Three-way metric unfolding via alternating weighted least squares

Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.We wish to thank the editor and reviewers for their insightful comments.     

Combinatorial data analysis: Association and partial association

A combinatorial data analysis strategy is reviewed that is designed to compare two arbitrary measures of proximity defined between the objects from some set. Based on a particular cross-product definition of correspondence between these two numerically specified notions of proximity (typically represented in the form of matrices), extensions are then pursued to indices of partial association that relate the observed pattern of correspondence between the first two proximity measures to a third. The attendant issues of index normalization and significance testing are discussed; the latter is approached through a simple randomization model implemented either through a Monte Carlo procedure or distributional approximations based on the first three moments. Applications of the original comparison strategy and its extensions to partial association may be developed for a variety of methodological and substantive tasks. Besides rank correlation, we emphasize the topics of spatial autocorrelation for one variable and spatial association between two and mention the connection to the usual randomization approach for one-way analysis-of-variance.     

Statistical consistency and hypothesis testing for nonmetric multidimensional scaling

The properties of nonmetric multidimensional scaling (NMDS) are explored by specifying statistical models, proving statistical consistency, and developing hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. For these models, statistical consistency often depends crucially upon how error enters the model and how data are collected and summarized (e.g., by means, medians, or rank statistics). A maximum likelihood estimator for NMDS is developed, and its relationship to the standard Shepard-Kruskal estimation method is described. This maximum likelihood framework is used to develop a method for testing the overall fit of the model.     

Identification with another person: Manipulated by means of subliminal stimulation

Studied problems of identification, using a meta-contrast design. The first stimulus (A) was always the word ME. In experiment 1 , the second stimulus (B) depicted an aggressor and a victim facing each other. The subliminal A was flashed either on the victim or the aggressor or completely withheld. In experiment 2 , B showed two persons standing against different backgrounds: an open horizon or a closed room. It was assumed that the subject would be "forced" to identify with that figure in B on which A was flashed. Subjects in experiment 1 were 18 psychiatric patients and in experiment 2 , 32 professional artists. The results showed that the subliminal manipulation had been effective: e.g., when led by A to identify with the aggressor, projective-sensitive and borderline subjects were confused and even reported perceptual difficulties; when led to identify with the open side, highly creative artists, as opposed to less creative ones, reported more positive impressions of the B theme.     

Symmetry and transitivity of conditional relations in monkeys (Cebus apella) and pigeons (Columba livia)

In Experiment 1 six monkeys were tested with discriminative relations that were backward relative to their training in a 0-second conditional (“symbolic”) matching procedure. Although there was some indication of backward associations, the evidence was generally weak, and statistical evaluations did not reach conventional significance levels. Unlike children, who show backward associations to the point of symmetry, monkeys and pigeons display at best only weak and transient backward associations. In Experiment 2 associative transitivity was assessed across two sets of conditional matching tasks. All four monkeys tested demonstrated strong transitivity. In contrast, in Experiment 3 there was no evidence of transitivity in three pigeons tested under conditions closely comparable to those of Experiment 2. These results may identify some key features of interspecies differences and contribute to analyses of serial learning in animals.     

Flicker fusion frequency and organic syndrome in alcoholics

Flicker fusion frequencies of 48 healthy controls and of 35 alcoholics were measured to detect possible associations between flicker fusion and signs of nonspecific brain damage, the aim of the study. FFF was statistically significantly lower in patients addicted to alcohol than in healthy subjects. Lower flicker fusion frequencies were associated with the severeness of organic psychosis as rated psychopathologically. The hypothesis that addiction to alcohol is a sign of diffuse, nonspecific, organic brain damage was discussed.