Further considerations of a general d′ in multidimensional space

Thomas (Psychonom. Bull. Rev. 6 (1999) 224) proposed a generalization of d′,d_g′ for multidimensional distributions and demonstrated that it is not equivalent to Euclidean distance as had been assumed in some previous studies. In this note, it is further shown not to be a metric in the general sense as it fails the triangle inequality. Also, a rigorous proof is offered of the claim (found in Thomas, Psychonom. Bull. Rev. 6 (1999) 224) that in order for the definition of d_g′ to correspond to the quantity that is estimated from data in the traditional way (using hits and false alarms) one must assume a distance classifier (proved in the case of equal covariance matrices). If one assumes optimal responding instead, then the estimated d′ corresponds to (the square root of) Mahalanobis distance. This latter observation clears up an apparent paradox between the fact that d_g′ is not a metric and Ashby and Perrin's (Psychol. Rev. 95 (1988) 124) statement relating the weighted Euclidean scaling model and a signal detection model of similarity that would yield a distance classifier.     

Assessing sensitivity in a multidimensional space: some problems and a definition of a general d'

This article provides a formal definition for a sensivity measure,d′ _g , between two multivariate stimuli. In recent attempts to assess perceptual representations using qualitative tests on response probabilities, the concept of ad′ between two multidimensional stimuli has played a central role. For example, Kadlec and Townsend (1992a, 1992b) proposed several tests based on multidimensional signal detection theory that allow conclusions concerning the perceptual and/or decisional interactions of stimulus dimensions. One proposition, referred to as thediagonal d′test, relies on specific stimulus subsets of a feature-complete factorial identification task to infer perceptual separability. Also, Ashby and Townsend (1986), in a similar manner, attempted to relate perceptual independence to dimensional orthogonality in Tanner’s (1956) model, which also involvesd′ between two multivariate signals. An analysis of the proposedd′ _g reveals shortcomings in the diagonald′ test and also demonstrates that the assumptions behind equating perceptual independence to dimensional orthogonality are too weak. Thisd′ _g can be related to a common measure of statistical distance, Mahalanobis distance, in the special case of equal covariance matrices.     

From theory to implementation: Building a multidimensional space for face recognition

The purpose of the present study was to empirically construct a multidimensional model of face space based upon Valentine’s [Valentine, T. (1991). A unified account of the effects of distinctiveness, inversion, and race in face recognition. Quarterly Journal of Experimental Psychology, 43A, 161-204; Valentine, T. (2001). Face-space models of face recognition. In M. J. Wenger, & J. T. Townsend, (Eds.). Computational, geometric, and process perspectives on facial cognition: Contexts and challenges. Scientific psychology series (pp. 83-113). Mahwah, NJ: Erlbaum] metaphoric model. Two-hundred and ten participants ranked 200 faces on a 21-dimensional space composed of internal facial features. On the basis of these dimensions an index of distance from the center of the dimensional space was calculated. A factor analysis revealed six factors which highlighted the importance of both featural and holistic processes in face recognition. Testing the model in relation to facial distinctiveness and face recognition strengthened its validity by emphasizing the relevance of the constructed multidimensional space for face recognition. The data are discussed within the framework of theoretical models of face recognition.     

Anticipatory coarticulation in aphasia: acoustic and perceptual data

Two experiments investigated speech motor planning in aphasia by contrasting the degree of labial and lingual anticipatory coarticulation evident in normal subjects' speech with that found in the speech of aphasic subjects. In the first experiment, Linear Predictive Coding (LPC) analyses were conducted for the initial consonants of CV [si su ti tu ki ku] and CCV [sti stu ski sku] productions by 6 normal and 10 aphasic (5 anterior, 5 posterior) subjects. For normal subjects' productions, reliable coarticulatory shift was found for almost all measurements, indicating that acoustic correlates for anticipatory coarticulation obtain for [s], [t], and [k] in a prevocalic environment, as well as when [s] is the initial consonant of a CCV syllable. The data for the aphasic subjects were statistically indistinguishable from those of the normal subject group, and there were no differences noted as a function of aphasia type. In the second experiment, a subset of the consonantal stimuli produced by the normal and aphasic subjects was presented to a group of 10 naive listeners for a vowel identification task. Listeners were able to identify the productions of all subjects at a level well above chance. In addition, small but statistically significant Group differences were observed, with the [sV], [skV], and [tV] productions by anterior aphasics showing significantly lower perceptual scores than those of normal subjects.     

Probabilistic multidimensional scaling: Complete and incomplete data

Simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the Hefner model. This model is a probabilistic, multidimensional scaling model, which assigns a multivariate normal distribution to each stimulus point. It is shown that for such a model, standard nonmetric and metric algorithms are not appropriate. A procedure is also described for constructing incomplete data sets, by taking into consideration the degree of familiarity the subject has for each stimulus. Maximum likelihood estimates are developed both for complete and incomplete data sets. This research was supported by National Science Grant No. SOC76-20517. The first author would especially like to express his gratitude to the Netherlands Institute for Advanced Study for its very substantial help with this research.     

Escher in color space: Individual-differences multidimensional scaling of color dissimilarities collected with a gestalt formation task

The structure of color perception can be examined by collectingjudgments about color dissimilarities. In the procedure used here, stimuli are presented three at a time on a computer monitor and the spontaneous grouping of most-similar stimuli into gestalts provides the dissimilarity comparisons. Analysis with multidimensional scaling allows such judgments to be pooled from a number of observers without obscuring the variations among them. The anomalous perceptions of color-deficient observers produce comparisons that are represented well by a geometric model of compressed individual color spaces, with different forms of deficiency distinguished by different directions of compression. The geometrical model is also capable of accommodating the normal spectrum of variation, so that there is greater variation in compression parameters between tests on normal subjects than in those between repeated tests on individual subjects. The method is sufficiently sensitive and the variations sufficiently large that they are not obscured by the use of a range of monitors, even under somewhat loosely controlled conditions.     

Analyzing recognition performance with sparse data

Experiments in which recognition performance is measured sometimes involve only a small number of observations per subject, rendering d' analysis unreliable (Schooler & Shiffrin, 2005). Here, we introduce, in signal detection models, subject-specific random variables to account for heterogeneous hit and false alarm rates among individuals. Population d' effects for comparing groups are estimated, in this approach, by pooling information from a sample of subjects across experimental conditions. The method is validated by a simulation study and is illustrated with an analysis of the effect of neutral and emotional words on recognition performance, employing the emotional Stroop task (Lee & Shih, 2007).     

Individual differences in perceptual space for tactile textures: evidence from multidimensional scaling

Ratio scaling was used to obtain from 5 subjects estimates of the subjective dissimilarity between the members of all possible pairs of 17 tactile surfaces. The stimuli were a diverse array of everyday surfaces, such as corduroy, sandpaper, and synthetic fur. The results were analyzed using the multidimensional scaling (MDS) program ALSCAL. There was substantial, but not complete, agreement across subjects in the spatial arrangement of perceived textures. Scree plots and multivariate analysis suggested that, for some subjects, a two-dimensional space was the optimal MDS solution, whereas for other subjects, a three-dimensional space was indicated. Subsequent to their dissimilarity scaling, subjects rated each stimulus on each of five adjective scales. Consistent with earlier research, two of these (rough/smooth and soft/hard) were robustly related to the space for all subjects. A third scale, sticky/slippery, was more variably related to the dissimilarity data: regressed into three-dimensional MDS space, it was angled steeply into the third dimension only for subjects whose scree plots favored a nonplanar solution. We conclude that the sticky/slippery dimension is perceptually weighted less than the rough/smooth and soft/hard dimensions, materially contributing to the structure of perceptual space only in some individuals.     

Normal ogive model on the continuous response level in the multidimensional latent space

The homogeneous case of the continuous response model is expanded to the multi-dimensional latent space, and the normal ogive model is presented. The operating density characteristic of the continuous item response and the vector of basic functions are developed. It is found out that there is a vector of sufficient statistics for estimating the subject's vector of latent traits, given the item parameter vectors. The relationship between the model and the linear factor analysis is observed. The matrix of item response information functions is introduced. Some additional observations are also made.The work described in this paper was partly carried out while the author was at Bowling Green State University with the support of its Research Associateship in the summer, 1972.     

The systematic misrepresentation of bilingual-crossed aphasia data and its consequences

The evidence from bilingual-crossed aphasia which has been used to support a bilingualism-right hemisphere effect for language representation and/or processing is critically reevaluated. Data gathered by the case survey method are shown to have been misrepresented in the literature. The argument based on a single group study of right-lesioned subjects is shown to rest upon a fundamental misinterpretation of those data. The consequences of such misrepresentation and misinterpretation as reflected in recent research are discussed.     

Escher in color space: individual-differences multidimensional scaling of color dissimilarities collected with a gestalt formation task.

The structure of color perception can be examined by collecting judgments about color dissimilarities. In the procedure used here, stimuli are presented three at a time on a computer monitor and the spontaneous grouping of most-similar stimuli into gestalts provides the dissimilarity comparisons. Analysis with multidimensional scaling allows such judgments to be pooled from a number of observers without obscuring the variations among them. The anomalous perceptions of color-deficient observers produce comparisons that are represented well by a geometric model of compressed individual color spaces, with different forms of deficiency distinguished by different directions of compression. The geometrical model is also capable of accommodating the normal spectrum of variation, so that there is greater variation in compression parameters between tests on normal subjects than in those between repeated tests on individual subjects. The method is sufficiently sensitive and the variations sufficiently large that they are not obscured by the use of a range of monitors, even under somewhat loosely controlled conditions.     

Analyzing experimental data using the Rasch model

We present a method for studying experimental data based on a psychometric model, the “Rasch model” (Rasch, 1966; Thissen & Steinberg, 1986). We illustrate the method with the use of a data set in the field of concept research. More specifically, we investigate whether a conjunctive concept can be seen as an additive combination of its constituents. High correlations between model and data are obtained, but a formal goodness-of-fit test indicates that the model does not completely account for the data. We then alter the Rasch model in such a way as to capture our idea of why the model deviates from the data. This results in higher correlations and a strong increase in goodness-of-fit. It is concluded that our ideas, as incorporated in the model, adequately summarize the data. More generally, this research illustrates that applying the Rasch model and altering it according to one’s hypotheses is an excellent way to analyze experimental data.     

Comprehension in aphasia: a cross-linguistic study

Broca's aphasics and normal controls were tested to determine relative sparing and impairment of word order, grammatical morphology, and semantic information in a sentence interpretation task. Patients were native speakers of English, German, or Italian, languages that vary drastically in the "cue validity" or information value of these three sources of information. Word order was selectively spared while grammatical morphology was selectively impaired in all three languages. Nevertheless, language-specific patterns of sentence interpretation remained in Broca's aphasics, even within the impaired morphological component, supporting an interpretation in terms of "accessing" rather than a "loss." Testing with Wernicke's aphasics, anomics, and some additional age-matched controls suggested that the selective vulnerability of morphology is not specific to agrammatic patients, at least in this paradigm.     

Wernicke''s aphasia in a 10-year-old boy

We report the case of a ten-year-old boy, who, after herpes simplex encephalitis, presented a sensory aphasia having much in common with Wernicke's aphasia in adults. The genesis of neologisms appeared very similar to the mechanisms described by Buckingham and Kertesz (1974, Brain and Language, 1, 43-61). The findings are discussed in the light of theories of hemispheric specialization and of age-related semiologies.