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Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data

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  • Leendert van Maanen
  • Joaquina Couto
  • Mael Lebreton

Abstract

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.

Suggested Citation

  • Leendert van Maanen & Joaquina Couto & Mael Lebreton, 2016. "Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-11, November.
  • Handle: RePEc:plo:pone00:0167377
    DOI: 10.1371/journal.pone.0167377
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    References listed on IDEAS

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    1. David K. Levine & Drew Fudenberg, 2006. "A Dual-Self Model of Impulse Control," American Economic Review, American Economic Association, vol. 96(5), pages 1449-1476, December.
    2. Ian Krajbich & Björn Bartling & Todd Hare & Ernst Fehr, 2015. "Rethinking fast and slow based on a critique of reaction-time reverse inference," Nature Communications, Nature, vol. 6(1), pages 1-9, November.
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    Cited by:

    1. Joaquina Couto & Leendert van Maanen & Maël Lebreton, 2020. "Investigating the origin and consequences of endogenous default options in repeated economic choices," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-19, August.

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