Indecision on decisional separability

The theoretical framework of General Recognition Theory (GRT; Ashby & Townsend, Psychological Review, 93, 154-179, 1986) coupled with the empirical analysis tools of Multidimensional Signal Detection Analysis (MSDA; Kadlec & Townsend, Multidimensional models of perception and recognition, pp. 181-228, 1992) have become one important method for assessing dimensional interactions in perceptual decision-making. In this article, we critically examine MSDA and characterize cases where it is unable to discriminate two kinds of dimensional interactions: perceptual separability and decisional separability. We performed simulations with known instances of violations of perceptual or decisional separability, applied MSDA to the data generated by these simulations, and evaluated MSDA on its ability to accurately characterize the perceptual versus decisional source of these simulated dimensional interactions. Critical cases of violations of perceptual separability are often mischaracterized by MSDA as violations of decisional separability.     

Independence and separability of volume and mass in the size-weight illusion

Numerous size-weight illusion models were classified in the present article according to general recognition theory (Ashby & Townsend, 1986), wherein the illusion results from a lack of perceptual separability, perceptual independence, decisional separability, or a combination of the three. These options were tested in two experiments in which a feature-complete factorial design and multidimensional signal detection analysis were used (Kadlec & Townsend, 1992a, 1992b). With haptic touch alone, the illusion was associated with a lack of perceptual and decisional separability. When the participant viewed the stimulus in his or her hand, the illusion was associated only with a lack of decisional separability. Visual input appeared to improve the discrimination of mass, leaving only the response bias due to expectation.     

A decisional component of holistic encoding

It has been proposed (see, specifically, M. J. Farah, K. D. Wilson, M. Drain, & J. N. Tanaka, 1998) that human faces are used in cognition as undifferentiated wholes. General recognition theory (GRT; F. G. Ashby & J. T. Townsend, 1986) is used to represent hypotheses regarding the possible sources for the behavioral evidence supporting holistic representation. Specifically, it is suggested that holism can be understood in terms of violations of informational independence, informational separability, or decisional separability, as these constructs are defined in GRT. Stimuli were presented upright, inverted, and in an encoding task that emphasized the meaningful nature of the stimuli. Patterns of performance (recognition hit rates) were consistent with prior studies. However, there were only a handful of violations of informational separability. Instead, consistent violations of decisional separability suggested a decisional basis for holistic effects.     

Development and the continuum of dimensional separability

Recent studies of adult perception may be interpreted in terms of a continuum from the integral to the separable perception of multidimensional variation. Three experiments examined the existence of such a continuum across developmental levels. These experiments are important because several developmental studies suggest that the separability of dimensions increases with age. Despite this assumed developmental trend, it was hypothesized that therelative separability of dimensions does not change with age. The results of the three experiments did not support the hypothesis. The ordering of dimensions by their relative separability changes with development. These results suggest that the relative separability and potential separability of dimensions are not fixed. In light of the results, it is hypothesized that the integrality or separability of dimensions in adult perception is primarily determined by perceptual learning and not by the inherent characteristics of combinations of stimulus dimensions.     

Decisional separability, model identification, and statistical inference in the general recognition theory framework

Recent work in the general recognition theory (GRT) framework indicates that there are serious problems with some of the inferential machinery designed to detect perceptual and decisional interactions in multidimensional identification and categorization (Mack, Richler, Gauthier, & Palmeri, 2011). These problems are more extensive than previously recognized, as we show through new analytic and simulation-based results indicating that failure of decisional separability is not identifiable in the Gaussian GRT model with either of two common response selection models. We also describe previously unnoticed formal implicational relationships between seemingly distinct tests of perceptual and decisional interactions. Augmenting these formal results with further simulations, we show that tests based on marginal signal detection parameters produce unacceptably high rates of incorrect statistical significance. We conclude by discussing the scope of the implications of these results, and we offer a brief sketch of a new set of recommendations for testing relationships between dimensions in perception and response selection in the full-factorial identification paradigm.     

Multidimensional signal detection analyses (MSDA) for testing separability and independence: A Pascal program

A Pascal (Turbo 6.0) program for testing perceptual separability, decisional separability, and perceptual independence—three types of independence defined in the context of general recognition theory (GRT)—is presented. GRT is essentially a multidimensional extension of signal detectability theory (Green & Swets, 1966) and has been employed in complete-identification experimental paradigms to examine whether information processing of stimulus dimensions is perceptually and/or decisionally separable and/or perceptually independent. The definitions of these different forms of “independence” are provided, the experimental design is described, and the program, MSDA, is described and demonstrated.     

A continuum of dimensional separability

Recent studies of children’s perception may be interpreted in terms of a developmental continuum from integrality to separability in the perception of multidimensional variation. Two experiments examined the existence of such a continuum in adult perception. The first experiment indicated that there are dimensional combinations that are neither clearly integral nor separable for adults. Rather, such a combination results in performance patterns intermediate between those found with integral and separable dimensions. The second experiment tested one conceptualization of a continuum of dimensional separability in a speeded classification task. By this conceptualization, the perceived structures of multidimensional variation are orderable by thedegree to which the component dimensions are differentiated. Consistent with this view, performances with three-dimensional combinations are shown to be differentially dependent on dimensional and wholistic relations. The importance of the joint consideration of developmental and adult issues in the perception of multidimensional variation is briefly discussed.     

Learning and attention in multidimensional identification and categorization: separating low-level perceptual processes and high-level decisional processes

Four observers completed identification and categorization tasks. Learning and attention processes were examined by applying general recognition theory (F. G. Ashby & J. T. Townsend, 1986), which separates perceptual, decisional, and attentional processes. Learning led to decision regions that became more nearly optimal. Learning had little effect on perceptual processes in identification and decisional integration categorization tasks but affected perceptual processes in decisional selective attention categorization tasks, leading to perceptual selective attention. These findings suggest that (a) identification and categorization invoke decision strategies that are localized in the striatum (F. G. Ashby, E. M. Waldron, W. W. Lee, & A. Berkman, 2001) and (b) perceptual and decisional attention systems exist and are mediated by distinct brain structures (M. I. Posner & S. E. Petersen, 1990).     

General recognition theory extended to include response times: Predictions for a class of parallel systems

General Recognition Theory (GRT; Ashby & Townsend, 1986) is a multidimensional theory of classification. Originally developed to study various types of perceptual independence, it has also been widely employed in diverse cognitive venues, such as categorization. The initial theory and applications have been static, that is, lacking a time variable and focusing on patterns of responses, such as confusion matrices. Ashby proposed a parallel, dynamic stochastic version of GRT with application to perceptual independence based on discrete linear systems theory with imposed noise (Ashby, 1989). The current study again focuses on cognitive/perceptual independence within an identification classification paradigm. We extend stochastic GRT and its implicated methodology for cognitive/perceptual independence, to an entire class of parallel systems. This goal is met in a distribution-free manner and includes all linear and non-linear systems satisfying very general conditions. A number of theorems are proven concerning stochastic forms of independence. However, the theorems all assume the stochastic version of decisional separability. A vital task remains to investigate the consequences of failures of stochastic decisional separability.     

Technical clarification to Silbert and Thomas (2013): “Decisional separability,model identification,and statistical inference in the general recognition theory framework”

We offer a minor technical correction to the published proof of part (ii) of the main theorem in Silbert and Thomas (Psychonomic Bulletin & Review, 20, 1–20, 2013) that somewhat limits the scope of the equivalence observed in that work. Specifically, in order for a mean shift integrality with decisional separability to be mimicked by a perceptually separable but nondecisionally separable configuration, one needs to assume stimulus invariance. This holds when all of the covariance matrices in the stimulus configuration are equal to each other. We note that part (i) of the theorem is unaffected by this modification; an empirical finding of perceptual separability and the failure of decisional separability can be mimicked by a perceptually nonseparable, decisionally separable configuration without restricting the covariance matrices to be equal. We also note that stimulus invariance is often assumed in simple designs (e.g., Macmillan & Ornstein in Journal of the Acoustical Society of America, 97, 1261–1285, 1998), due to the implausibility of different perceptual correlations being present within stimuli perched very closely in perceptual space.     

Lateral interception I: operative optical variables, attunement, and calibration

J. J. Gibson (1966, 1979) suggested that improvement in perception and action can be attributed in part to changes in which variable is attended to. Such reattunement has been demonstrated with observers making judgments in response to simulations. The present study sought attunement changes in the perception of real events and in visually guided action. In 3 experiments, adults judged the passing distance of or attempted to catch balls. Discrete measures and the predictions of a modified required velocity model (e.g., R. J. Bootsma, V. Fayt, F. T. J. M. Zaal, & M. Laurent, 1997) were used to reveal which variables were exploited. Participants differed from each other and, to some extent, changed in the optical variables used, in catching as well as judging. Nevertheless, the changes were much smaller than in previous simulation-judgment studies; calibration was also found to underlie the improvements in performance.     

Linear separability in superordinate natural language concepts

Two experiments are reported in which linear separability was investigated in superordinate natural language concept pairs (e.g., toiletry-sewing gear). Representations of the exemplars of semantically related concept pairs were derived in two to five dimensions using multidimensional scaling (MDS) of similarities based on possession of the concept features. Next, category membership, obtained from an exemplar generation study (in Experiment 1) and from a forced-choice classification task (in Experiment 2) was predicted from the coordinates of the MDS representation using log linear analysis. The results showed that all natural kind concept pairs were perfectly linearly separable, whereas artifact concept pairs showed several violations. Clear linear separability of natural language concept pairs is in line with independent cue models. The violations in the artifact pairs, however, yield clear evidence against the independent cue models.     

Accessing similarity and dimensional relations: effects of integrality and separability on the discovery of complex concepts

A series of studies investigated how stimulus integrality and separability impact the cognitive accessibility of similarity and dimensional relations. A good deal of previous work has established that stimulus integrality and separability differentially determine perception; here, the question is whether they also have differential effects on conception. Are the principles that govern perception also principles that can be readily discovered in concept learning tasks? Is a similarity-based rule especially easy to abstract from integral stimuli and a dimensionally-based rule especially easy to abstract from separable stimuli? In Experiments 1 and 2, we measured the relative ease with which the two types of rules (similarity and dimensional) are discovered by adults with the two types of stimuli (integral and separable). In experiment 1, the two rules were made redundant and we asked which rule the subjects learned. In Experiment 2, one rule was made relevant and the other irrelevant, and we compared relative speeds of learning. The results from the studies led us to conclude (a) that dimensionally based rules are more accessible from separable than from integral stimuli; (b) that similarity-based rules are more accessible from integral than from separable stimul; and (c) that, in general, subjects have a bias to access dimensional relations in this type of task. Experiment 3 pursued an additional suggestion from Experiments 1 and 2 that the dimensional relations within integral stimuli are sometimes accessible, more so when larger interstimulus differences are encountered. In confirmation, Experiment 3 demonstrated that adult subjects are more successful in applying a dimensional rule to pairs of integral stimuli that differ by a small amount if they also have exposure to pairs of integral stimuli that differ by a large amount. In a later discussion, it was argued that such a finding is consistent with the notion that the "dimensions" of integral stimuli are merely arbitrary directions in the integral stimulus space, and some relevant pilot data to that effect were presented. Finally, Experiment 4 took up a developmental issue. Young children have sometimes produced perceptual responses governed by similarity relations when presented with stimuli that are separable for adults. Will they more readily access similarity-based or dimensionally-based relations from such stimuli in the concept learning tasks here? The results showed that both kindergarteners and fifth graders more readily access the dimensional relations. A final discussion integrated the findings from the several experiments, taking up the following issues: (a) the relation between the perception and the conception of stimulus relations and (b) the nonprimacy of the dimensional axes in the integral stimulus space.     

The Impact of Performance-Contingent Rewards on Perceived Autonomy and Competence

Two studies examined the impact of performance-contingent rewards on perceived autonomy, competence, and intrinsic motivation. Autonomy was measured in terms of both decisional and affective reports. The first study revealed an undermining effect of performance-contingent rewards on affective reports of autonomy among university students, and an increase in reports of competence. Decisional autonomy judgements were unaffected by rewards. The second study replicated this pattern of findings among elementary school children. These results help resolve Cognitive Evaluation Theory's (E. L. Deci & R. M. Ryan, 1985; R. M. Ryan, V. Mims, & R. Koestner, 1983) and Eisenberger, Rhoades, et al.'s (R. Eisenberger, L. Rhoades, & J. Cameron, 1999) divergent positions on the impact of performance-contingent rewards on autonomy. The studies also included measures of intrinsic motivation.     

Expanding the search for a linear separability constraint on category learning

Formal models of categorization make different predictions about the theoretical importance of linear separability. Prior research, most of which has failed to find support for a linear separability constraint on category learning, has been conducted using tasks that involve learning two categories with a small number of members. The present experiment used four categories with three or nine patterns per category that were either linearly separable or not linearly separable. With overall category structure equivalent across category types, the linearly separable categories were found to be easier to learn than the not linearly separable categories. An analysis of individual participants' data showed that there were more participants operating under a linear separability constraint when learning large categories than when learning small ones. Formal modeling showed that an exemplar model could not account for many of these data. These results are taken to support the existence of multiple processes in categorization.     

判断框架对时序知觉位置启动效应的影响

研究采用包含两种判断框架（判断刺激出现的先后次序）的时序判断任务探讨了决策偏向对时序知觉位置启动效应的影响。实验结果表明,时序知觉中存在着位置启动效应,而且在两个靶刺激出现时间间隔不同时,被试在“哪个靶刺激先出现”和“哪个靶刺激后出现”两种判断框架下的正确率存在显著差异,但在两个靶刺激同时出现时并没有出现显著的判断框架效应。因此,本研究推测时序知觉位置启动效应的作用机制不仅包括知觉增强加工过程,而且也与认知决策有关,这为反应偏向理论提供了新的支持证据。     

Perceptual and decisional factors influencing the discrimination of inversion in the Thatcher illusion

The Thatcher illusion (Thompson, 1980) is considered to be a prototypical illustration of the notion that face perception is dependent on configural processes and representations. We explored this idea by examining the relative contributions of perceptual and decisional processes to the ability of observers to identify the orientation of two classes of forms-faces and churches-and a set of their component features. Observers were presented with upright and inverted images of faces and churches in which the components (eyes, mouth, windows, doors) were presented either upright or inverted. Observers first rated the subjective grotesqueness of all of the images and then performed a complete identification task in which they had to identify the orientation of the overall form and the orientation of each of the interior features. Grotesqueness ratings for both classes of image showed the standard modulation of rated grotesqueness as a function of orientation. The complete identification results revealed violations of both perceptual and decisional separability but failed to reveal any violations of within-stimulus (perceptual) independence. In addition, exploration of a simple bivariate Gaussian signal detection model of the relationship between identification performance and judged grotesqueness suggests that within-stimulus violations of perceptual independence on their own are insufficient for producing the illusion. This lack of evidence for within-stimulus configurality suggests the need for a critical reevaluation of the role of configural processing in the Thatcher illusion. (PsycINFO Database Record (c) 2011 APA, all rights reserved).     

Perceived association between diagnostic and non-diagnostic cues of women’s sexual interest: General Recognition Theory predictors of risk for sexual coercion

Young men’s errors in sexual perception have been linked to sexual coercion. The current investigation sought to explicate the perceptual and decisional sources of these social perception errors, as well as their link to risk for sexual violence. General Recognition Theory (GRT; [Ashby, F. G., & Townsend, J. T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154-179]) was used to estimate participants’ ability to discriminate between affective cues and clothing style cues and to measure illusory correlations between men’s perception of women’s clothing style and sexual interest. High-risk men were less sensitive to the distinction between women’s friendly and sexual interest cues relative to other men. In addition, they were more likely to perceive an illusory correlation between women’s diagnostic sexual interest cues (e.g., facial affect) and non-diagnostic cues (e.g., provocative clothing), which increases the probability that high-risk men will misperceive friendly women as intending to communicate sexual interest. The results provide information about the degree of risk conferred by individual differences in perceptual processing of women’s interest cues, and also illustrate how translational scientists might adapt GRT to examine research questions about individual differences in social perception.     

Semiorders with separability properties

We analyze different separability conditions that characterize the numerical representability of semiorders through a real-valued function and a strictly positive threshold. Any necessary and sufficient condition for the numerical representability of an interval order by means of two real-valued functions is proved to also characterize the Scott–Suppes representability of semiorders provided that a key additional condition of regularity with respect to sequences holds.     

Dimensional separability or flexibility of attention? Age trends in perceiving configural stimuli

The hypothesis that perceptual development proceeds from less to greater dimensional separability was tested by giving a speeded classification task to first and fouth graders. In Experiment 1, children sorted line drawings of a cartoon figure into two piles according to his eyes (open or closed) or his mouth (smiling or frowning). First graders exhibited the pattern characteristic of integral dimensions: An interference effect was found when dimensions were combined orthogonally and a facilitation effect when dimensions were correlated, relative to a condition in which only one dimension varied. Fourth graders exhibited an optional separable pattern: There was facilitation in the correlated condition but no interference in the orthogonal condition. These results support the hypothesis that development proceeds toward greater flexibility of attention rather than simply toward increasing separability. A flexible field hypothesis of visual attention was suggested to explain how older children can exercise such optional separability. This hypothesis correctly predicted the asymmetrical relation between dimensions found in Experiments 2 and 3: For both first and fourth graders, the eyes of a cartoon figure (open or closed) and his location (right or left) were nonseparable when the eyes were relevant and separable (or optional separable) when location was relevant.