Linear programming techniques for multidimensional analysis of preferences

This paper offers a new methodology for analyzing individual differences in preference judgments with regard to a set of stimuli prespecified in a multidimensional attribute space. The individual is modelled as possessing an ideal point denoting his most preferred stimulus location in this space and a set of weights which reveal the relative saliences of the attributes. He prefers those stimuli which are closer to his ideal point (in terms of a weighted Euclidean distance measure). A linear programming model is proposed for external analysisi.e., estimation of the coordinates of his ideal point and the weights (involved in the Euclidean distance measure) by analyzing his paired comparison preference judgments on a set of stimuli, prespecified by their coordinate locations in the multidimensional space. A measure of poorness of fit is developed and the linear programming model minimizes this measure overall possible solutions. The approach is fully nonmetric, extremely flexible, and uses paired comparison judgments directly. The weights can either be constrained nonnegative or left unconstrained. Generalizations of the model to consider ordinal or interval preference data and to allow an orthogonal transformation of the attribute space are discussed. The methodology is extended to perform internal analysis,i.e., to determine the stimuli locations in addition to weights and ideal points by analyzing the preference judgments of all subjects simultaneously. Computational results show that the methodology for external analysis is unbiased—i.e., on an average it recovers the true ideal point and weights. These studies also indicate that the technique performs satisfactorily even when about 20 percent of the paired comparison judgments are incorrectly specified.The authors wish to express their deep appreciation to J. Douglas Carroll and Joseph B. Kruskal for their most valuable comments on an earlier version of this paper.     

Probabilistic inferences,discrimination, and stimulus interference in comparative judgement

Comparative judgements of successive stimuli involve constant errors. Here, two theories of these errors are considered. For the wave theory of discrimination, constant errors directly originate from discrimination operations. For the inferential theory, the same errors are due to probabilistic inferences drawn after discrimination. Previous studies suggest that the second of two successively compared stimuli has more influence on the comparative response. The results of the present experiment, in which successive lines as comparison stimuli were used, confirm this suggestion. The wave theory does not explain these results, while the inferential theory explains them in terms of probabilistic inferences. Analysis of response frequencies and response times indicates that there was a response bias in favour of the longer response. Interfering lines appearing before the first comparison line significantly affected response frequency, response time, and discriminability, whereas interpolated lines significantly affected only response frequency and response time. The inferential theory does not explain these effects on response time, while the wave theory explains them as due to modifications of response bias. These results suggest the possibility that the two theories describe independent sources of constant errors.     

Demonstration of an aftereffect occurring in the tactile-kinesthetic domain

Summary The aim of this work is the demonstration of a tactile-kinesthetic aftereffect. A sequence of stimuli was offered to adult subjects whose task was to compare two weights presented simultaneously to both hands by means of a Piéron gravimeter. In Experiment 1 the inspection stimuli consisted of two successive presentations of unequal weights for a period of 2 × 10 s. The test stimuli consisted of two equal weights rapidly following an inspection stimulus. Control stimuli consisting of two equal weights not preceded by an inspection stimulus were interspersed in the sequence. The results obtained confirm the existence of a contrast effect after presentation of an inspection stimulus. In Experiment 2 the inspection stimuli consisted of a single presentation of two unequal weights for a period of 20 s. The results confirm those of the first experiment and provide data enabling the contrast effect obtained to be interpreted as a Köhler-type aftereffect. In order to avoid confusion with the kinesthetic-figural aftereffect, we propose to call the effect demonstrated here the Gravimetric Aftereffect.     

Internal approach to external sets and universes

In this article we show how the universe of HST, Hrbaek set theory (a nonstandard set theory of external type, which includes, in particular, the ZFC Replacement and Separation schemata for all formulas in the language containing the membership and standardness predicates, and Saturation for standard size families of internal sets, but does not include the Power set axiom) admits a system of subuniverses which keep the Replacement, model Power set and Choice (in fact all of ZFC, with the exception of the Regularity axiom, which indeed is replaced by the Regularity over the internal subuniverse), and also keep as much of Saturation as it is necessary.This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.Partially supported by AMS grants in 1993 – 1995 and DFG grants in 1994 – 1995. Robert Goldblatt     

A thurstonian pairwise choice model with univariate and multivariate spline transformations

A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables. The utility of a stimulus is related to its values on the physical variables either by means of an additive univariate spline model or by means of multivariate spline model. In the additive univariate spline model, a separate univariate spline transformation is estimated for each physical dimension and the utility of a stimulus is assumed to be an additive combination of these transformed values. In the multivariate spline model, the utility of a stimulus is assumed to be a general multivariate spline function in the physical variables. The use of B splines for estimating the transformation functions is discussed and it is shown how B splines can be generalized to the multivariate case by using as basis functions tensor products of the univariate basis functions. A maximum likelihood estimation procedure for the Thurstone Case V model with spline transformation is described and applied for illustrative purposes to various artificial and real data sets. Finally, the model is extended using a latent class approach to the case where there are unreplicated paired comparisons data from a relatively large number of subjects drawn from a heterogeneous population. An EM algorithm for estimating the parameters in this extended model is outlined and illustrated on some real data.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. The authors are indebted to Ulf Böckenholt and Yoshio Takane for useful comments on an earlier draft of this paper.     

Motivation×Expectancy×Value: A functional measurement approach

Functional measurement methodology was applied to test theMotive×Expectancy×Value (MEV) model of human motivation. Subjects judged the value of hypothetical games of chance in which hunger, chance of winning a sandwich, and sandwich preference were varied along with similar information concerning a drink. Graphical tests showed excellent agreement between the data and the theoretical properties of parallelism and linear fan shape. Exact statistical tests of goodness of fit confirmed these graphical tests. Despite the complexity of the task, which required integration of six pieces of information, subjects' judgments obeyed a simple cognitive algebra. Applications of functional measurement were suggested for approach-avoidance conflict, level of aspiration, work motivation, and achievement motivation. These methods can provide exact tests of the behavior models in terms of the subjective values at the level of the individual. They thus provide a unified nomothetic-ideographic approach to motivation theory.This work was supported by National Science Foundation grants MBS 74-19124 and BNS 75-21235, and by grants from the National Institute of Mental Health to the Center for Human Information Processing, University of California, San Diego. We wish to thank Donna Rodes for her assistance in the conduct of this experiment.     

“Anchor-range” results with “same” and “different” responses and similar and dissimilar stimuli

Summary Blocks of pairs of dissimilar (anchor-like) circles were unexpectedly followed by single pairs of similar circles and vice versa. The dissimilar circles were 3 and 10 mm in diameter, and the similar circles were 3 and 5 mm, 5 and 7 mm, and 7 and 10 mm in diameter. In a second experiment, the dissimilar and similar circles did not overlap in size (e.g., they were 1.5 and 5 mm and 7 and 10 mm, respectively). The same responses to the unexpected same pairs of similar circles were faster than the same responses to the identical pairs in the blocks. In contrast, the different responses to the unexpected different pairs of similar circles were slower than the different responses to the identical pairs in the blocks. Similar stimuli accelerate same responses and slow down different responses. So the time results (and the error results as well) suggest that the context of the block dissimilar circles increased the perceived similarity of the unexpected similar circles. These anchor-range results are not explained by Thurstonian theories, which are based on the absolute properties of stimuli. Instead, they imply that the relation between the similar circles in the context of the relation between the dissimilar circles affected performance.     

Endogenous Ketamine-Like Compounds and the NDE: If So, So What?

This commentary on Karl Jansen's ketamine model for the near-death experience expands upon and raises additional questions about several issues and hypotheses: self-experimentation as a source of data; ketamine's similarities to and differences from classical hallucinogens; the need for quantification of unusual subjective states; clinical research and toxicological implications of this model; drugs as gateways to religious states; and evolutionary versus religious significance of naturally occurring compounds released in the near-death state. I suggest future research that could help explicate several of these areas.Formerly Associate Professor of Psychiatry at the University of New Mexico School of Medicine     

Author Index • Volume 119 • 2004

Authors Index

Author Index Volume 119 2004     

Allgemeinpsychologische Untersuchungen zum Vigilanzverhalten

Zusammenfassung Mit Hilfe eines 2×2×2-Designs wurde die Wirkung der Anzahl der Signalflächen, Anzahl der irrelevanten Reize und Art der Motivation auf die Vigilanzleistung untersucht. Dabei zeigte sich, daß die Wahrscheinlichkeiten von verpaßten Signalen und falschen Alarmen mit der Anzahl der Signalquellen zunehmen. Die Menge der Nicht-Signale gleicher Modalität wie die Signalreize beeinflußt weder die Signalentdeckungen noch die falschen Alarme.Weiterhin wurde versucht, eine Systematisierung von Motivationswirkungen in Vigilanzaufgaben im Rahmen des detection-Modells vorzunehmen. Bei großen Gewinnen für richtige Signalentdeckungen und geringen Verlusten für falsche Alarme (Risiko-Motivation) ergab sich eine wesentlich höhere Entdeckungswahrscheinlichkeit und eine geringfügig höhere Rate von falschen Alarmen als bei geringen Gewinnen für richtige Signalentdeckungen und hohen Kosten für falsche Alarme (Vorsichts-Motivation). Weiterhin zeigte sich unter Risiko-Motivation ein Abfall der Entdeckungswahrscheinlichkeit und bei Vorsichts-Motivation ein Anstieg, während sich die entsprechenden Raten der falschen Alarme im Verlauf der Aufgabe nicht signifikant veränderten.

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Experimental application of detection theory to vigilance behaviour

Summary In a 2×2×2-design the effects of number of dials, number of irrelevant stimuli and kind of motivation were combined. It was found out, that probabilities of missed signals and false alarms increased with spatial uncertainty. The number of irrelevant stimuli, which were of equal sensory modality as the relevant stimuli, had no influence either on detection probability or on false alarms rate.Further attempt was made to systematize effects of motivation on vigilance performance in the detection model. With great values for hits and small costs for false alarms (risky motivation) there was an essentially higher detection pobability and a slightly higher false alarms rate than with small values for hits and high costs for false detections (cautious motivation). The probabilities of detections decreased under risky motivation and increased under cautious motivation as the watch prolonged, whereas the corresponding probabilities of false alarms showed no significant changes.

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Teil I der Dissertation, die im Januar 1969 der Philosophischen Fakultät der Freien Universität Berlin vorgelegt wurde.     

Interaction of color and geometric cues in depth perception: When does “red” mean “near”?

Luminance and color are strong and self-sufficient cues to pictorial depth in visual scenes and images. The present study investigates the conditions under which luminance or color either strengthens or overrides geometric depth cues. We investigated how luminance contrast associated with the color red and color contrast interact with relative height in the visual field, partial occlusion, and interposition to determine the probability that a given figure presented in a pair is perceived as nearer than the other. Latencies of near responses were analyzed to test for effects of attentional selection. Figures in a pair were supported by luminance contrast (Experiment 1) or isoluminant color contrast (Experiment 2) and combined with one of the three geometric cues. The results of Experiment 1 show that the luminance contrast of a color (here red), when it does not interact with other colors, produces the same effects as achromatic luminance contrasts. The probability of near increases with the luminance contrast of the color stimulus, the latencies for near responses decrease with increasing luminance contrast. Partial occlusion is found to be a strong enough pictorial cue to support a weaker red luminance contrast. Interposition cues lose out against cues of spatial position and partial occlusion. The results of Experiment 2, with isoluminant displays of varying color contrast, reveal that red color contrast on a light background supported by any of the three geometric cues wins over green or white supported by any of the three geometric cues. On a dark background, red color contrast supported by the interposition cue loses out against green or white color contrast supported by partial occlusion. These findings reveal that color is not an independent depth cue, but is strongly influenced by luminance contrast and stimulus geometry. Systematically shorter response latencies for stronger near percepts demonstrate that selective visual attention reliably detects the most likely depth cue combination in a given configuration.     

Successive intervals scaling of paired comparisons

In this paper a method is developed for analyzing data resulting from the use of a modification of the usual paired comparisons procedure which allows for ratings of size of difference. The scaling model is essentially an extension of the Thurstonian successive intervals model. The method is applied to scaling of a set of nine immoral actions and the results agree rather well with those from conventional successive intervals scaling of the same stimuli.This study was supported by a grant from the Swedish Council for Social Science Research.     

Expectations of Counselling: A Comparison Between Evangelical Christians and Non-Evangelical Christians

A sample of 211 adults returned a questionnaire that was a modified version of Tinsley's (1982) Expectations about Counselling: Brief Form. The sample was recruited from an evangelical Anglican Church, an evangelical Anglican theological college, a doctor's surgery and a number of educational establishments. Analysis of the data compared subjects' choice of counselor between evangelical Christians and non-evangelical Christians. Results indicate that evangelical Christians do not have significantly lower expectations about counseling, in comparison with non-evangelical Christians, except in the Directiveness and Attractiveness sections. There was, though, a significantly higher expectation of the counselor with regard to Religious Behavior by evangelical Christians in contrast to non-evangelical Christians.     

“What Button Do I Press?” the Consequences of Conducting a Service Learning Project with Senior Citizens

In an effort to build interest in the two-year old service learning center and to fulfill its mission to integrate academic life with service in thoughtful and relevant ways, a competition was held to award developmental grants to faculty to create innovative courses incorporating service learning. The winning proposal from the business school used a business ethics course as the vehicle for formally introducing service into the business curriculum. This paper will tell the story of the intended and unintended consequences of building collaboration on several levels: between generations, between college and community, between faculty and college resources, between student teams, and between theory and practice.     

Involuntary retrieval in alphabet-arithmetic tasks: Task-mixing and task-switching costs

This study explores the effects of memory retrieval in task switching. To this end, item-specific stimulus-to-task mappings were manipulated in two alphabet-arithmetic experiments. Letter-stimuli were presented and the responses were verbal letter names. The task was either to name the next letter in the alphabet, (e.g., C D, task plus), or to name the preceding letter (e.g., C B, task minus). The mapping of individual stimuli to the two tasks (and thus to responses) was either consistent (CM) or varied (VM). In Experiment 1, performance was worse for VM items relative to CM items, indicating item-specific task-mapping effects. These task-mapping effects also contributed to mixing costs (i.e., worse performance in mixed-task blocks than in pure-task blocks) but not to switch costs (worse performance in task-switch trials than in repeat trials within mixed blocks). Experiment 2 manipulated pure and mixed tasks between-participants, and the data again showed differential effects of the task-mapping manipulation on mixing costs and switch costs. This suggests that, in these memory-dependent, alphabet-arithmetic tasks, interference due to involuntary task (and/or response) retrieval primarily increases general multi-task effects, such as maintaining activation of the current task.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Discrimination and matching within and between hues measured by reaction times: some implications for categorical perception and levels of information processing

Summary Same-different reaction times (RTs) were obtained for pairs of color samples ranging perceptually from blue to green. In Experiment 1, observers responded with same if both stimuli in a pair were from the same hue category (i.e., blue-blue or green-green) or different if the two stimuli were from different hue categories (i.e., blue-green or green-blue). RT for same responses was faster for pairs of physically identical stimuli (A-A) than for pairs of physically different stimuli (A-a) belonging to the same hue. RT for different responses was faster for larger physical differences across a boundary between hues (A-B 6 step) than for smaller physical differences (A-B 2 step). Experiment 2 replicated and extended these findings: In one phase observers matched pairs of stimuli as same or different by categorical similarity as in Experiment 1, and in a second phase observers matched the same stimulus pairs, this time by physical similarity. Matching by categorical similarity replicated the pattern of results found in Experiment 1. Matching by physical similarity showed that RTs for different responses were equivalently fast independent of the physical difference between A-B pairs, but were faster for A-B than for A-a comparisons. Further, matching identity was faster under categorical match instructions than under physical match instructions. Results of the two experiments support a model of parallel processing of physical and categorical stimulus information in color perception. Further, these reaction-time data and their implications in color perception (for hues) parallel reaction-time data and their implications in speech perception (for phonemes).     

A latent class approach to fitting the weighted Euclidean model,clascal

A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.The second author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek.     

Individuelle Lernstrategien von Totenkopfäffchen bei der Diskriminierung von visuellen Sequenzen

Zusammenfassung Durch 5 Lehrprogramme wurden Totenkopfäffchen in einer instrumentellen Verhaltenssituation darauf trainiert, Sequenzen von zwei Lichtern (weiß und blau; A und B) voneinander zu unterscheiden. In Programm 5 wurden alle 4 Permutationen der Elemente A und B, also AB, BA, AA und BB als Lichtreize verwendet. Die Beantwortung von B in AB wurde belohnt.Die Analyse der Strategien der Tiere in Programm 5 ergab verschiedene Strategien für verschiedene Tiere bei der Konfrontation mit den verschiedenen Sequenzen trotz des gleichen Vortrainings der Tiere: Zufallsbeantwortung, Beantwortung des zweiten Lichtes der Sequenzen, Beantwortung von B in 2. Position, Beantwortung nach jedem Stimulus A und jedes Stimulus A in 1. Position.Von 7 Tieren erreichten 4 die für diese Diskriminierung notwendige Strategie Beantwortung von B nach Stimulus A.3 Tiere verbliehen bis zum Schluß in der Strategie Beantwortung nach einem Stimulus A in 1. Position, die eine Vorstufe der Sequenzendiskriminierung darstellt.Durch die durchgeführte Analyse ist auch eine Beurteilung von Beantwortungsschemata möglich, die noch keine Diskriminierung von Sequenzen darstellen und damit eine Beurteilung dessen ermöglicht, was einem Versuchttier von der dargebotenen Information relevant geworden ist. Das Verhaltensmodell ist entwickelt zur Verwendung bei verschiedenen Manipulationen im Zentralnervensystem (Ausschaltungen, Psychopharmaka), bei den Effekten in den zeitlichen Parametern des Lernprozesses zu erwarten sind oder beurteilt werden sollen.

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Individual learning strategies for discrimination between visual sequences in squirrel monkeys

Summary Squirrel monkeys were trained to discriminate between the four permutations of a two-element sequence of colored lights (white and blue, A-B). Five teaching programs were developed to direct the animals' activity in an instrumental behavioral situation. In Program 5 the animals were confronted with all possible sequences in randomized order and were only rewarded if they pressed a lever in the B-part of sequence AB.Analysis of the animals' strategies revealed different strategies in different animals when exposed to program 5, although the animals had undergone the same training previously: Random responding, responding to the second part of each sequence, responding to B in the second position of a sequence, responding after each stimulus A, and responding after each stimulus A in the first position of a sequence.Four out of 7 animals reached the necessary strategy for real discrimination of sequences, namely responding to B after a stimulus A.Three animals faited to advance beyond the strategy responding after a stimulus A in the first position of a sequence, which represents the closest strategy before real discrimination of the sequences.The analysis performed makes it possible to find out which cues the animals use in the performance of the task, even if the animal has not yet reached true discrimination between sequences.The experimental model has been developed for use as a sensitive instrument for the detection or assessment of changes in the temporal parameters of the learning process in experiments where manipulations of the central nervous system (lesions, drug) make such changes likely.

     

Effect of image orientation on the eye direction aftereffect

After observing a face with the eyes looking to the left or right (adaptation stimulus), the perception of the eye direction of the subsequent face (test stimulus) is biased in the opposite direction of the adapted eye direction; this is called the eye direction aftereffect (EDAE). In the present study, the adaptation stimuli were rotated 90° (clockwise or counterclockwise) or 180° relative to the viewer. The EDAE was measured using upright test stimuli. For the 90° rotation, prior observation of the leftward and rightward eye directions biased the perceived eye directions of the upright test stimuli to the right and left, respectively. These results suggest that the adaptation was induced utilizing an object-based (or face-based) reference frame. For the 180° rotation, however, the results suggest that the adaptation was induced in a viewer-centered reference frame. The involvement of an object-based reference frame suggests that the EDAE reflected the adaptation of a relatively higher-level mechanism at least when the rotation angle from the upright position did not exceed 90°.