Regular Minimality and Thurstonian-type modeling

A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision rules. It has also been shown, however, that a broad class of Thurstonian-type models, called “well-behaved” (and including, e.g., models with multivariate normal perceptual representations whose parameters are smooth functions of stimuli) cannot simultaneously account for two empirically plausible properties of same–different comparisons, Regular Minimality (which essentially says that “being least discriminable from” is a symmetric relation) and nonconstancy of the minima of discrimination probabilities (the fact that different pairs of least discriminable stimuli are discriminated with different probabilities). These results have been obtained for stimulus spaces represented by regions of Euclidean spaces. In this paper, the impossibility for well-behaved Thurstonian-type models to simultaneously account for Regular Minimality and nonconstancy of minima is established for a much broader notion of well-behavedness applied to a much broader class of stimulus spaces (any Hausdorff arc-connected ones). The universality of Thurstonian-type models with independent perceptual images and deterministic decision rules is shown (by a simpler proof than before) to hold for arbitrary stimulus spaces.     

On minima of discrimination functions

A discrimination function ψ(x,y) assigns a measure of discriminability to stimulus pairs x,y (e.g., the probability with which they are judged to be different in a same-different judgment scheme). If for every x there is a single y least discriminable from x, then this y is called the point of subjective equality (PSE) for x, and the dependence h(x) of the PSE for x on x is called a PSE function. The PSE function g(y) is defined in a symmetrically opposite way. If the graphs of the two PSE functions coincide (i.e., g≡h⁻¹), the function is said to satisfy the Regular Minimality law. The minimum level functions are restrictions of ψ to the graphs of the PSE functions. The conjunction of two characteristics of ψ, (1) whether it complies with Regular Minimality, and (2) whether the minimum level functions are constant, has consequences for possible models of perceptual discrimination. By a series of simple theorems and counterexamples, we establish set-theoretic, topological, and analytic properties of ψ which allow one to relate to each other these two characteristics of ψ.     

On the limits of infants' quantification of small object arrays

Recent work suggests that infants rely on mechanisms of object-based attention and short-term memory to represent small numbers of objects. Such work shows that infants discriminate arrays containing 1, 2, or 3 objects, but fail with arrays greater than 3 [Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: Evidence from infants' manual search. Developmental Science, 6, 568-584; Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants' choice of more: Object files versus analog magnitudes. Psychological Science, 13(2), 150-156]. However, little is known about how infants represent arrays exceeding the 3-item limit of parallel representation. We explored possible formats by which infants might represent a 4-object array. Experiment 1 used a manual search paradigm to show that infants successfully discriminated between arrays of 1 vs. 2, 2 vs. 3, and 1 vs. 3 objects. However, infants failed to discriminate 1 vs. 4 despite the highly discriminable ratio, providing the strongest evidence to date for object-file representations underlying performance in this task. Experiment 2 replicated this dramatic failure to discriminate 1 from 4 in a second paradigm, a cracker choice task. We then showed that infants in the choice task succeeded at choosing the larger quantity with 0 vs. 4 crackers and with 1 small vs. 4 large crackers. These results suggest that while infants failed to represent 4 as “exactly 4”, “approximately 4”, “3”, or as even as “a plurality”, they did represent information about the array, including the existence of a cracker or cracker-material and the size of the individual objects in the array.     

Sources and influence of perceptual variance: Comment on Dzhafarov's Regular Minimality Principle

Dzhafarov [(2002). Multidimensional Fechnerian scaling: Pairwise comparisons, regular minimality, and nonconstant self-similarity. Journal of Mathematical Psychology, 46, 583-608] claims that Regular Minimality (RM) is a fundamental property of “same-different” discrimination probabilities and supports his claim with some empirical evidence. The key feature of RM is that the mapping, h, between two observation areas based on minimum discrimination probability is invertible. Dzhafarov [(2003a). Thurstonian-type representations for “same-different” discriminations: Deterministic decisions and independent images. Journal of Mathematical Psychology, 47, 184-204; (2003b). Thurstonian-type representations for “same-different” discriminations: Probabilistic decisions and interdependent images. Journal of Mathematical Psychology, 47, 229-243] also demonstrates that well-behaved Thurstonian models of “same-different” judgments are incompatible with RM and Nonconstant Self-Similarity (NCSS). There is extensive empirical support for the latter. Stimulus and neural sources of perceptual noise are discussed and two points are made:

Point 1: Models that require discrimination probabilities for noisy stimuli to possess the property that h is invertible would be too restrictive.

Point 2: In the absence of stimulus noise, violations of RM may be so subtle that their detection would be unlikely.

     

Temporal processing capabilities in repetition conduction aphasia

This study investigates the temporal resolution capacities of the central-auditory system in a subject (NP) suffering from repetition conduction aphasia. More specifically, the patient was asked to detect brief gaps between two stretches of broadband noise (gap detection task) and to evaluate the duration of two biphasic (WN-3) continuous noise elements, starting with white noise (WN) followed by 3 kHz bandpass-filtered noise (duration discrimination task). During the gap detection task, the two portions of each stimulus were either identical (“intra-channel condition”) or differed (“inter-channel condition”) in the spectral characteristics of the leading and trailing acoustic segments. NP did not exhibit any deficits in the intra-channel condition of the gap detection task, indicating intact auditory temporal resolution across intervals of 1–3 ms. By contrast, the inter-channel condition yielded increased threshold values. Based upon the “multiple-looks” model of central-auditory processing, this profile points at a defective integration window operating across a few tens of milliseconds – a temporal range associated with critical features of the acoustic speech signal such as voice onset time and formant transitions. Additionally, NP was found impaired during a duration discrimination task addressing longer integration windows (ca. 150 ms). Concerning speech, this latter time domain approximately corresponds to the duration of stationary segmental units such as fricatives and long vowels. On the basis of our results we suggest, that the patient’s auditory timing deficits in non-speech tasks may account, at least partially, for his impairments in speech processing.     

The embodied cognition theory and the motor component of “yes” and “no” verbal responses

Most of the experiments which give theories of embodied cognition their empirical anchorage only take into consideration the motor responses induced by the task or the motor component of the visual stimulus. And yet, these motor responses are often associated with a linguistic answer. Our hypothesis is that “YES” and “NO” verbal responses have a motor component. In a first experiment we showed that producing a verbal response (YES vs. NO) involves motor planning (pushing vs. pulling): participants push a lever more quickly when they have to answer “yes” than “no”, and conversely, they pull a lever more quickly when they have to answer “no” than “yes”. Moreover, in a second experiment, we showed that perceiving the words “YES” and “NO”, on its own, leads to the same motor planning than when “yes” and “no” answers actually have to be produced. Participants detect the word “YES” faster when they have to push a lever than when they have to pull it and conversely they detect the word “NO” faster when they have to pull the lever than when they have to push it down. These results are discussed in reference to “online” and “offline embodiment” concepts and to the cognitive linguistic theories.     

Dual scaling of comparison and reference stimuli in multi-dimensional psychological space

Dzhafarov and Colonius (Psychol. Bull. Rev. 6 (1999)239; J. Math. Psychol. 45(2001)670) proposed a theory of Fechnerian scaling of the stimulus space based on the psychometric (discrimination probability) function of a human subject in a same-different comparison task. Here, we investigate a related but different paradigm, namely, referent-probe comparison task, in which the pair of stimuli (x and y) under comparison assumes substantively different psychological status, one serving as a referent and the other as a probe. The duality between a pair of psychometric functions, arising from assigning either x or y to be the fixed reference stimulus and the other to be the varying comparison stimulus, and the 1-to-1 mapping between the two stimulus spaces X and Y under either assignment are analyzed. Following Dzhafarov and Colonius, we investigate two properties characteristic of a referent-probe comparison task, namely, (i) Regular cross-minimality—for the pair of stimulus values involved in referent-probe comparison, each minimizes a discrimination probability function where the other is treated as the fixed reference stimulus; (ii) Nonconstant self-similarity—the value of the discrimination probability function at its minima is a nonconstant function of the reference stimulus value. For the particular form of psychometric functions investigated, it is shown that imposing the condition of regular cross-minimality on the pair of psychometric functions forces a consistent (but otherwise still arbitrary) mapping between X and Y, such that it is independent of the assignment of reference/comparison status to x and to y. The resulting psychometric differentials under both assignments are equal, and take an asymmetric, dualistic form reminiscent of the so-called divergence measure that appeared in the context of differential geometry of the probability manifold with dually flat connections (Differential Geometric Methods in Statistics, Lecture Notes in Statistics, Vol. 28, Springer, New York, 1985). The pair of divergence functions on X and on Y, respectively, induce a Riemannian metric in the small, with psychometric order (defined in Dzhafarov & Colonius, 1999) equal to 2. The difference between the Finsler-Riemann geometric approach to the stimulus space (Dzhafarov & Colonius, 1999) and this dually-affine Riemannian geometric approach to the dual scaling of the comparison and the reference stimuli is discussed.     

Effects of ownership expressed by the first-person possessive pronoun

The present study examined the behavioral effects of the first-person possessive pronoun. In each trial, a noun (e.g. cup or bread) was presented to participants after visual presentation of a possessive pronoun “wo de” (Chinese for “my”) or “ta de” (Chinese for “his”), which formed ownership. Half participants were assigned to contextual encoding (CE) condition in which they were required to judge whether they liked the item expressed by a noun from the first or third-person perspective. The rest were assigned to perceptual encoding (PE) condition in which they were asked to judge what color the noun was. A subsequent recall test was performed. The results showed that there were significant memory and response advantages for nouns in “my” ownership under both conditions. The results were discussed with reference to self-specificity and other effects in the current study.     

Using morphology when spelling in a shallow orthographic system: The case of Spanish

Deep orthographies usually represent morphology and phonology simultaneously; both resources are necessary for spelling. In shallow orthographies, such as Spanish, phonology would be enough to spell most words. However, morphological knowledge may also take part in spelling. This study examined how Spanish children in 1st (N = 148), 2nd (N = 155) and 3rd grade (N = 155) use morphological information to spell plural nouns and verbs. A word dictation task was designed. The task included high and low frequency plural nouns ending in “s” (morphological “-s” condition) and verbs in the 2nd person ending in “s” (morphological “-s” condition). A lexical condition including words with a final “s” which was not morphologically motivated was used as a control condition (lexical “-s” condition). The results show that, although Spanish spelling is influenced by phonology, morphological information is also used. These results are discussed in relation to current models of word spelling.     

Self-injurious behavior in institutionalized,severely/profoundly retarded adults—Prevalence data and staff agreement

Staff agreement on the identification of 18 different types of self-injurious behavior (SIB) and the prevalence of SIB were assessed in a population of 91 severely and profoundly retarded residents in a large facility for mentally retarded people in West Germany (FRG). The survey included 27 direct care staff; groups of three to five rated the behavior of 8 to 27 residents from their own wards. Agreement was calculated with two different formulas for multiple raters. The data suggest that the standard definition of SIB [Tate, B. G.,& Baroff, G. S. (1966).Behavior Research and Therapy, 4, 281–287], together with a list of the most common SIB topographies, yields variable and generally low staff agreement. The data for the prevalence statistics were derived from cases in which at least 50% of the staff had indicated the occurrence of an SIB topography in a resident. Sixty of the 91 residents exhibited some form of SIB; of these, 15 demonstrated only one type, 12 two, and 33 three or more SIB topographies. The data corroborate the notion of the two taxonomic classes of social and nonsocial SIB. Contrary to other classifications the data indicate that ruminative vomiting belongs to the social SIB class.The author wishes to express his gratitude to Dr. Udo Lück, chief psychologist of the Diakoniezentrum Hephata, who made this study possible by his interest and support. The help of Walter Edlinger in collecting the data and of Prof. Hartmann Scheiblechner in giving methodological advice is also greatly appreciated.     

Stimulus frequency in the identification of line segments

Summary In a complete identification experiment line segments with 0, 45, 90, and 135 degrees orientation were exposed tachistoscopically as stimuli. The four stimuli were identified under three successive frequency conditions: In the first condition the stimuli occurred with equal frequency, in the second condition the stimulus probabilities were 0.4, 0.3, 0.2, and 0.1, and in the third condition the stimulus probabilities were 0.2, 0.1, 0.4, and 0.3. A 4×4 stimulus-responses confusion matrix was obtained from each condition and subject. The hit rates obtained for a more frequent stimulus (P=0.4 or 0.3) were higher than the hit rates obtained for a less frequent stimulus, and the same relation held between the proportions of an incorrect response corresponding to a more frequent stimulus and a less frequent stimulus. The confusion matrices were analysed according to the perceptual all-or-none model which allows separation of the effects of stimulus frequency on sensory and on decision processes in identification. Results showed marked effects of stimulus frequency on the decision processes yet no systematic effects on the sensory processes. Attempts to decompose the effects of stimulus frequency on the decision processes failed.Paper presented at the Symposium: Heinrich Düker — Impulse seiner Forschung. 20. Tagung experimentell arbeitender Psychologen, Marburg, 1978     

The effect of within-pair variation and instructions on the transposition behavior of kindergarten and third grade children

The reported studies examined the test choices of kindergarten and third-grade children in the two-stimulus size transposition problem in response to variations in (a) the magnitude of the size difference between two objects (the within-pair difference), (b) the distance between training and test pairs (“near” and “far” tests), and (c) verbal instructions. It was hypothesized that third graders would be sensitive to variations in the degree of the difference between two objects and to instructions which identify specific aspects of the stimulus array. In contrast, kindergarteners were expected to base their choices upon the direction of the difference, and thus transpose regardless of within-pair variations and instructions. Results generally confirmed these expectations, supporting the notion that children at these ages differ in their organization of the stimulus field and in the scale of measurement they apply to objects differing in size.     

Simple discrimination in stingless bees (Melipona quadrifasciata): Probing for select‐ and reject‐stimulus control

Simple and conditional discrimination training may produce various types of controlling relations. Responses may be controlled primarily by the positive stimulus (select–control relation) or by the negative stimulus (reject–control relation; the subject excludes the negative stimulus and chooses the positive). Bees learn to respond in simple and conditional discriminations. However, no study has searched for reject–control responding in Melipona bees. We trained Melipona quadrifasciata on a simple discrimination task (S+ vs. S‐; e.g., blue vs. yellow) and then probed for stimulus control with two types of probe trials, S+ versus a new stimulus (Select–control probes) and S‐ versus a new stimulus (Reject–control probes). For Group Different, a new‐stimulus color (e.g., white) was used in one type of probe and another color (e.g., black) was used in the other type. For Group Same, a single new‐stimulus color was used in both types of probes. On Select probes, the bees always preferred S+ to the new stimulus. On Reject probes, results were mixed. Depending on the colors used in training and probing, bees responded to both stimuli, and even preferred the S‐. The data suggest no control by the negative function of the S‐ and support the select‐stimulus control hypothesis of responding.     

Temporal order perception of auditory stimuli is selectively modified by tonal and non-tonal language environments

The close relationship between temporal perception and speech processing is well established. The present study focused on the specific question whether the speech environment could influence temporal order perception in subjects whose language backgrounds are distinctively different, i.e., Chinese (tonal language) vs. Polish (non-tonal language). Temporal order thresholds were measured for both monaurally presented clicks and binaurally presented tone pairs. Whereas the click experiment showed similar order thresholds for the two language groups, the experiment with tone pairs resulted in different observations: while Chinese demonstrated better performance in discriminating the temporal order of two “close frequency” tone pairs (600 Hz and 1200 Hz), Polish subjects showed a reversed pattern, i.e., better performance for “distant frequency” tone pairs (400 Hz and 3000 Hz). These results indicate on the one hand a common temporal mechanism for perceiving the order of two monaurally presented stimuli, and on the other hand neuronal plasticity for perceiving the order of frequency-related auditory stimuli. We conclude that the auditory brain is modified with respect to temporal processing by long-term exposure to a tonal or a non-tonal language. As a consequence of such an exposure different cognitive modes of operation (analytic vs. holistic) are selected: the analytic mode is adopted for “distant frequency” tone pairs in Chinese and for “close frequency” tone pairs in Polish subjects, whereas the holistic mode is selected for “close frequency” tone pairs in Chinese and for “distant frequency” tone pairs in Polish subjects, reflecting a double dissociation of function.     

Complexity effects on the children's gambling task

The children's gambling task (CGT [Kerr, A., & Zelazo, P. D. (2004). Development of “Hot” executive function: The children's gambling task. Brain and Cognition, 55, 148–157]) involves integrating information about losses and gains to maximize winnings when selecting cards from two decks. Both cognitive complexity and control (CCC) theory and relational complexity (RC) theory attribute younger children's difficulty to task complexity. In CCC theory, identification of the advantageous deck requires formulation of a higher-order rule so that gains and losses can be considered in contradistinction. According to RC theory, it entails processing the ternary relation linking three variables (deck, magnitude of gain, magnitude of loss). We designed two less complex binary-relational versions in which either loss or gain varied across decks, with the other held constant. The three closely matched versions were administered to 3–5-year-olds. Consistent with complexity explanations, children in all age groups selected cards from the advantageous deck in the binary-relational versions, but only 5-year-olds did so on the ternary-relational CGT.     

Spatial cueing in time–space synesthetes: An event-related brain potential study

Some people report that they consistently and involuntarily associate time events, such as months of the year, with specific spatial locations; a condition referred to as time–space synesthesia. The present study investigated the manner in which such synesthetic time–space associations affect visuo-spatial attention via an endogenous cuing paradigm. Reaction times and ERPs were recorded as 12 time–space synesthetes and 12 control participants did a peripheral target detection task, cued by three different types of centrally presented cues: arrows pointing left or right, direction words “left” or “right”, and month names associated with either the left or the right side of the synesthete’s mental calendar (e.g., “October” or “May”). Cues were followed by probes on the left or right side of the screen, and participants responded to the probes with button presses. Behavioral and ERP data suggested that for synesthetes, month words functioned more effectively as cues to direct attention in space. In synesthetes but not controls, a comparison of ERPs to probes cued by months revealed effects of cue validity on the P3b component peaking 370 ms post-onset and on the subsequent positive slow wave (pSW) observed 600–900 ms post-onset (both larger for invalid probes). No effects of cue validity were observed on early visual potentials (N1) for probes cued by months. The findings suggest that in these time–space synesthetes cue validity influenced post-perceptual processes, such as stimulus evaluation and categorization, with no evidence for enhanced visual processing.     

Reconstructing Distances among Objects from Their Discriminability

We describe a principled way of imposing a metric representing dissimilarities on any discrete set of stimuli (symbols, handwritings, consumer products, X-ray films, etc.), given the probabilities with which they are discriminated from each other by a perceiving system, such as an organism, person, group of experts, neuronal structure, technical device, or even an abstract computational algorithm. In this procedure one does not have to assume that discrimination probabilities are monotonically related to distances, or that the distances belong to a predefined class of metrics, such as Minkowski. Discrimination probabilities do not have to be symmetric, the probability of discriminating an object from itself need not be a constant, and discrimination probabilities are allowed to be 0’s and 1’s. The only requirement that has to be satisfied is Regular Minimality, a principle we consider the defining property of discrimination: for ordered stimulus pairs (a,b), b is least frequently discriminated from a if and only if a is least frequently discriminated from b. Regular Minimality generalizes one of the weak consequences of the assumption that discrimination probabilities are monotonically related to distances: the probability of discriminating a from a should be less than that of discriminating a from any other object. This special form of Regular Minimality also underlies such traditional analyses of discrimination probabilities as Multidimensional Scaling and Cluster Analysis. This research was supported by the NSF grant SES 0318010 (E.D.), Humboldt Research Award (E.D.), Humboldt Foundation grant DEU/1038348 (H.C. & E.D.), and DFG grant Co 94/5 (H.C.).     

Categorical perception of emotional facial expressions in preschoolers

Adults perceive emotional facial expressions categorically. In this study, we explored categorical perception in 3.5-year-olds by creating a morphed continuum of emotional faces and tested preschoolers’ discrimination and identification of them. In the discrimination task, participants indicated whether two examples from the continuum “felt the same” or “felt different.” In the identification task, images were presented individually and participants were asked to label the emotion displayed on the face (e.g., “Does she look happy or sad?”). Results suggest that 3.5-year-olds have the same category boundary as adults. They were more likely to report that the image pairs felt “different” at the image pair that crossed the category boundary. These results suggest that 3.5-year-olds perceive happy and sad emotional facial expressions categorically as adults do. Categorizing emotional expressions is advantageous for children if it allows them to use social information faster and more efficiently.