Effects on indscal of non-orthogonal perceptions of object space dimensions

A general question is raised concerning the possible consequences of employing the very popular INDSCAL multidimensional scaling model in cases where the assumptions of that model may be violated. Simulated data are generated which violate the INDSCAL assumption that all individuals perceive the dimensions of the common object space to be orthogonal. INDSCAL solutions for these various sets of data are found to exhibit extremely high goodness of fit, but systematically distorted object spaces and negative subject weights. The author advises use of Tucker's three-mode model for multidimensional scaling, which can account for non-orthogonal perceptions of the object space dimensions. It is shown that the INDSCAL model is a special case of the three-mode model.     

The approximation of a group stimulus space by averaging responses to selected subsets of the stimuli

This paper presents a simple random procedure for selecting subsets of stimulus pairs for presentation to subjects. The resulting set of ratings from the group of subjects allows the construction of a group (average) space through the use of the computer program TORSCA-9 or equivalent programs. The procedure is applied to both real and simulated data. It is found that subjects need only make between 20% and 50% of the usual judgements to reconstruct a reasonably accurate group space.     

Differentiability of Kruskal's stress at a local minimum

It is shown that Kruskal's multidimensional scaling loss function is differentiable at a local minimum. Or, to put it differently, that in multidimensional scaling solutions using Kruskal's stress distinct points cannot coincide.     

The joint analysis of direct ratings,pairwise preferences,and dissimilarities

In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. Examples might be direct ratings of the stimuli, pairwise preference judgments, and physical measurements of the stimuli with respect to various properties. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms described for fitting these to data. A number of hypothesis tests are developed and an example offered.The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada.     

The complement of a point subset in a projective space and a Grassmann space

In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be recovered in that complement. Then we apply this result to show something similar for Grassmann spaces.     

The organization of conspecific face space in nonhuman primates

Humans and chimpanzees demonstrate numerous cognitive specializations for processing faces, but comparative studies with monkeys suggest that these may be the result of recent evolutionary adaptations. The present study utilized the novel approach of face space, a powerful theoretical framework used to understand the representation of face identity in humans, to further explore species differences in face processing. According to the theory, faces are represented by vectors in a multidimensional space, the centre of which is defined by an average face. Each dimension codes features important for describing a face's identity, and vector length codes the feature's distinctiveness. Chimpanzees and rhesus monkeys discriminated male and female conspecifics’ faces, rated by humans for their distinctiveness, using a computerized task. Multidimensional scaling analyses showed that the organization of face space was similar between humans and chimpanzees. Distinctive faces had the longest vectors and were the easiest for chimpanzees to discriminate. In contrast, distinctiveness did not correlate with the performance of rhesus monkeys. The feature dimensions for each species’ face space were visualized and described using morphing techniques. These results confirm species differences in the perceptual representation of conspecific faces, which are discussed within an evolutionary framework.     

The influence of intention on masked priming: a study with semantic classification of words

Unconscious perception is commonly described as a phenomenon that is not under intentional control and relies on automatic processes. We challenge this view by arguing that some automatic processes may indeed be under intentional control, which is implemented in task-sets that define how the task is to be performed. In consequence, those prime attributes that are relevant to the task will be most effective. To investigate this hypothesis, we used a paradigm which has been shown to yield reliable short-lived priming in tasks based on semantic classification of words. This type of study uses fast, well practised classification responses, whereby responses to targets are much less accurate if prime and target belong to a different category than if they belong to the same category. In three experiments, we investigated whether the intention to classify the same words with respect to different semantic categories had a differential effect on priming. The results suggest that this was indeed the case: Priming varied with the task in all experiments. However, although participants reported not seeing the primes, they were able to classify the primes better than chance using the classification task they had used before with the targets. When a lexical task was used for discrimination in experiment 4, masked primes could however not be discriminated. Also, priming was as pronounced when the primes were visible as when they were invisible. The pattern of results suggests that participants had intentional control on prime processing, even if they reported not seeing the primes.     

Constrained latent class analysis: Simultaneous classification and scaling of discrete choice data

A reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data. Latent class-specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal-point or vector model that yields a graphical, multidimensional representation of the classification results. In addition, background variables can be incorporated as an aid to interpreting the latent class-specific response probabilities. The analyses of synthetic and real data sets illustrate the proposed method.The authors thank Yosiho Takane, the editor and referees for their valuable suggestions. Authors are listed in reverse alphabetical order.     

Increasing item complexity: A possible cause of scale shrinkage for unidimensional item response theory

When the three-parameter logistic model is applied to tests covering a broad range of difficulty, there frequently is an increase in mean item discrimination and a decrease in variance of item difficulties and traits as the tests become more difficult. To examine the hypothesis that this unexpected scale shrinkage effect occurs because the items increase in complexity as they increase in difficulty, an approximate relationship is derived between the unidimensional model used in data analysis and a multidimensional model hypothesized to be generating the item responses. Scale shrinkage is successfully predicted for several sets of simulated data.The author is grateful to Robert Mislevy for kindly providing a copy of his computer program, RESOLVE.     

Analysis of asymmetry by a slide-vector

The slide-vector scaling model attempts to account for the asymmetry of a proximity matrix by a uniform shift in a fixed direction imposed on a symmetric Euclidean representation of the scaled objects. Although no method for fitting the slide-vector model seems available in the literature, the model can be viewed as a constrained version of the unfolding model, which does suggest one possible algorithm. The slide-vector model is generalized to handle three-way data, and two examples from market structure analysis are presented.     

The processing of task-irrelevant emotion and colour in the Approach-Avoidance Task

When processing information about human faces, we have to integrate different sources of information like skin colour and emotional expression. In 3 experiments, we investigated how these features are processed in a top-down manner when task instructions determine the relevance of features, and in a bottom-up manner when the stimulus features themselves determine process priority. In Experiment 1, participants learned to respond with approach-avoidance movements to faces that presented both emotion and colour features (e.g. happy faces printed in greyscale). For each participant, only one of these two features was task-relevant while the other one could be ignored. In contrast to our predictions, we found better learning of task-irrelevant colour when emotion was task-relevant than vice versa. Experiment 2 showed that the learning of task-irrelevant emotional information was improved in general when participants’ awareness was increased by adding NoGo-trials. Experiment 3 replicated these results for faces and emotional words. We conclude that during the processing of faces, both bottom-up and top-down processes are involved, such that task instructions and feature characteristics play a role. Ecologically significant features like emotions are not necessarily processed with high priority. The findings are discussed in the light of theories of attention and cognitive biases.     

Causality, criticality, and reading words: distinct sources of fractal scaling in behavioral sequences

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition.     

The situated person: Effects of construct accessibility on situation construals and interpersonal perception

Three studies examined the interrelationship between primed constructs, situation construal, and person perception. Previous research on priming and person perception has generally neglected the situational context. We predicted that when rich situational information is included, primed constructs can lead to assimilation effects on situation construals, which can in turn lead to contrast effects in person perceptions. Study 1 demonstrated that when situation information is included in the experimental context, primes lead to contrast in person perceptions. Study 2, employing a subliminal methodology, demonstrated that these effects could not be accounted for via previous explanations of contrast effects, such as correction-based mechanisms, that require overt recognition of the priming stimuli by the participants. Study 3 demonstrated that the contrastive effects of the priming stimuli on person perception obtained in Studies 1 and 2 are in fact due to the intervening assimilative effects of the priming stimuli on situation construal—that is, the primed constructs led to contrast effects on perceptions of the actor via their assimilative effects on perceptions of the situation in which that actor was embedded. Additionally, moderator variables demonstrated that this effect is most pronounced when the target actor’s behavior is described as relatively unambiguous or situation focus is increased.     

The integration of multidimensional scaling and multivariate analysis with optimal transformations

The recent history of multidimensional data analysis suggests two distinct traditions that have developed along quite different lines. In multidimensional scaling (MDS), the available data typically describe the relationships among a set of objects in terms of similarity/dissimilarity (or (pseudo-)distances). In multivariate analysis (MVA), data usually result from observation on a collection of variables over a common set of objects. This paper starts from a very general multidimensional scaling task, defined on distances between objects derived from one or more sets of multivariate data. Particular special cases of the general problem, following familiar notions from MVA, will be discussed that encompass a variety of analysis techniques, including the possible use of optimal variable transformation. Throughout, it will be noted how certain data analysis approaches are equivalent to familiar MVA solutions when particular problem specifications are combined with particular distance approximations.This research was supported by the Royal Netherlands Academy of Arts and Sciences (KNAW). An earlier version of this paper was written during a stay at McGill University in Montréal; this visit was supported by a travel grant from the Netherlands Organization for Scientific Research (NWO). I am grateful to Jim Ramsay and Willem Heiser for their encouragement and helpful suggestions, and to the Editor and referees for their constructive comments.     

Using a multidimensional scaling approach to investigate the underlying basis of ease of learning judgments

Jönsson, F. U. & Lindström, B. R. (2009) Using a multidimensional scaling approach to investigate the underlying basis of ease of learning judgments. Scandinavian Journal of Psychology, 51, 103–108. Before studying a material it is of strategic importance to first assess its difficulty, so called Ease of Learning (EOL) judgments. A multidimensional scaling (MDS) procedure was used to investigate the underlying basis of EOL judgments for 24 nouns, which to the authors’ knowledge has not been done before. In addition, Judgments of Learning (JOL) followed by a free recall test was performed. The MDS analysis indicated that EOL judgments for the nouns are based on multiple cues (dimensions), namely word length, frequency, and concreteness. Moreover, the concreteness values of the nouns, as judged by an independent group, were correlated with both the JOLs and the concreteness dimension from the MDS analysis. This indicates that EOLs and JOLs for single words are based, to some extent, on the same cues.