Perhaps Unidimensional Is Not Unidimensional

Dodds, Pennie; Rae, Babette; Brown, Scott

doi:10.1111/cogs.12003

Cited by 2 publications

(2 citation statements)

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“…The accumulation process laid out here and shown in Figure 2 can be mimicked by a correlated multiple-accumulator LBA (see Kvam, 2019a, , Figure 8), which can be implemented by a simple neural circuit (Tajima et al, 2019, , supplementary note 3). Certainly, the model can be informed by a better understanding of the similarity relations between the available responses, which may suggest that (for example) edge categories are more distinct or that the underlying construct does not map onto a purely unidimensional representation (Dodds et al, 2012;Kvam & Turner, 2021). Converging evidence from behavioral approaches like multidimensional scaling (Shepard, 1962) and neural similarity measures like representational similarity analysis or neural decoding rates (Kriegeskorte et al, 2008;Raizada & Connolly, 2012) should shed light on better ways to translate physical stimuli into psychological representations that can be incorporated into a model like ours.…”

Section: Figure 15mentioning

confidence: 99%

A unified theory of discrete and continuous responding

Kvam¹,

Marley²,

Heathcote³

2021

Preprint

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Understanding the cognitive processes underlying choice requires theories that can disentangle the representation of stimuli from the processes that map these representations onto observed responses. We develop a dynamic theory of how stimuli are mapped onto discrete (choice) and continuous response scales. It proposes that the mapping from stimuli to the input to an evidence accumulation process is accomplished using multiple reference points or "anchors". Evidence is accumulated until a threshold amount for a particular response is obtained, with the relative balance of support for each anchor at that time determining the response. We tested this Multiple Anchored Accumulation Theory (MAAT) using the results of two experiments requiring discrete or continuous responses to line length and color stimuli. We manipulated the number of options for discrete responses, the number of different stimuli, and the similarity amongst them, and compared the outcomes to continuous response conditions. We show that MAAT accounts for several key phenomena: more accurate choices and more skewed response distributions near the ends of a response scale; a decrease in accuracy and response speed as the number of discrete choice options increases; and longer response times and lower accuracy when discrete responses were more similar to one another. Our empirical and modeling results suggest that discrete and continuous response tasks can share a common evidence representation, and that the decision process is sensitive to the perceived similarity among the response options.

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Section: Figure 15mentioning

confidence: 99%

A unified theory of discrete and continuous responding

Kvam¹,

Marley²,

Heathcote³

2021

Preprint

View full text Add to dashboard Cite

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“…Work byDodds et al (2012) has actually suggested that the ends of some scales may come back around and become more similar to one another, creating a sort of 'ring' shape to the similarity between alternatives. This is easily handled…”

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confidence: 99%

A geometric framework for modeling dynamic decisions among arbitrarily many alternatives

Kvam

2019

Journal of Mathematical Psychology

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Multiple-choice and continuous-response tasks pose a number of challenges for models of the decision process, from empirical challenges like context effects to computational demands imposed by choice sets with a large number of outcomes. This paper develops a general framework for constructing models of the cognitive processes underlying both inferential and preferential choice among any arbitrarily large number of alternatives. This geometric approach represents the alternatives in a choice set along with a decision maker's beliefs or preferences in a "decision space," simultaneously capturing the support for different alternatives along with the similarity relations between the alternatives in the choice set. Support for the alternatives (represented as vectors) shifts over time according to the dynamics of the belief / preference state (represented as a point) until a stopping rule is met (state crosses a hyperplane) and the corresponding selection is made. This paper presents stopping rules that guarantee optimality in multi-alternative inferential choice, minimizing response time for a desired level of accuracy, as well as methods for constructing the decision space, which can result in context effects when applied to preferential choice.

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Perhaps Unidimensional Is Not Unidimensional

Cited by 2 publications

References 30 publications

A unified theory of discrete and continuous responding

A unified theory of discrete and continuous responding

A geometric framework for modeling dynamic decisions among arbitrarily many alternatives

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