
Contents
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Introduction Introduction
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General Recognition Theory General Recognition Theory
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The Multivariate Normal Model The Multivariate Normal Model
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Applying GRT to Data Applying GRT to Data
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Fitting the GRT Model to Identification Data Fitting the GRT Model to Identification Data
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Computing the Likelihood Function Computing the Likelihood Function
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Estimating the Parameters Estimating the Parameters
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Evaluating Goodness of Fit Evaluating Goodness of Fit
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The Summary Statistics Approach The Summary Statistics Approach
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Macro-Analyses Macro-Analyses
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Micro-Analyses Micro-Analyses
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An Empirical Example An Empirical Example
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Extensions to Response Time Extensions to Response Time
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The RT-Distance Hypothesis The RT-Distance Hypothesis
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Process Models of RT Process Models of RT
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Neural Implementations of GRT Neural Implementations of GRT
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Conclusions Conclusions
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Acknowledgments Acknowledgments
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Note Note
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Glossary Glossary
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References References
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2 Multidimensional Signal Detection Theory
Get accessF. Gregory Ashby Department of Psychological & Brain Sciences University of California Santa Barbara, CA
Fabian A. Soto Department of Psychological & Brain Sciences University of California Santa Barbara, CA
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Published:10 December 2015
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Abstract
Multidimensional signal detection theory is a multivariate extension of signal detection theory that makes two fundamental assumptions, namely that every mental state is noisy and that every action requires a decision. The most widely studied version is known as general recognition theory (GRT). General recognition theory assumes that the percept on each trial can be modeled as a random sample from a multivariate probability distribution defined over the perceptual space. Decision bounds divide this space into regions that are each associated with a response alternative. General recognition theory rigorously defines and tests a number of important perceptual and cognitive conditions, including perceptual and decisional separability and perceptual independence. General recognition theory has been used to analyze data from identification experiments in two ways: (1) fitting and comparing models that make different assumptions about perceptual and decisional processing, and (2) testing assumptions by computing summary statistics and checking whether these satisfy certain conditions. Much has been learned recently about the neural networks that mediate the perceptual and decisional processing modeled by GRT, and this knowledge can be used to improve the design of experiments where a GRT analysis is anticipated.
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