How to Assess the Existence of Competing Strategies in Cognitive Tasks: A Primer on the Fixed-Point Property
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{"title"=>"How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property", "type"=>"journal", "authors"=>[{"first_name"=>"Leendert", "last_name"=>"Van Maanen", "scopus_author_id"=>"21740137700"}, {"first_name"=>"Ritske", "last_name"=>"De Jong", "scopus_author_id"=>"7201415283"}, {"first_name"=>"Hedderik", "last_name"=>"Van Rijn", "scopus_author_id"=>"21740285500"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "scopus"=>"2-s2.0-84940335105", "pui"=>"373867512", "doi"=>"10.1371/journal.pone.0106113", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "sgr"=>"84940335105", "pmid"=>"25170893"}, "id"=>"464688d9-83ec-3272-807d-fb80ccf05c26", "abstract"=>"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.", "link"=>"http://www.mendeley.com/research/assess-existence-competing-strategies-cognitive-tasks-primer-fixedpoint-property", "reader_count"=>13, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>1, "Researcher"=>3, "Student > Ph. D. Student"=>4, "Student > Master"=>1, "Student > Bachelor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>1, "Researcher"=>3, "Student > Ph. D. Student"=>4, "Student > Master"=>1, "Student > Bachelor"=>3}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Medicine and Dentistry"=>3, "Agricultural and Biological Sciences"=>2, "Neuroscience"=>2, "Philosophy"=>1, "Psychology"=>4}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Neuroscience"=>{"Neuroscience"=>2}, "Psychology"=>{"Psychology"=>4}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Unspecified"=>{"Unspecified"=>1}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"Hungary"=>1}, "group_count"=>0}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1656291"], "description"=>"<p>Bayes factors (A) and F statistics (B) differ with the number of observations (lines) and the standard deviation of the Gaussian kernel. (C) The precision of the estimated crossing points varies with the number of observations. obs: the number of observations (i.e., repeated measures).</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156640, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g006", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bayes_factors_F_statistics_and_precision_as_a_function_of_the_number_of_observations_and_kernel_width_/1156640", "title"=>"Bayes factors, F statistics and precision as a function of the number of observations and kernel width.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656285"], "description"=>"<p>(A) Bayes factors for mixture data (solid black line) and shifted data (dashed red line). (B) F-values for mixture data (solid black line) and shifted data (dashed red line). (C) The average differences between the crossing points for mixture data (solid black lines) and shifted data (dashed red lines). (D) Base distributions of Simulation 2. Solid line represents Process 1, dashed lines represent alternatives of Process 2. In particular, the dashed lines represent the smallest <i>d'</i>, the largest <i>d'</i>, and the smallest <i>d'</i> for which the BF of the shifted distribution is larger than 1. (E) .5 mixture distribution (solid black line) and the middle shifted distribution (dashed red line) for the smallest <i>d'</i> for which the BF of the shifted distribution is larger than 1. For reference, the base distributions are also displayed (dotted lines). (F) Density differences of the three observed mixture distributions (black lines) and the three observed shift distributions for the smallest <i>d'</i> for which the BF of the shifted distribution is larger than 1. The solid black line represents the density difference between the base distributions, which is equal for the mixture and shift data. Because the mixture proportion is .5, the density differences of the base distributions with the third distribution are equal and the dashed black line represents both.</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156634, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g004", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_range_of_base_distributions_for_which_the_fixed_point_property_can_be_computed_Simulation_2_/1156634", "title"=>"The range of base distributions for which the fixed-point property can be computed (Simulation 2).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656294"], "description"=>"<p>Averaged density (A, D) density difference curves (B, E), and boxplots for the distributions of crossing points (C, F) for the data from De Jong (2000), Experiment 2. The top row (A, B, C) shows the short blocks, the bottom row (D, E, F) shows the long blocks.</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156643, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g007", "stats"=>{"downloads"=>0, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Averaged_density_density_differences_and_crossing_points_for_De_Jong_2000_Experiment_2_/1156643", "title"=>"Averaged density, density differences, and crossing points for De Jong (2000), Experiment 2.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656274"], "description"=>"<p>Panel A shows density plots for two base distributions. The blue line reflects an RT distribution for Strategy 1 (d1), with a mean of 500 ms and a standard deviation of 100, the red line an RT distribution (d2) for Strategy 2 (mean = 600, SD = 150). Panel B shows three mixtures of the two base distributions with mixture proportions as indicated in the legend. The vertical line shown in both panels is drawn at the common coordinate or fixed-point at ∼590 ms.</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156623, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g001", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_fixed_point_property_/1156623", "title"=>"Illustration of the fixed-point property.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656275"], "description"=>"<p>Probability density (A, C) and density difference (B, D) for data with (A, B) and without (C, D) a fixed-point. The densities in A correspond to binary mixture distributions with mixture proportions of .1 (black line), .3 (red line), and .9 (green line), respectively. The densities in C correspond to shifted distributions with mean <i>µ<sub>1</sub> = 1.2</i> (black line), <i>µ<sub>2</sub> = 1.6</i> (red line), and <i>µ<sub>3</sub> = 2.8</i> (green line). The solid lines in B and D indicate the difference between the black and red lines in A and C; the dashed lines indicate the difference between the black and green lines; the dotted lines indicate the difference between the red and green lines. The vertical lines in B and D indicate the location of the crossing points.</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156624, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g002", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Probability_density_and_density_difference_for_data_with_and_without_a_fixed_point_/1156624", "title"=>"Probability density and density difference for data with and without a fixed-point.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656287"], "description"=>"<p>Bayes factors (A) and F statistics (B) differ with sample size (lines) and the standard deviation of the Gaussian kernel. (C) The precision of the estimated crossing points does not vary with sample size. samp: sample size (i.e., the number of participants).</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156636, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g005", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bayes_factors_F_statistics_and_precision_as_a_function_of_sample_size_and_kernel_width_/1156636", "title"=>"Bayes factors, F statistics and precision as a function of sample size and kernel width.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656280"], "description"=>"<p>Averaged density (A), density difference curves (B), and boxplots for the distributions of crossing points (C) for the data from Simulation 1.</p>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156630, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113.g003", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Averaged_density_density_differences_and_crossing_points_for_Simulation_1_/1156630", "title"=>"Averaged density, density differences, and crossing points for Simulation 1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-08-29 03:15:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1656295"], "description"=>"<div><p>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.</p></div>", "links"=>[], "tags"=>["probability", "R package", "response time distributions", "reaction time", "Cognitive Tasks", "response time data", "strategy", "base distributions", "Response times", "use tests", "mixture proportion"], "article_id"=>1156644, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Leendert van Maanen", "Ritske de Jong", "Hedderik van Rijn"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106113", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_How_to_Assess_the_Existence_of_Competing_Strategies_in_Cognitive_Tasks_A_Primer_on_the_Fixed_Point_Property_/1156644", "title"=>"How to Assess the Existence of Competing Strategies in Cognitive Tasks: A Primer on the Fixed-Point Property", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-08-29 03:15:24"}

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{"start_date"=>"2014-01-01T00:00:00Z", "end_date"=>"2014-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Behavior", "average_usage"=>[333]}]}
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