Correlated racing evidence accumulator models

Reynolds, Angus; Kvam, Peter D.; Osth, Adam F; Heathcote, Andrew

doi:10.1016/j.jmp.2020.102331

Cited by 11 publications

(16 citation statements)

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“…There is less agreement on the mechanisms supporting metacognitive judgments of confidence about such decisions (Yeung & Summerfield, 2014). Although various confidence mechanisms have been proposed, they differ drastically in their nature, from Vickers's balance of evidence, which is based on a nonnormative race model of choice (Vickers, 1979; see also De Martino et al, 2013;Merkle & Van Zandt, 2006;Reynolds et al, 2020), to the more recent two-stage, dynamic signal detection theory (SDT) model (Pleskac & Busemeyer, 2010), which is based on a normative, integration-toboundary choice model. One problem with the latter type of models is that if evidence continues to be collected until the integrated evidence reaches a constant boundary (corresponding to the expected posterior probability; Fig.…”

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confidence: 99%

The Cognition/Metacognition Trade-Off

et al. 2022

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Integration to boundary is an optimal decision algorithm that accumulates evidence until the posterior reaches a decision boundary, resulting in the fastest decisions for a target accuracy. Here, we demonstrated that this advantage incurs a cost in metacognitive accuracy (confidence), generating a cognition/metacognition trade-off. Using computational modeling, we found that integration to a fixed boundary results in less variability in evidence integration and thus reduces metacognitive accuracy, compared with a collapsing-boundary or a random-timer strategy. We examined how decision strategy affects metacognitive accuracy in three cross-domain experiments, in which 102 university students completed a free-response session (evidence terminated by the participant’s response) and an interrogation session (fixed number of evidence samples controlled by the experimenter). In both sessions, participants observed a sequence of evidence and reported their choice and confidence. As predicted, the interrogation protocol (preventing integration to boundary) enhanced metacognitive accuracy. We also found that in the free-response sessions, participants integrated evidence to a collapsing boundary—a strategy that achieves an efficient compromise between optimizing choice and metacognitive accuracy.

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confidence: 99%

The Cognition/Metacognition Trade-Off

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“…MULTIPLY ANCHORED ACCUMULATION THEORY scenarios where the number of responses is very large. To yield an approach that simultaneously handles both continuous and discrete responses, we instead base our new model on the geometric (Kvam, 2019a) and multiple threshold race (Reynolds, Garton, et al, 2021;Reynolds, Kvam, et al, 2020) frameworks for modeling dynamic choice.…”

Section: Model Overviewmentioning

confidence: 99%

“…There have been a number of proposals for how response boundaries can be used to map a small number of accumulators onto a greater number of responses, which we examine in Supplemental Materials. Here, we focus on the circular boundary model shown in Figure 1, which corresponds to the asymptotic limit of both the multiple threshold race (Reynolds, Garton, et al, 2021;Reynolds, Kvam, et al, 2020) and the geometric framework for modeling decisionmaking (Kvam, 2019a;Kvam & Turner, 2021). A single boundary allows discrete and continuous cases to use a commensurate stopping rule, as with the circular diffusion model (Smith, 2019;Smith & Corbett, 2019).…”

Section: Response Time and Response Selectionmentioning

confidence: 99%

“…Likert (1932) scales have a long history of extensive use in such areas, but there are many known limitations of such discrete measures (Paulhus, 1991). The addition of a continuous measure like response time or confidence, or additional responses like best-worst rankings, provide richer insights into the cognitive processes underlying responses and allow a researcher to make inferences that are not possible with simple binary choice data (Hawkins et al, 2014; Louviere et al, 2015; Reynolds, Kvam, et al, 2020). Of course, the degree to which we can determine whether the true underlying constructs we seek to measure are discrete or continuous is a major challenge (Luce, 1997), and there are cases like item response theory where we would like to use a discrete scale because the different levels of a continuum cannot be fully distinguished (Hambleton & Swaminathan, 2013).…”

Section: Extrapolating To the Continuummentioning

confidence: 99%

“…The main hurdle to overcome with respect to previous models it that they associate a unique accumulator (and corresponding accumulation rate and threshold) with each possible response, which is difficult to translate to scenarios where the number of responses is very large. To yield an approach that simultaneously handles both continuous and discrete responses, we instead base our new model on the geometric (Kvam, 2019a) and multiple threshold race (Reynolds, Garton, et al, 2021; Reynolds, Kvam, et al, 2020) frameworks for modeling dynamic choice.…”

Section: Model Overviewmentioning

confidence: 99%

See 2 more Smart Citations

A unified theory of discrete and continuous responding.

Kvam¹,

Marley²,

Heathcote³

2023

Psychological Review

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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 onto continuous response scales. It proposes that the mapping from a stimulus to an internal representation and then 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 among them, and compared the outcomes to continuous response conditions. We show that MAAT accounts for several key phenomena: more accurate, faster, and more skewed distributions of responses near the ends of a response scale; lower accuracy and slower responses as the number of discrete choice options increases; and longer response times and lower accuracy when alternative responses are more similar to the target response. 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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Evaluating false positive rates of standard and hierarchical measures of metacognitive accuracy

Rausch,

Zehetleitner

2023

Metacognition Learning

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A key aspect of metacognition is metacognitive accuracy, i.e., the degree to which confidence judgments differentiate between correct and incorrect trials. To quantify metacognitive accuracy, researchers are faced with an increasing number of different methods. The present study investigated false positive rates associated with various measures of metacognitive accuracy by hierarchical resampling from the confidence database to accurately represent the statistical properties of confidence judgements. We found that most measures based on the computation of summary-statistics separately for each participant and subsequent group-level analysis performed adequately in terms of false positive rate, including gamma correlations, meta-d′, and the area under type 2 ROC curves. Meta-d′/d′ is associated with a false positive rate even below 5%, but log-transformed meta-d′/d′ performs adequately. The false positive rate of HMeta-d depends on the study design and on prior specification: For group designs, the false positive rate is above 5% when independent priors are placed on both groups, but the false positive rate is adequate when a prior was placed on the difference between groups. For continuous predictor variables, default priors resulted in a false positive rate below 5%, but the false positive rate was not distinguishable from 5% when close-to-flat priors were used. Logistic mixed model regression analysis is associated with dramatically inflated false positive rates when random slopes are omitted from model specification. In general, we argue that no measure of metacognitive accuracy should be used unless the false positive rate has been demonstrated to be adequate.

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Correlated racing evidence accumulator models

Abstract: Many models of response time that base choices on the first evidence accumulator to win a race to threshold rely on statistical independence between accumulators to achieve mathematical tractability (e.g.,

Cited by 11 publications

References 50 publications

The Cognition/Metacognition Trade-Off

The Cognition/Metacognition Trade-Off

A unified theory of discrete and continuous responding.

Evaluating false positive rates of standard and hierarchical measures of metacognitive accuracy

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