Selective attention and the formation of linear decision boundaries: Reply to Maddox and Ashby (1998).

Nosofsky, Robert M.

doi:10.1037/0096-1523.24.1.322

Cited by 17 publications

(20 citation statements)

References 59 publications

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“…Good examples are colors varying in brightness and saturation, or tones varying in loudness and pitch. Nosofsky (1987Nosofsky ( , 1998 and McKinley and Nosofsky (1996) provided evidence that when observers learn to classify integral-dimension stimuli, they fail to form orthogonal linear boundaries along single dimensions, even when such boundaries would produce nearly optimal performance. Instead, the patterns of performance observed under such conditions are more consistent with the idea that similarity comparisons to stored exemplars drive classification (McKinley & Nosofsky, 1996;Nosofsky & Palmeri, 1997).…”

Section: Discussionmentioning

confidence: 99%

“…In the context of criticizing an article by McKinley and Nosofsky (1996), Maddox and Ashby (1998) have also argued that model fits involving only averaged data can be misleading. While expressing fundamental agreement with this general point, Nosofsky (1998) replied that the particular criticisms raised by Maddox and Ashby (1998) were misguided. See Maddox and Ashby (1998) and Nosofsky (1998) for details regarding this particular debate.…”

Section: Notesmentioning

confidence: 99%

“…While expressing fundamental agreement with this general point, Nosofsky (1998) replied that the particular criticisms raised by Maddox and Ashby (1998) were misguided. See Maddox and Ashby (1998) and Nosofsky (1998) for details regarding this particular debate.…”

Section: Notesmentioning

confidence: 99%

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A rule-plus-exception model for classifying objects in continuous-dimension spaces

Nosofsky

Palmeri

1998

Psychonomic Bulletin & Review

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125

102

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The authors propose a rule-plus-exception (RULEX) model for how observers classify stimuli residing in continuous-dimension spaces. The model follows in the spirit of the discrete-dimension version of RULEX developed by . According to the model, observers learn categories by forming simple logical rules along single dimensions and by remembering occasional exceptions to those rules. In the continuous-dimension version of RULEX, the rules are formalized in terms of linear decision boundaries that are orthogonal to the coordinate axes of the psychological space. In addition, a similarity-comparison process governs whether stored exceptions are used to classify an object. The model provides excellent quantitative fits both to averaged classification transfer data and to distributions of generalizations observed at the individual-participant level. The modeling analyses suggest that, when multiple rules are available for solving a problem, averaged classification data often represent a probabilistic mixture of idiosyncratic rule-plus-exception strategies.

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Section: Discussionmentioning

confidence: 99%

Section: Notesmentioning

confidence: 99%

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A rule-plus-exception model for classifying objects in continuous-dimension spaces

Nosofsky

Palmeri

1998

Psychonomic Bulletin & Review

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125

102

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“…A bivariate normal distribution is described by a mean and variance along each dimension, as well as a covariance term, /lx' /lv' cr}, cr~, cov x v ' where the subscripts x and y denote dimensions x and y. Figure 1 depicts hypothetical equal likelihood contours for four tifiable, from the parameters that define the decision process (see Nosofsky, 1998, for a discussion). For example, the attention weight parameter, W, in the generalized context model modifies the similarity relations among items in the psychological space and thus has a strong effect on the equal similarity contour that separates the psychological space into two regions-c-one in which the probability ofresponding "A" is greater than .5 and the other in which the probability is less than .5.…”

Section: Effects Of Perceptual Representation On Categorization Perfomentioning

confidence: 99%

On the relation between decision rules and perceptual representation in multidimensional perceptual categorization

Maddox

Bogdanov

2000

Perception & Psychophysics

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This article examines the relation between changing categorization decision rules and the nature of the underlying perceptual representation. Observers completed a matching task that required them to adjust the length and orientation of a single line stimulus until they perceived it to "match" a second line stimulus (Alfonso-Reese, 1996. The same observers then completed four categorization tasks with the same stimuli. Data from the matching task were used to estimate a perceptual representation for each stimulus and observer. Three hypotheses regarding potential interactions between categorization decision rules and perceptual representation were examined. One assumed that there was no interaction between decision rules and perceptual representation. The second assumed that linear categorization rules affect the perceptual representation differently from nonlinear categorization rules. The third assumed that dimensional integration rules affected the perceptual representation differently from decision rules that require the observer to set a criterion along one stimulus dimension while ignoring the other; this is referred to as decisional selective attention. The results suggested that (l) the matching task perceptual representation provided a good account of the categorization data, (2) decisional selective attention affected the perceptual representation differently from decisional integration, and (3) decisional selective attention generally decreased the perceptual variability along the attended dimension.Categorization is a primary component of many behaviors ofall organisms (Alcock, 1989). In general, each category exemplar can be decomposed into a set of values along multiple basic stimulus dimensions, each of which is continuous rather than binary valued (e.g., Ashby, 1992a;. For example, category exemplars may vary along the dimensions of size, length, orientation, color, location, frequency, and amplitude. Because each dimension is processed differently by the perceptual system, it is important to understand the nature of the perceptual representation and how it affects categorization performance (Alfonso- Reese, 1997;Ashby & Lee, 1991;Nosofsky, 1986). Conversely, recent research suggests that the act of categorization might alter the structure of the perceptual representation (e.g., Ashby & Lee, 1991;Goldstone, 1994;Nosofsky, 1986). In particular, different categorization rules might alter the structure of the perceptual representation in different ways. This article addresses both of these issues within a single exThis research was supported in part by National Science Foundation Grant SBR-9796206 and NIH Grant ROI MH59196. We thank Helena Kadlec, Robin Thomas, and an anonymous reviewer for helpful comments on an earlier draft ofthis manuscript. We also thank Greg Ashby, Leslie Cohen, Randy Diehl, Bill Geisler, David Gilden, Art Markman, and Tom Thornton for discussions that influenced this work. Correspondence should be addressed to W. T. Maddox, Department of Psychology, Mezes Hall 330, Universit...

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“…In the two category structures where both dimensions are relevant, there is overwhelming evidence for the implementation of the GCM using uniform priors. This implies that, in these conditions, participants do not seem to allocate their attention optimally over both of the stimulus dimensions (Nosofsky, 1998b;Nosofsky & Johansen, 2000). These conclusions are consistent with those of Nosofsky (1989), made on the basis of point parameter estimates found by fitting the GCM without explicit priors on parameters.…”

Section: Discussionmentioning

confidence: 99%

Using priors to formalize theory: Optimal attention and the generalized context model

Vanpaemel

Lee

2012

Psychon Bull Rev

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Formal models in psychology are used to make theoretical ideas precise and allow them to be evaluated quantitatively against data. We focus on one important-but underused and incorrectly maligned-method for building theoretical assumptions into formal models, offered by the Bayesian statistical approach. This method involves capturing theoretical assumptions about the psychological variables in models by placing informative prior distributions on the parameters representing those variables. We demonstrate this approach of casting basic theoretical assumptions in an informative prior by considering a case study that involves the generalized context model (GCM) of category learning. We capture existing theorizing about the optimal allocation of attention in an informative prior distribution to yield a model that is higher in psychological content and lower in complexity than the standard implementation. We also highlight that formalizing psychological theory within an informative prior distribution allows standard Bayesian model selection methods to be applied without concerns about the sensitivity of results to the prior. We then use Bayesian model selection to test the theoretical assumptions about optimal allocation formalized in the prior. We argue that the general approach of using psychological theory to guide the specification of informative prior distributions is widely applicable and should be routinely used in psychological modeling.

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Selective attention and the formation of linear decision boundaries: Reply to Maddox and Ashby (1998).

Cited by 17 publications

References 59 publications

A rule-plus-exception model for classifying objects in continuous-dimension spaces

A rule-plus-exception model for classifying objects in continuous-dimension spaces

On the relation between decision rules and perceptual representation in multidimensional perceptual categorization

Using priors to formalize theory: Optimal attention and the generalized context model

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