Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.
The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixtu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2016-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC5125698?pdf=render |
| _version_ | 1819260510941478912 |
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| author | Leendert van Maanen Joaquina Couto Mael Lebreton |
| author_facet | Leendert van Maanen Joaquina Couto Mael Lebreton |
| author_sort | Leendert van Maanen |
| collection | DOAJ |
| description | The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes. |
| first_indexed | 2024-12-23T19:27:04Z |
| format | Article |
| id | doaj.art-74e213bcfbd141acacf166f85dba9bcf |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-23T19:27:04Z |
| publishDate | 2016-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-74e213bcfbd141acacf166f85dba9bcf2022-12-21T17:34:00ZengPublic Library of Science (PLoS)PLoS ONE1932-62032016-01-011111e016737710.1371/journal.pone.0167377Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.Leendert van MaanenJoaquina CoutoMael LebretonThe notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.http://europepmc.org/articles/PMC5125698?pdf=render |
| spellingShingle | Leendert van Maanen Joaquina Couto Mael Lebreton Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data. PLoS ONE |
| title | Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data. |
| title_full | Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data. |
| title_fullStr | Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data. |
| title_full_unstemmed | Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data. |
| title_short | Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data. |
| title_sort | three boundary conditions for computing the fixed point property in binary mixture data |
| url | http://europepmc.org/articles/PMC5125698?pdf=render |
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