Testing Separability and Independence of Perceptual Dimensions with General Recognition Theory: A Tutorial and New R Package (grtools) (original) (raw)
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A Test for Perceptual Independence With Dissimilarity Data
Applied Psychological Measurement, 1991
The dominance axiom states that the dissimilarity of a pair of stimuli differing on two dimensions must exceed the dissimilarities of the corresponding pairs of stimuli that differ on only one of the dimensions. This axiom is presented as a test of dissimilarity data to determine if the dimensions of the perceptual space are perceived independently, and as a diagnostic tool in assessing the INDSCAL model's assumption of independent
Independence and separability in the perception of complex non-speech 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 [ f 0], 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 f 0 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.
PLOS Computational Biology, 2018
Many research questions in visual perception involve determining whether stimulus properties are represented and processed independently. In visual neuroscience, there is great interest in determining whether important object dimensions are represented independently in the brain. For example, theories of face recognition have proposed either completely or partially independent processing of identity and emotional expression. Unfortunately, most previous research has only vaguely defined what is meant by "independence," which hinders its precise quantification and testing. This article develops a new quantitative framework that links signal detection theory from psychophysics and encoding models from computational neuroscience, focusing on a special form of independence defined in the psychophysics literature: perceptual separability. The new theory allowed us, for the first time, to precisely define separability of neural representations and to theoretically link behavioral and brain measures of separability. The framework formally specifies the relation between these different levels of perceptual and brain representation, providing the tools for a truly integrative research approach. In particular, the theory identifies exactly what valid inferences can be made about independent encoding of stimulus dimensions from the results of multivariate analyses of neuroimaging data and psychophysical studies. In addition, commonly used operational tests of independence are re-interpreted within this new theoretical framework, providing insights on their correct use and interpretation. Finally, we apply this new framework to the study of separability of brain representations of face identity and emotional expression (neutral/sad) in a human fMRI study with male and female participants.
Varieties of perceptual independence
Psychological Review, 1986
Several varieties of perceptual independence are investigated. These include sampling independence, dimensional orthogonality, stimulus separability and integrality, and performance parity. A general multivariate perceptual theory is developed, and a precise definition of perceptual independence is offered. Each of these related concepts is then examined within the framework of this theory, and their theoretical interrelationships are explicated. It is shown that none of the concepts are equivalent to perceptual independence but that if separability holds, then sampling independence is equivalent to perceptual independence. Several simple tests of separability are suggested that can be applied to the same data as sampling independence. Dimensional orthogonality is shown to test for independence only if some strong distributional assumptions are made about the perceptual effects of stimuli. Reaction time and information-based performance parity criteria are examined. The potential for empirically testing each of these concepts is discussed. The stimuli of perception are many dimensional. Tones may vary in frequency, intensity, and duration. Individual characters in text may vary in size, orientation, shape, and the number of line segments they contain (among other things). Even the fruit that we eat may vary in size, shape, texture, sugar content, and the wavelength of light it reflects. A fundamentally important problem is to determine how these dimensions are combined in perceptual processing. Because of this, a notion central to almost all theories of perception, whether they are aimed at the visual, the auditory, or some other modality, is that of perceptual independence. At a macroscopic verbal level, there is agreement among most theoreticians about the meaning of this term. The components A and B of the two-dimensional stimulus AB are said to be independently perceived if the perception of each is in no way contingent on or interacts with the perception of the other, or somewhat more rigorously, if the probability of simultaneously perceiving both components A and B is equal to the probability of perceiving component A times the probability of perceiving component B (e.g., Garner & Morton, 1969; Green & Birdsall, 1978; Wandmacher, 1976). Unfortunately, perceptions are not usually directly observable; instead they first pass through some decision process that uses the perceptions to select a response appropriate to the general experimental milieu. Decision or judgment processes therefore fundamentally alter direct perceptions (i.e., the early stages of perception), thereby making the above definition of perceptual independence difficult to test.
Psychonomic Bulletin & Review, 2013
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 . 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.
Parallel versus serial processes in multidimensional stimulus discrimination
Perception & Psychophysics, 1966
Although considerable effort has been devoted to the description of processes underlying discriminations along single dimensions, there have been few attempts to derermine whether or how these elementary processes are combined when discrimination requires the consideration of more than one stimulus dimension. In the present experiment,5s were required to indicate whether two simultaneously presented multidimensional visual stimuli were identical or different. The response measure was reaction time, and Ss had a monetary incentive to respond both quichly and accurately. It was concluded that the most appropriate model for this tash is one that assumes that dimensions are compared serially, and that the order in which dimensions are compared varies from triaHo-trial. Further, when a pair differs along several dimensions, Ss do not necessarily examine every dimension before initiating the response "Different."
Independence in the perception of complex non-speech sounds
Journal of The Acoustical Society of America, 2007
Kingston, Diehl, Kirk, and Castleman [Kingston, J., Diehl, R. L., Kirk, C. J., Castleman, W.A., 2008. On the perceptual structure of distinctive features: The [voice] contrast. Journal of Phonetics, 36, 28-54] present a sophisticated experimental design and detection theoretic analysis of the internal auditory structure of phonological contrasts. However, a potentially important aspect of multidimensional detection theory-the covariance structure of assumed underlying multivariate Gaussian perceptual densities-was left unexplored. We discuss Kingston et al.'s approach in the context of a general definition of multidimensional d 0 and present a description of two distinct configurations of perceptual densities requiring fundamentally different interpretations that account equally well for the ''mean-shift integrality'' results reported by Kingston et al. We end with a brief discussion of approaches to distinguishing these underlying configurations empirically. r
A psychophysical approach to dimensional separability* 1
Cognitive psychology, 1984
Combinations of some physically independent dimensions appear to fuse into a single perceptual attribute, whereas combinations of other dimensions leave the dimensions perceptually distinct. This apparent difference in the perceived distinctiveness of visual dimensions has previously been explained by the postulation of two types of internal representations-integral and separable. It is argued that apparent integrality, as well as its intermediate forms, can result from a single type of representation (the separable type), due to various degrees of correspondence between physical and separable psychological dimensions. Three experiments tested predictions of this new conceptualization of dimensional separability. Experiment 1 demonstrated that a physical dimension corresponding to a separable psychological dimension did not produce interference, whereas a physical dimension not corresponding to a separable psychological dimension did produce interference. Experiment 2 showed that the pattern of results obtained in Experiment 1 could not be accounted for by similarity relations between stimuli. Experiment 3 showed that degrees of correspondence could account for different amounts of interference as well as an inverse relationship between interference and condensation time. These findings imply that previous definitions of integrality are inadequate. Two new converging criteria are proposed, based on the invariance of perceived values on psychological dimensions and on the effect of rotating a configuration of stimuli in a multidimensional space. The present findings furthermore raise the possibility that a single type of internal representation may sufficiently account for all phenomena previously believed to arise from integrality. Certain stimulus dimensions, such as shape and color, are phenomenologically distinct in a compelling fashion; whereas others, such as brightness and saturation, are in combination perceived as a more unitary entity. Some theorists have suggested that younger children perceive holistically, whereas older children learn to differentiate perceptual dimen-This research was supported by the Office of Naval Research Contract NOO014-76-C-0648. This paper is based in part on a PhD dissertation completed by Patricia Cheng under the advisorship of Robert Pachella. We thank David Meyer, Wilfred Kincaid, Gary Olson, and members of the ONR research group for their helpful comments, Carol Luckhart for running half of the subjects and analyzing part of the data, and especially Keith Holyoak and Patricia Somers for their generous help. We also thank Naomi Weisstein and three anonymous referees for their helpful comments and suggestions on an earlier draft of this paper. Reprint requests should be addressed to