Absolute identification with simple and complex stimuli

It is well known that people can perfectly identify only a handful of distinct unidimensional stimuli, such as line lengths, but can identify thousands of complex stimuli, such as letters and words. This result is consistent with capacity limits in identifying unidimensional stimuli but not complex stimuli. The experiments reported here tested this theoretical dissociation using Luce's (1963) Similarity Choice Model to measure the psychological distance between stimuli in line-length-identification and letter-identification tasks. The psychological distance between line-length stimuli decreased with the number of to-be-identified stimuli; this result is concordant with capacity limits in unidimensional absolute identification. Surprisingly, the opposite result held in letter identification. Psychological distance between letters increased with an increased number of to-be-identified stimuli. This result indicates an opposite type of processing deficit: People process letters more efficiently with more choices.     

How a cognitive psychologist came to seek universal laws

My early fascination with geometry and physics and, later, with perception and imagination inspired a hope that fundamental phenomena of psychology, like those of physics, might approximate universal laws. Ensuing research led me to the following candidates, formulated in terms of distances along shortest paths in abstract representational spaces: Generalization probability decreases exponentially and discrimination time reciprocally with distance. Time to determine the identity of shapes and, provisionally, relation between musical tones or keys increases linearly with distance. Invariance of the laws is achieved by constructing the representational spaces from psychological rather than physical data (using multidimensional scaling) and from considerations of geometry, group theory, and symmetry. Universality of the laws is suggested by their behavioral approximation in cognitively advanced species and by theoretical considerations of optimality. Just possibly, not only physics but also psychology can aspire to laws that ultimately reflect mathematical constraints, such as those of group theory and symmetry, and, so, are both universal and nonarbitrary.     

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.     

Bayesian generalization with circular consequential regions

Generalization–deciding whether to extend a property from one stimulus to another stimulus–is a fundamental problem faced by cognitive agents in many different settings. Shepard (1987) provided a mathematical analysis of generalization in terms of Bayesian inference over the regions of psychological space that might correspond to a given property. He proved that in the unidimensional case, where regions are intervals of the real line, generalization will be a negatively accelerated function of the distance between stimuli, such as an exponential function. These results have been extended to rectangular consequential regions in multiple dimensions, but not for circular consequential regions, which play an important role in explaining generalization for stimuli that are not represented in terms of separable dimensions. We analyze Bayesian generalization with circular consequential regions, providing bounds on the generalization function and proving that this function is negatively accelerated.     

When not to accentuate the positive: Re-examining valence effects in attribute framing

While the expanding body of attribute framing literature provides keen insights into individual judgments and evaluations, a lack of theoretical perspective inhibits scholars from more fully extending research foci beyond a relatively straightforward examination of message content. The current research applies construal level theory to attribute framing research. The authors conduct a meta-analysis of 107 published articles and then conceptually expand this knowledge base by synthesizing attribute framing research and construal level concepts. Results suggest that attribute framing is most effective when there is congruence between the construal level evoked in a frame and the evaluator’s psychological distance from the framed event. A follow-up experiment confirms that the congruence between a frame’s construal level and psychological distance—not simply its valence—appears to be driving attribute framing effects. This research proposes to shift the focus in attribute framing research from that of message composition to a more complex relationship between the message and the recipient.     

Multidimensional Fechnerian Scaling: Perceptual Separability

A new definition of the perceptual separability of stimulus dimensions is given in terms of discrimination probabilities. Omitting technical details, stimulus dimensions are considered separable if the following two conditions are met: (a) the probability of discriminating two sufficiently close stimuli is computable from the probabilities with which one discriminates the projections of these stimuli on the coordinate axes; (b) the psychometric differential for discriminating two sufficiently close stimuli that differ in one coordinate only does not depend on the value of their matched coordinates (the psychometric differential is the difference between the probability of discriminating a comparison stimulus from a reference stimulus and the probability with which the reference is discriminated from itself). Thus defined perceptual separability is analyzed within the framework of the regular variation version of multidimensional Fechnerian scaling. The result of this analysis is that the Fechnerian metric of a stimulus space with perceptually separable dimensions has the structure of a Minkowski power metric with respect to these dimensions. The exponent of this metric equals the psychometric order of the stimulus space, or 1, whichever is greater.     

Statistical Learning of Unfamiliar Sounds as Trajectories Through a Perceptual Similarity Space

In typical statistical learning studies, researchers define sequences in terms of the probability of the next item in the sequence given the current item (or items), and they show that high probability sequences are treated as more familiar than low probability sequences. Existing accounts of these phenomena all assume that participants represent statistical regularities more or less as they are defined by the experimenters—as sequential probabilities of symbols in a string. Here we offer an alternative, or possibly supplementary, hypothesis. Specifically, rather than identifying or labeling individual stimuli discretely in order to predict the next item in a sequence, we need only assume that the participant is able to represent the stimuli as evincing particular similarity relations to one another, with sequences represented as trajectories through this similarity space. We present experiments in which this hypothesis makes sharply different predictions from hypotheses based on the assumption that sequences are learned over discrete, labeled stimuli. We also present a series of simulation models that encode stimuli as positions in a continuous two‐dimensional space, and predict the next location from the current location. Although no model captures all of the data presented here, the results of three critical experiments are more consistent with the view that participants represent trajectories through similarity space rather than sequences of discrete labels under particular conditions.     

心理距离对跨期选择和风险选择的影响

通过考察时间距离、社会距离和概率距离对跨期选择和风险选择的影响, 探究跨期选择和风险选择心理过程的相似性, 并检验不同心理距离影响决策的相似性。结果发现, 无论是时间距离(实验1)、社会距离(实验2)、还是概率距离(实验3), 心理距离越远, 被试在跨期选择中越倾向于延迟选项, 在风险选择中越倾向于风险选项。研究认为, 在跨期选择和风险选择中, 选项的表征结构和选项整体评价时不同选项特征的相对权重具有相似性。随着心理距离增加, 与高识解相联系的金额特征的相对权重增加, 与低识解相联系的时间和概率特征的相对权重降低, 这使得被试更倾向于选择金额较大的延迟和风险选项。同时, 研究发现三类心理距离对两类决策有相似影响, 进一步验证了不同心理距离的本质相似性。     

Perhaps Unidimensional Is Not Unidimensional

Miller (1956) identified his famous limit of 7 ± 2 items based in part on absolute identification—the ability to identify stimuli that differ on a single physical dimension, such as lines of different length. An important aspect of this limit is its independence from perceptual effects and its application across all stimulus types. Recent research, however, has identified several exceptions. We investigate an explanation for these results that reconciles them with Miller’s work. We find support for the hypothesis that the exceptional stimulus types have more complex psychological representations, which can therefore support better identification. Our investigation uses data sets with thousands of observations for each participant, which allows the application of a new technique for identifying psychological representations: the structural forms algorithm of Kemp and Tenenbaum (2008) . This algorithm supports inferences not possible with previous techniques, such as multidimensional scaling.     

A foundation for support theory based on a non-Boolean event space

A new foundation is presented for the theory of subjective judgments of probability known in the psychological literature as “Support Theory”. It is based on new complementation operations that, unlike those of classical probability theory (set-theoretic complementation) and classical logic (negation), need not satisfy the principles of the Law of The Excluded Middle and the Law of Double Complementation. Interrelationships between the new complementation operations and the Kahneman and Tversky judgmental heuristic of availability are described.     

Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space

A mathematical model is developed in an attempt to relate errors in multiple stimulus-response situations to psychological inter-stimulus and inter response distances. The fundamental assumptions are (a) that the stimulus and response confusions go on independently of each other, (b) that the probability of a stimulus confusion is an exponential decay function of the psychological distance between the stimuli, and (c) that the probability of a response confusion is an exponential decay function of the psychological distance between the responses. The problem of the operational definition of psychological distance is considered in some detail.This paper is based upon the theoretical sections of a Ph.D. dissertation submitted to the Graduate School of Yale University and upon subsequent modification carried out on a National Academy of Sciences-National Research Council Postdoctoral Associateship at the Naval Research Laboratory. The author is particularly indebted to Drs. C. I. Hovland, R. P. Abelson, and B. S. Rosner for their generous advice and support. Helpful criticisms have also been contributed by Drs. G. A. Miller, F. A. Logan, W. D. Garvey, J. G. Holland, and H. Glaser.     

Identification asymmetry of parafoveal stimulus pairs

Three experiments, involving 8, 10, and 10 naive participants, respectively, were conducted to examine the phenomenon in which the peripheral member of a parafoveally appearing stimulus pair is more accurately identified than the central. In the first experiment, the asymmetry was observed with stimulus pairs which had but one distinguishing feature; this could have implications for the notion that feature perturbations between stimuli provide the basis for the effect. The second experiment eliminated an explanation based upon acuity at the position of the midpoint of the stimulus configuration, since the asymmetry remains when this position is held constant. The involvement of response or decision factors seems unlikely, since the third experiment found the effect with blocked presentations involving responses to only one member of the pair. It is concluded that accounts which appeal to difficulties in separating stimuli from the overall pair configuration fail to explain more accurate identification of the peripheral stimulus when the pair is positioned at a constant distance from fixation.     

Reply to William R. Ferrell’s paper “A model for realism of confidence judgments: Implications for underconfidence in sensory discrimination”

Ferrell’s decision-variable partition model and our subjective distance model belong to the same family of Thurstonial models. The subjective distance model is limited to sensory discrimination with the method of constant stimuli and rooted in such notions as discriminal dispersion and sense distance. Ferrell’s model is intended to be wider in scope and to apply to both cognitive and sensory tasks. Both models need supplementary assumptions to predict calibration phenomena. The point of departure for us is the fact that the model predicts under-confidence under “guessing” and the empirical finding that people are about 100% correct when they report “absolutely certain.” Ferrell makes assumptions about cutoffs on the decision variable. The respondent is assumed to adjust or not adjust cutoffs according to “cues to difficulty.” We disagree with Ferrell’s claim that the hard-easy effect is explained by the respondent’s failure to adjust cutoffs sufficiently when there is a change in level of difficulty, and argue that this amounts to little more than a translation of the hard-easy effect into the lingua of Ferrell’s decision-variable partition model. Our argument is that the hard-easy effect is a consequence of the post hoc division of items according to solution probability. In addition, error variance may contribute to regression effects that enlarge the hard-easy effect. Finally, in contrast to Ferrell’s position, we regard inference (cognitive uncertainty) and discrimination (sensory uncertainty) as different psychological processes. An understanding of calibration in these two areas requires separate models.     

心理距离视角下的行为决策

决策是指决策者对将产生不同结果的多个备择方案的评估与选择。无论决策结果涉及的是金钱、健康、环境或是其他事物,它们都同时具有多重属性,如发生的概率,发生的时间,发生的地点,发生在谁身上等,这些属性会和结果量一起影响人们对结果效用的评价和对备择方案的选择。以往有关风险决策、跨期决策和社会决策的理论分别探究结果的概率属性、时间属性和人际属性如何与结果量一起共同决定人们的效用评估与选择,并提出了各自不同的决策模型。然而,心理距离理论则认为,决策结果的概率、时间、空间、人际等属性本质上都可被表征为结果在决策者心中的心理距离。这意味着风险、跨期和社会决策模型有可能经由心理距离而得以统一。近几年来,众多研究围绕这一思想开展了一系列实验研究,分析了各种心理距离的同质性,探索了基于心理距离的心理折扣现象及其规律,探讨了时间、概率、人际、空间距离对个体决策的影响。在此基础上,未来研究还应更加重视对多特征决策的研究,探索心理距离之间的替换率和通币问题,探究心理距离的本质及其整合方式,以期形成统一的决策理论模型。     

Problematic effects of aggregation in z ROC analysis and a hierarchical modeling solution

The confidence-rating recognition memory paradigm has been used extensively for testing theories of memory. Current methods for analyzing confidence-rating data require that data be aggregated over participants, items, or both. We show that this aggregation threatens claims of curvature in zROCs and distorts estimates of signal-distribution variance—the very findings that are used to make fine-grained distinctions between competing models. We develop a hierarchical signal detection model that accounts for variability from the sampling of participants and items in addition to variability from the underlying psychological processes. The model provides for accurate signal detection parameter estimates. With accurate estimates, the validity of benchmark findings in recognition memory may be assessed.     

The effect of semantic distance in yes/no and go/no-go semantic categorization tasks

The effect of semantic distance (Lund & Burgess, 1996) was examined in three semantic categorization experiments. Experiment 1, a yes/no task that required participants to make animal/nonanimal judgments by responding to both sets of stimuli (Forster & Shen, 1996), revealed no effect of semantic distance. Experiment 2, a go/no-go task that required participants to respond to only the experimental (i.e., nonanimal) items, revealed a large effect of semantic distance. In addition, response latencies were longer and error rates were lower to the experimental items in Experiment 2 than to those in Experiment 1. These findings were replicated in Experiment 3, in which semantic distance and task condition were manipulated within subjects. We conclude that these results are consistent with (1) the view that the go/no-go tasks elicited more extensive processing of the experimental items and (2) a connectionist account of semantic activation, whereby processing is facilitated by the presence of semantic neighbors.     

解释水平视角下的乐观偏差效应

研究基于解释水平理论,考查心理距离对乐观偏差效应的影响。实验从心理距离的事件概率维度、时间距离维度、空间距离维度入手,采用自编的材料对677名被试进行测量,探讨心理距离的远近对乐观偏差产生的影响。结果表明,被试对未来生活事件的判断存在总体上的乐观偏差。在较远的心理距离条件下,被试表现出更大的乐观偏差;而在较近的心理距离中,乐观偏差效应明显减小。但在时间距离维度以及消极事件的概率维度上,表现出与总体乐观偏差不一致的现象。     

Implications of an Emerging Integration of Universal and Culturally Specific Psychologies

ABSTRACT— Psychological researchers increasingly recognize that human behavior reflects a complex interplay of universal human capacities, cultural responses to unique histories and circumstances, and individual differences. Many psychological processes appear to reflect culturally specific instantiations of universal capacities. Current integrative research focuses on further clarifying definitions of universality and on refining methods for identifying universal and cultural components of psychological processes. In this article, we consider implications of this emerging integration. To illustrate possible implications for psychology, we apply it to the study of psychopathology. We report on formal models that explain why some cultures embrace dysfunction among members. We then use the integrative framework to describe methods for determining whether putative disorders bring universal or contextual life dysfunction and to clarify etiological models of three disorders. Models of psychopathology can be more informed and precise if they include careful consideration of both universal and cultural influences on behavior.     

Exemplar similarity, study list homogeneity, and short-term perceptual recognition

Kahana and Sekuler (2002) conducted short-term perceptual recognition experiments and modeled the data with a noisy exemplar similarity model. They found model-based evidence that list homogeneity (i.e., the degree to which exemplars on a study list are similar to one another) exerted a significant impact on recognition performance--a finding that is not predicted by standard global familiarity models. A potential limitation of their experiments is that they tested complex stimuli in which psychological similarities among exemplars may have been misspecified. Also, the relative importance of list homogeneity was not compared with that of alternative forms of parametric variation in the model. We conducted conceptual replications of their experiments, using a simpler set of stimuli in which interexemplar similarities could be more precisely measured. Extensive model-based comparisons reveal, in accord with the results of Kahana and Sekuler, strong evidence for a role of listhomogeneity on old-new recognition performance. We suggest that subjects systematically adjust their response criteria on the basis of the homogeneity of the study list items.     

Similarity, kernels, and the triangle inequality

Similarity is used as an explanatory construct throughout psychology and multidimensional scaling (MDS) is the most popular way to assess similarity. In MDS, similarity is intimately connected to the idea of a geometric representation of stimuli in a perceptual space. Whilst connecting similarity and closeness of stimuli in a geometric representation may be intuitively plausible, Tversky and Gati [Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89(2), 123-154] have reported data which are inconsistent with the usual geometric representations that are based on segmental additivity. We show that similarity measures based on Shepard’s universal law of generalization [Shepard, R. N. (1987). Toward a universal law of generalization for psychologica science. Science, 237(4820), 1317-1323] lead to an inner product representation in a reproducing kernel Hilbert space. In such a space stimuli are represented by their similarity to all other stimuli. This representation, based on Shepard’s law, has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli. Furthermore, this representation has the psychologically appealing property that the distance between stimuli is bounded.