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.     

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 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.     

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 Stochastic Version of General Recognition Theory

General recognition theory (GRT) is a multivariate generalization of signal detection theory. Past versions of GRT were static and lacked a process interpretation. This article presents a stochastic version of GRT that models moment-by-moment fluctuations in the output of perceptual channels via a multivariate diffusion process. A decision stage then computes a linear or quadratic function of the outputs from the perceptual channels, which drives a univariate diffusion process that determines the subject's response. Conditions are established under which the stochastic and static versions of GRT make identical accuracy predictions. These equivalence relations show that traditional estimates of perceptual noise may often be corrupted by decisional influences. Copyright 2000 Academic Press.     

A theory of interactive parallel processing: new capacity measures and predictions for a response time inequality series

The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels' dependencies that incorporates standard independent and coactive parallel models as special cases. The metatheory is applied to OR and AND experimental paradigms, and the authors establish new theorems relating response time performance in these designs to earlier and novel issues. One notable outcome is the remarkable processing efficiency associated with linear parallel-channel systems that include mutually positive interactions. The results may offer insight into perceptual and cognitive configural-holistic processing systems.     

Independence and separability in the perception of complex nonspeech sounds

All sounds are multidimensional, yet the relationships among auditory dimensions have been studied only infrequently. General recognition theory (GRT; Ashby & Townsend, 1986) is a multidimensional generalization of signal detection theory and, as such, provides powerful tools well suited to the study of the relationships among perceptual dimensions. However, previous uses of GRT have been limited in serious ways. We present methods designed to overcome these limitations, and we use these methods to apply GRT to investigations of the relationships among auditory perceptual dimensions that previous work suggests are independent (frequency, duration) or not (fundamental frequency [ f0], spectral shape). Results from Experiment 1 confirm that frequency and duration do not interact decisionally, and they extend this finding with evidence of perceptual independence. Results from Experiment 2 show that f0 and spectral shape tend to interact perceptually, decisionally, or both, and that perceptual interactions occur within, but not between, stimuli (i.e., the interactions suggest correlated noise across processing channels corresponding to perceptually separable dimensions). The results are discussed in relation to lower level sensory modeling and higher level cognitive and linguistic issues.     

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.     

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).     

Perceptual independence of size and weight by dynamic touch

Historically, the existence of a size-weight illusion has led to the conclusion that perceptions of size and weight are not independent. A dependence of perceived heaviness on physical volume (perceptual separability), however, is different from a dependence on perceived volume (perceptual independence). Three experiments were conducted to evaluate perceptual independence. The relations between perceived size and weight and physical size and mass were evaluated in Experiment 1. Perceived weight, length, and width were structured only by the corresponding physical variables, whereas variations in volume were not separable from variations in mass. F. G. Ashby and J. T. Townsend's (1986) test for perceptual independence was applied in Experiment 2. Perceived weight was independent of perceived length and volume. Experiment 3 used a magnitude estimation paradigm to investigate the extent to which information-perception relations could be related to the observed patterns of separability and independence.     

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.     

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.     

Separating perceptual and decisional attention processes in the identification and categorization of integral-dimension stimuli

Four observers performed matching, identification, and categorization with stimuli that varied along the integral dimensions: brightness and saturation. General recognition theory (F. G. Ashby & J. T. Townsend, 1986) was applied to quantify the separate influences of perceptual and decisional processes within and across tasks, with a focus on separating perceptual from decisional attention processes. Good accounts of the identification data were obtained from perceptual matching representation. This perceptual representation provided a good account of the categorization data, except when decisional selective attention to 1 stimulus dimension was required. Decisional selective attention reduced the attended-dimension perceptual variance relative to the unattended-dimension perceptual variance, with a larger reduction resulting when brightness, as opposed to saturation was attended. Implications for color vision research are discussed.     

Separating perceptual processes from decisional processes in identification and categorization

Four observers completed perceptual matching, identification, and categorization tasks using separable-dimension stimuli. A unified quantitative approach relating perceptual matching, identification, and categorization was proposed and tested. The approach derives from general recognition theory (Ashby & Townsend, 1986) and provides a powerful method for quantifying the separate influences of perceptual processes and decisional processes within and across tasks. Good accounts of the identification data were obtained from an initial perceptual representation derived from perceptual matching. The same perceptual representation provided a good account of the categorization data, except when selective attention to one stimulus dimension was required. Selective attention altered the perceptual representation by decreasing the perceptual variance along the attended dimension. These findings suggest that a complete understanding of identification and categorization performance requires an understanding of perceptual and decisional processes. Implications for other psychological tasks are discussed.     

Separating perceptual processes from decisional processes in identification and categorization.

Four observers completed perceptual matching, identification, and categorization tasks using separable-dimension stimuli. A unified quantitative approach relating perceptual matching, identification, and categorization was proposed and tested. The approach derives from general recognition theory (Ashby & Townsend, 1986) and provides a powerful method for quantifying the separate influences of perceptual processes and decisional processes within and across tasks. Good accounts of the identification data were obtained from an initial perceptual representation derived from perceptual matching. The same perceptual representation provided a good account of the categorization data, except when selective attention to one stimulus dimension was required. Selective attention altered the perceptual representation by decreasing the perceptual variance along the attended dimension. These findings suggest that a complete understanding of identification and categorization performance requires an understanding of perceptual and decisional processes. Implications for other psychological tasks are discussed.     

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).     

Mutual information, perceptual independence, and holistic face perception

The concept of perceptual independence is ubiquitous in psychology. It addresses the question of whether two (or more) dimensions are perceived independently. Several authors have proposed perceptual independence (or its lack thereof) as a viable measure of holistic face perception (Loftus, Oberg, & Dillon, Psychological Review 111:835–863, 2004; Wenger & Ingvalson, Learning, Memory, and Cognition 28:872–892, 2002). According to this notion, the processing of facial features occurs in an interactive manner. Here, I examine this idea from the perspective of two theories of perceptual independence: the multivariate uncertainty analysis (MUA; Garner & Morton, Definitions, models, and experimental paradigms. Psychological Bulletin 72:233–259, 1969), and the general recognition theory (GRT; Ashby & Townsend, Psychological Review 93:154–179, 1986). The goals of the study were to (1) introduce the MUA, (2) examine various possible relations between MUA and GRT using numerical simulations, and (3) apply the MUA to two consensual markers of holistic face perception^—recognition of facial features (Farah, Wilson, Drain, & Tanaka, Psychological Review 105:482–498, 1998) and the composite face effect (Young, Hellawell, & Hay, Perception 16:747–759, 1987). The results suggest that facial holism is generated by violations of several types of perceptual independence. They highlight the important theoretical role played by converging operations in the study of holistic face perception.     

An investigation of perceptual and decisional influences on the perception of hierarchical forms

When observers are asked to identify the global and local dimensions of hierarchical forms, their responses are typically faster when the dimensions are consistent rather than inconsistent. This effect, which we refer to as the dimensional consistency effect, has been demonstrated numerous times in paradigms requiring responses to a single dimension. However, most hypotheses regarding dimensional consistency effects address the simultaneous perception of both dimensions, and the manner in which the information about these dimensions may (or may not) 'interact'. Most explanations of the dimensional consistency effect attribute the effect to perceptual influences. The present study uses the constructs of general recognition theory (Ashby and Townsend, 1986 Psychological Review 93 154-179) to represent the source of the effect in terms of both perceptual and decisional influences. In addition, a complete identification response paradigm was used to collect data on the simultaneous perception of both global and local dimensions of hierarchical forms. Analyses of multidimensional signal detection measures and fits of parametric models of the perceptual space were used to guide inferences, with all sources of evidence pointing to both perceptual and decisional influences.     

Holistic processing of faces: perceptual and decisional components

Researchers have used several composite face paradigms to assess holistic processing of faces. In the selective attention paradigm, participants decide whether one face part (e.g., top) is the same as a previously seen face part. Their judgment is affected by whether the irrelevant part of the test face is the same as or different than the relevant part of the study face. This failure of selective attention implies holistic processing. However, the authors show that this task alone cannot distinguish between perceptual and decisional sources of holism. The distinction can be addressed by the complete identification paradigm, in which both face parts are judged to be same or different, combined with analyses based on general recognition theory (F. G. Ashby & J. T. Townsend, 1986). The authors used a different paradigm, sequential responses, to relate these 2 paradigms empirically and theoretically. Sequential responses produced the same results as did selective attention and complete identification. Moreover, disruptions of holistic processing by systematic misalignment of the faces corresponded with systematic and significant changes in the decisional components, but not in the perceptual components, that were extracted using general recognition theory measures. This finding suggests a significant decisional component of holistic face processing in the composite face task.     

Multiple attention systems in perceptual categorization

Five observers categorized inverted L-shaped stimuli according to the length of the horizontal line segment. A centrally located spatial cue preceded the stimulus on each trial. On 80% of the trials, the (relevant) horizontal line segment fell within the cued location, and on 20% of the trials the (irrelevant) vertical line segment fell within the cued location. The empirical results provide support for the hypothesis that perceptual attention can focus on the stimulus attribute inside the spatially cued location at the same time that decisional attention is focused on the (relevant) horizontal attribute--that is, the results suggest that perceptual and decisional attention can function independently during categorization. Decision bound models and extended generalized context models that assume separate perceptual and decisional attention systems were fitted to the data. Versions of the models that assume that the spatial cue affected perceptual attention were superior to versions that assume no effect on perceptual attention. These theoretical analyses support the functional independence hypothesis and suggest that formal theories of categorization should model the effects of perceptual and decisional attention separately.