Mapclus: A mathematical programming approach to fitting the adclus model

We present a new algorithm, MAPCLUS (MAthematicalProgrammingCLUStering), for fitting the Shepard-Arabie ADCLUS (forADditiveCLUStering) model. MAPCLUS 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. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, we consider an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividualDifferencesCLUStering).We are indebted to Scott A. Boorman, W. K. Estes, J. A. Hartigan, Lawrence J. Hubert, Carol L. Krumhansl, Joseph B. Kruskal, Sandra Pruzansky, Roger N. Shepard, Edward J. Shoben, Sigfrid D. Soli, and Amos Tversky for helpful discussions of this work, as well as the anonymous referees for their suggestions and corrections on an earlier version of this paper. We are also grateful to Pamela Baker and Dan C. Knutson for technical assistance. The research reported here was supported in part by LEAA Grant 78-NI-AX-0142 and NSF Grants SOC76-24512 and SOC76-24394.     

An analysis of auditory alphabet confusions

The present study, using the nonhierarchical overlapping clustering algorithm MAPCLUS to fit the Shepard-Arabie (1979) ADCLUS model, attempted to derive a set of features that would accurately describe the auditory alphabet confusions present in the data matrices of Conrad (1964) and Hull (1973). Separate nine-cluster solutions accounted for 80% and 89% of the variance in the matrices, respectively. The clusters revealed that the most frequently confused letter names contained common vowels and phonetically similar consonants. Further analyses using INDCLUS, an individual differences extension of the MAPCLUS algorithm and ADCLUS model, indicated that while the patterns of errors in the two matrices were remarkably similar, some differences were also apparent. These differences reflected the differing amounts of background noise present in the two studies.     

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.     

Indclas: A three-way hierarchical classes model

A three-way three-mode extension of De Boeck and Rosenberg's (1988) two-way two-mode hierarchical classes model is presented for the analysis of individual differences in binary object × attribute arrays. In line with the two-way hierarchical classes model, the three-way extension represents both the association relation among the three modes and the set-theoretical relations among the elements of each model. An algorithm for fitting the model is presented and evaluated in a simulation study. The model is illustrated with data on psychiatric diagnosis. Finally, the relation between the model and extant models for three-way data is discussed.The research reported in this paper was partially supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg).     

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.     

Relation of number of different responses to group size and stimulus words in a discrete free-association situation

FlekkØy, K., Holme, I. & Mohn, E. Relation of number of different responses to group size and stimulus words in a discrete free-association situation. Scand. J. Psychol., 1973, 14, 4–8.-An exploration of the total number (D) of different responses given to a stimulus word in a single-word, free-association situation showed that (1) the first 50 Kent-Rosanoff words (in Norwegian) were highly heterogeneous with regard to D; (2) was an asymptotic function of the number of subjects; and (3) the larger D for schizophrenics may be attributed to their higher frequency of individual responses. It was also indicated that D may not be a valid measure of the magnitude of the associative potential of the individual.     

Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at theM-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.This research was supported by a Hong Kong UCG Earmarked Grant, CUHK 4026/97H. We are greatly indebted to D.E. Morisky and J.A. Stein for the use of their AIDS data in our example. We also thank the Editor, two anonymous reviewers, W.Y. Poon and H.T. Zhu for constructive suggestions and comments in improving the paper. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.     

Predictors of subjective well-being among college youth in Lebanon

The authors investigated the prevalence and predictors of subjective well-being (SWB) in a particular Middle Eastern culture: that of Lebanon. The authors examined personality constructs of self-esteem, optimism, and positive affect in relation to SWB. The authors surveyed a sample of 689 individuals between the ages of 17 and 24 by using four instruments with established cross-cultural validity: (a) the Satisfaction with Life Scale (SWLS; E. Diener, R. Emmons, R. J. Larsen, & S. Griffin, 1985), (b) the Positive and Negative Affect Schedule (PANAS; D. Watson, L. A. Clark, & A. Tellegen, 1988), (c) the Rosenberg Self-Esteem Scale (RSE; M. Rosenberg, 1965), and (d) the revised Life Orientation Test (LOT-R; M. F. Scheier, C. S. Carver, & M. W. Bridges, 1994). The results indicated that college youth's SWB was positively correlated with self-esteem, optimism, and positive affect. Examining the demographic variable of gender, the authors found that men had higher scores on positive affect than did women. A trend emerged that suggested that language dominance and socioeconomic status were associated with SWB levels. The results suggest that internal personality constructs are more predictive of satisfaction with life than are demographic variables.     

The applicability of deadline models: Comment on Glickman,Gray, and Morales (2005)

Glickman, Gray, and Morales (this issue) propose a statistical model for measuring the unobserved latency of stimulus-controlled processes. The model accounts for both speed and accuracy and does so by assuming participants set an internal deadline. If a stimulus-controlled response is not produced by the deadline, the participant then guesses. The applicability the model is discussed in this comment. The deadline model yields specific predictions for the case in which stimulus difficulty is manipulated in a within-block manner. In this case, it is reasonable to assume that stimulus difficulty does not affect the deadline. It is shown that in common perceptual and cognitive domains, extant data do not fully meet these predictions. Hence, practitioners need be aware of the possibility and consequences of model misspecification. This research is supported by NSF grant SES - 0095919 to J. Rouder, D. Sun, and P. Speckman.     

Logics of public communications

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. This paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24. Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 668283.     

Perry's Legacy: Models of Epistemological Development

This paper compares the different ways that intellectual development has been described by W. Perry (1970) and M. Belenky, B. Clinchy, N. Goldberger, and J. Tarule (1986); M. Baxter Magolda (1992); and P. King and K. Kitchener (1994). The similarities are summarized into a comprehensive, gender-neutral 4-stage model (E. J. West, 1996). The nature of the stages is discussed from both a constructivist-developmental perspective (H. G. Furth, 1981; A. Colby & L. Kohlberg, 1987) and using skill-complexity theory (M. L. Commons, E. J. Trudeau, S. A. Stein, F. A. Richards, & S. R. Krause, 1998; M. L. Commons, D. Danaher-Gilpin, P. M. Miller, & E. A. Goodheart, 2002). Educational implications are proposed.     

Racial Discrimination,Coping, Life Satisfaction,and Self‐Esteem Among African Americans

This article reports the results of a study that examined the coping strategies used by African Americans in managing the stressful effects of racism. A total of 213 participants (women, n = 137; men, n = 76) completed the Index of Race‐Related Stress (S. O. Utsey & J. G. Ponterotto, 1996), the Coping Strategy Indicator (J. H. Amirkhan, 1990), the Satisfaction With Life Scale (E. Diener, R. A. Emmons, R. J. Larsen, & S. Griffin, 1985), and the Rosenberg Self‐Esteem Scale (M. Rosenberg, 1965). Results indicated that women preferred avoidance coping for racism experienced on a personal level. For African Americans in general, seeking social support and racism condition were the best predictors of racism‐related stress. Life satisfaction and self‐esteem were best predicted by avoidance coping. Implications for the provision of counseling services to African Americans are discussed.     

Book Reviews Section

Book reviews in this article:
B urns , T homas J. (Editor) The Behavioral Aspects of Accounting Data for Performance Evaluation.
C ampbell , J ohn P., D unnette , M arvin D., L awler , E dward E., III, and W eick , K arl E., J r . Managerial Behavior, Performance, and Effectiveness.
K ast , F remont E. and R osenzweig , J ames E. Organization and Management: A Systems Approach.
P owell , R eed M. Race, Religion, and the Promotion of the American Executive.
W asmuth , W illiam J., S imonds , R ollin H., H ilgert , R aymond L., and L ee , H ak C hong . Human Resources Administration: Problems of Growth and Change.
M ueller , E va (with others). Technological Advance in an Expanding Economy: Its Impact on a Cross-section of the Labor Force.
B lake , R obert R. and M outon , J ane S rygley . The Grid for Sales Excellence: Benchmarks for Effective Salesmanship.
F rench , W endell . The Personnel Management Process: Human Resources Administration.
R eddin , W. J. Managerial Effectiveness.
B lack , J ames M. HOW to Get Results from Interviewing: A Practical Guide for Operating Management.
C ohen , J acob . Statistical Power Analysis for the Behavorial Sciences.
L ucas , R ex A. Men In Crisis:. A Study of a Mine Disaster.
G roff , G ene K. and M uth , J ohn F. (Editors) Operations Management: Selected Readings.
N i B hroin , N oirin . the motivation and Productivity of Young Women Workers.
E rdos , P aul L. Professional Mai Surveys.
A dams , S exton and F yffe , D on . The Corporate Promotables.
…Briefly Mentioned
Books and Materials Received     

Development and preliminary validation of the physiological hyperarousal scale for children

Considerable empirical support exists for the positive affect and negative affect components of the tripartite model of anxiety and depression proposed by L. A. Clark and D. Watson (1991); however, less attention has been paid to the physiological hyperarousal component of the model. The development of the Physiological Hyperarousal Scale for Children (PH-C; J. Laurent, S. J. Catanzaro, & T. E. Joiner Jr., 1995) is described. The psychometric properties of items are examined using students in Grades 6-12 (N = 398). Initial scale validation includes a joint factor analysis with the Positive and Negative Affect Scale for Children (PANAS-C; J. Laurent et al., 1999; J. Laurent, K. Potter, & S. J. Catanzaro, 1994). The relationship between the PH-C and existing measures that tap related constructs is examined. Together, the PH-C and PANAS-C provide a means to assess tripartite model constructs useful in differentiating anxiety and depression.     

Book Review Section

Book reviews in this article:
P orter , L yman W., and L awler , E dward E. III. Managerial Attitudes and Performance
G ellerman , S aul W. Management by Motivation
J ackson , D ouglas N., and M essick , S amuel (Eds.) Problems in Human Assessment
Predicting Managerial Success
B enge , E ugene J. A Performance Pay Plan for Salaried Employees
H inman , S usan L ee . A Predictive Validity Study of Creative Managerial Performance
M yers , C harles A. (Editor) The Impact of Computers on Management
F oltman , F elician F. White- and Blue-Collars in a Mill Shutdown: A Case Study in Relative Redundancy
J erkedal , Å ke . Top Management Education: An Evaluation Study
… Briefly Mentioned C oss , F rank . Recruitment Advertising
D onovan , J. J. (Editor) Recruitment and Selection in the Public Service
Books and Materials Received     

Review

F riedrich S eifert and R otraut S eifert -H elwig : Bilder und Urbilder , Erscheinungsformen des Archetypus
M. E sther H arding : The 'I' and the 'Not-I' : a study in the development of consciousness
W arner M uensterberger and S idney A xelrad (editors): The psychoanalytic study of society, III
S tanley A. L eavy (translation and introduction): The Freud journal of Lou Andreas Salome
R obert W aelder : Psychoanalytic avenues to art
Tripurā-Rahasya (JÑĀNAKHANDA)
E rwin R. G oodenough : The psychology of religious experiences
M ircea E liade (translated by J. M. Cohen): The two and the one
G ershom G. S cholem (translated by Ralph Manheim): On the Kabbalah and its symbolism
K. B annister and L. P incus : Shared phantasy in marital problems: therapy in a four-person relationship
I. B oszormenyi -N agy and J ames L. F ramo (eds.): Intensive family therapy
K. D abrowski : Positive disintegration , edited by J. Aronson     

Book Reviews

Books reviewed in this article:
E ngel , J ames F., K ollat , D avid T., and B lackwell , R oger D. Consumer Behavior.
L itwin , G eorge H., and S tringer , R obert A. J r . Motivation and Organizational Climate.
K irkpatrick , J ames J., E wen , R obert B., B arrett , R ichard S., and K atzell , R aymond A. Testing and Fair Employment: Fairness and Validity of Personnel Tests for Diferent Ethnic Groups.
G eist , H arold . The Psychological Aspects of Retirement.
H olden , P aul E., P ederson , C arlton A., and G ermane , G ayton E. Top Management.
C alvert , R obert , J r . Employing the Minority Group College Graduate (Recruiting, Evaluating Qualifications, Retaining Employees).
E dwards , A llen L. Experimental Design in Psychological Research
G laser , B arney G. (Editor) Organizational Careers: A Source-book for Theory.
Management Education and Development.
B ittel , L ester R. What Every Supervisor Should Know.
M c M urry , R obert N., and A rnold , J ames S. How to Build a Dynamic Sales Organization.
Z ytowski , D onald G. (Editor) Vocational Behavior: Readings in Theory and Research.
H erman , S tanley M. The Peopte Specialists.
Evaluation of Executive Performance.
M c F arland , D alton E. Personnel Management: Theory and Practice.
M ussen , P aul H., and R osenzweig , M ark R. (Eds.) Annual Review of Psychology, Volume 60, 1969.     

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).     

Modeling the effects of choice-set size on the processing of letters and words

Letters and words are better identified when there are fewer available choices. How do readers use choice-set restrictions? By analyzing new experimental data and previously reported data, the author shows that Bayes theorem-based models overestimate readers' use of choice-set restrictions. This result is discordant with choice-similarity models such as R. D. Luce's (1963a) similarity choice model, G. Keren and S. Baggen's (1981) letter recognition model, and D. W. Massaro and G. C. Oden's (1979) fuzzy logical model of perception. Other models posit that choice restrictions affect accuracy only by improving guessing (e.g., J. L. McClelland & D. E. Rumelhart's, 1981, interactive activation model). It is shown that these models underestimate readers' use of choice-set restrictions. Restriction of choice set does improve perception of letters and words, but not optimally. Decision models that may be able to explain this phenomenon are discussed.