column is proposed, which can also be applied to CA. A real data set is analyzed. This research is financed by NSERC of Canada. The author is grateful to the Editor, Professor B. Junker, to an Associate Editor and to three referees for their constructive comments.     

Regularized Multiple-Set Canonical Correlation Analysis

Multiple-set canonical correlation analysis (Generalized CANO or GCANO for short) is an important technique because it subsumes a number of interesting multivariate data analysis techniques as special cases. More recently, it has also been recognized as an important technique for integrating information from multiple sources. In this paper, we present a simple regularization technique for GCANO and demonstrate its usefulness. Regularization is deemed important as a way of supplementing insufficient data by prior knowledge, and/or of incorporating certain desirable properties in the estimates of parameters in the model. Implications of regularized GCANO for multiple correspondence analysis are also discussed. Examples are given to illustrate the use of the proposed technique. The work reported in this paper is supported by Grants 10630 and 290439 from the Natural Sciences and Engineering Research Council of Canada to the first and the second authors, respectively. The authors would like to thank the two editors (old and new), the associate editor, and four anonymous reviewers for their insightful comments on earlier versions of this paper. Matlab programs that carried out the computations reported in the paper are available upon request.     

Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima

Cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low-dimensional spatial representation ofK cluster points, to model a given square table of dissimilarities amongn stimuli or objects. The least squares loss function of cluster differences scaling, originally defined only on the residuals of pairs of objects that are allocated to different clusters, is extended with a loss component for pairs that are allocated to the same cluster. It is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described, including the appropriate degrees of freedom for each source. After developing a convergent algorithm for fitting the cluster differences model, it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by-product of the optimization. Finally, the paper introduces a fuzzy version of the loss function, which can be used in a successive approximation strategy for avoiding local minima. A simulation study demonstrates that this strategy significantly outperforms two other well-known initialization strategies, and that it has a success rate of 92 out of 100 in attaining the global minimum.     

结构方程模型拟合评鉴：整体拟合、内部拟合与复核效度检验

该文主要介绍了评价和鉴定结构方程中构建的模型与数据拟合程度的三个方面：整体拟合、内部拟合及复核效度检验.整体拟合评鉴主要是结合拟合指数,当拟合指数处于临界值时,应同时参照其他检验结果并根据模型构建的理论依据进行综合判断;内部拟合从项目质量检验、测验信度、平均变异萃取量和效度四个角度进行检验;复核效度检验在多样本分析中可分为宽松复核、温和复核和严格复核,但如果为研究样本所限,可以通过ECVI来实现.     

Probability matrix decomposition models

In this paper, we consider a class of models for two-way matrices with binary entries of 0 and 1. First, we considerBoolean matrix decomposition, conceptualize it as alatent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition models. Second,probability matrix decomposition (PMD) models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models. Third, an algorithm for the computation of the maximum likelihood (ML) and the maximum a posteriori (MAP) estimates of the parameters of PMD models is presented. This algorithm is an EM-algorithm, and is a special case of a more general algorithm that can be used for the whole class of LRMs. And fourth, as an example, a PMD model is applied to data on decision making in psychiatric diagnosis. This paper is based on a chapter of the first author's doctoral dissertation, written at the University of Leuven and supervised by Paul De Boeck.     

A noniterative method of joint correspondence analysis

Correspondence analysis leads to a graphical representation of the associations between categories of the row and column variables of a contingency table. Greenacre's (1988) formulation of joint correspondence analysis is a multivariate extension which finds the optimal joint display of contingency tables between all pairs of variables in a set. Greenacre presented a discrepancy function and an alternating least squares algorithm for its minimization. Boik (1996) presented an alternative algorithm, also of the alternating least squares type, for minimizing the same discrepancy function. In this paper, a noniterative procedure, not based on the minimization of any discrepancy function, is described.     

潜在剖面分析在组织行为领域中的应用

以个体为中心的研究路径将各个变量看作是相互依赖的一个系统, 基于多项特征(变量)将被试分为多个子群体, 分析子群体的前因与影响。以个体为中心的研究路径理解更加直观、更贴近实践, 受到越来越多的关注。潜在剖面分析(latent profile analysis, LPA)是以个体为中心研究路径的典型分析技术。在总结归纳以个体与以变量为中心两种研究路径异同、LPA与传统以个体为中心的分析技术差异后, 系统梳理了LPA在组织行为学领域的应用主题, 并从研究主题选取、样本要求、理论使用、剖面数量确定等方面归纳了LPA应用的步骤与注意事项。最后, 提出了未来研究的方向。