A new computational method to fit the weighted euclidean distance model

This paper describes a computational method for weighted euclidean distance scaling which combines aspects of an analytic solution with an approach using loss functions. We justify this new method by giving a simplified treatment of the algebraic properties of a transformed version of the weighted distance model. The new algorithm is much faster than INDSCAL yet less arbitrary than other analytic procedures. The procedure, which we call SUMSCAL (subjectivemetricscaling), gives essentially the same solutions as INDSCAL for two moderate-size data sets tested.Comments by J. Douglas Carroll and J. B. Kruskal have been very helpful in preparing this paper.     

THE SKILL OF PICTORIAL PERCEPTION: AN INTERPRETATION OF CROSS-CULTURAL EVIDENCE*

A theoretical framework is proposed for understanding perceptual skills in their functional context. Pictorial perception is construed as a functionally specialised skill whose pervasive importance in modern education derives from the proliferation of pictorial materials in Western culture. Drawing on cross-cultural research, the major components of the skill are identified as (1) detection of appropriate contexts for its application, (2) selection of a limiting frame of reference, (3) use of conventional criteria of fidelity to recognise depicted items, (4) sensitivity to impoverished depth cues, (5) an expectation of finding in the picture most of the information necessary for its disambiguation, and (6) various assumptions about the range of cognitive inferences that may legitimately be made ‘beyond the information given’. Training studies are interpreted as suggesting that the skill can be enhanced through guided experience.     

On the {↔, ∼} -reduct of the intuitionistic consequence operation

The intuitionistic consequence operation restricted to the language with (equivalence) and (negation) as the only connectives is axiomatized by means of a finite set of sequential rules of inference.To the memory of Professor Roman Suszko     

Learned helplessness in groups

Group learned helplessness is demonstrated in Experiment I. Groups of 2 tried to turn off noise by their joint action. In the solvable group (S), noise offset was contingent on their sequence of button pushing. In the yoked, unsolvable group (U), noise offset was independent of all sequences of button pushes they produced. In a practice group (O). subjects practiced coordinated sequences of button pushes with their partners, but heard no noise. Later, all 3 groups were tested in pairs in a shuttlebox which required coordinated joint responding to turn off noise. The unsolvable group escaped more poorly than the other 2 groups, paralleling helplessness effects with individuals. Experiment 2 and 3 found no transfer from individual helplessness training to group testing and no transfer from group helplessness training to individual testing. We suggest that the same mechanism, the expectation of response ineffectiveness, may mediate both individual and group learned helplessness.     

Fitting longitudinal reduced-rank regression models by alternating least squares

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. The method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model. In an example with cross-sectional data, it is shown how the results conform closely to results from eigenanalysis. Optimal scaling of nominal and ordinal variables is added in a third substep, and illustrated with two examples involving cross-sectional and longitudinal data.Financial support by the Institute for Traffic Safety Research (SWOV) in Leidschendam, The Netherlands is gratefully acknowledged.     

A note on partitioned determinants

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.     

Generalized eigenvalue problems with positive semi-definite matrices

In a recent paper in this journal McDonald, Torii, and Nishisato show that generalized eigenvalue problems in which both matrices are singular can sometimes be solved by reducing them to similar problems of smaller order. In this paper a more extensive analysis of such problems is used to sharpen and clarify the results of McDonald, Torii, and Nishisato. Possible extensions are also indicated. The relevant mathematical literature is reviewed briefly.