## The fixed-point property for competing strategies

When multiple strategies can be used to solve a type of problem, the observed response time distributions are often mixtures of multiple underlying base distributions each representing one of these strategies. For the case of two possible strategies, the observed response time distributions obey the fixed-point property. That is, there exists one reaction time that has the same probability of being observed irrespective of the actual mixture proportion of each strategy. In this paper we discuss how to compute this fixed-point, and how to statistically assess the probability that indeed the observed response times are generated by two competing strategies. Accompanying this paper is a free R package that can be used to compute and test the presence or absence of the fixed-point property in response time data, allowing for easy to use tests of strategic behavior.

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Download:
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The
fp package

The
online appendix
with a worked out example

The
paper
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How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property.
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Publications involving the fp package:
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Couto, J. ,
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Van Maanen, L.
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& Lebreton, M. (2020). Investigating the origin and consequences of endogenous default options in repeated economic choices.
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PLoS One 15
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, e023238.

Grange, J.A. (2016). Temporal distinctiveness in task switching: Assessing the mixture-distribution assumption.
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Frontiers in Psychology, 7,
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251

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Van Maanen, L.,
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Couto, J., & Lebreton, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data.
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PLOS One, 11, e0167377
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Van Maanen, L.
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(2016). Is there evidence for a mixture of processes in speed-accuracy trade-off behavior?
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Topics in Cognitive Sciences, 8,
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279-290

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Van Maanen, L.
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(2015). Speed-accuracy trade-off behavior: Response caution adjustment or mixing task strategies?
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Proceedings of the 13th International Conference for Cognitive Modeling
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Van Maanen, L
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., De Jong, R. & Van Rijn. H. (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property.
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PLOS One, 9,
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e106113.