Evaluation of Jackknife and Bootstrap for Defining Confidence Intervals for Pairwise Agreement Measures
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{"title"=>"Evaluation of Jackknife and Bootstrap for defining confidence intervals for pairwise agreement measures", "type"=>"journal", "authors"=>[{"first_name"=>"Ana", "last_name"=>"Severiano", "scopus_author_id"=>"37666063000"}, {"first_name"=>"João A.", "last_name"=>"Carriço", "scopus_author_id"=>"8266333200"}, {"first_name"=>"D. Ashley", "last_name"=>"Robinson", "scopus_author_id"=>"8570567000"}, {"first_name"=>"Mário", "last_name"=>"Ramirez", "scopus_author_id"=>"7201568476"}, {"first_name"=>"Francisco R.", "last_name"=>"Pinto", "scopus_author_id"=>"8060679500"}], "year"=>2011, "source"=>"PLoS ONE", "identifiers"=>{"sgr"=>"79956190902", "doi"=>"10.1371/journal.pone.0019539", "pui"=>"361789527", "pmid"=>"21611165", "scopus"=>"2-s2.0-79956190902", "issn"=>"19326203"}, "id"=>"090f3e7f-410f-3ea6-9000-09126ab364ca", "abstract"=>"Several research fields frequently deal with the analysis of diverse classification results of the same entities. This should imply an objective detection of overlaps and divergences between the formed clusters. The congruence between classifications can be quantified by clustering agreement measures, including pairwise agreement measures. Several measures have been proposed and the importance of obtaining confidence intervals for the point estimate in the comparison of these measures has been highlighted. A broad range of methods can be used for the estimation of confidence intervals. However, evidence is lacking about what are the appropriate methods for the calculation of confidence intervals for most clustering agreement measures. Here we evaluate the resampling techniques of bootstrap and jackknife for the calculation of the confidence intervals for clustering agreement measures. Contrary to what has been shown for some statistics, simulations showed that the jackknife performs better than the bootstrap at accurately estimating confidence intervals for pairwise agreement measures, especially when the agreement between partitions is low. The coverage of the jackknife confidence interval is robust to changes in cluster number and cluster size distribution.", "link"=>"http://www.mendeley.com/research/evaluation-jackknife-bootstrap-defining-confidence-intervals-pairwise-agreement-measures", "reader_count"=>43, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>2, "Student > Doctoral Student"=>1, "Researcher"=>6, "Student > Ph. D. Student"=>17, "Student > Postgraduate"=>3, "Student > Master"=>7, "Student > Bachelor"=>4, "Lecturer > Senior Lecturer"=>1, "Professor"=>2}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>2, "Student > Doctoral Student"=>1, "Researcher"=>6, "Student > Ph. D. Student"=>17, "Student > Postgraduate"=>3, "Student > Master"=>7, "Student > Bachelor"=>4, "Lecturer > Senior Lecturer"=>1, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Agricultural and Biological Sciences"=>18, "Veterinary Science and Veterinary Medicine"=>1, "Chemistry"=>1, "Computer Science"=>5, "Engineering"=>2, "Environmental Science"=>3, "Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>1, "Medicine and Dentistry"=>2, "Neuroscience"=>2, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Psychology"=>3}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Psychology"=>{"Psychology"=>3}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>1}, "Environmental Science"=>{"Environmental Science"=>3}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Engineering"=>{"Engineering"=>2}, "Chemistry"=>{"Chemistry"=>1}, "Neuroscience"=>{"Neuroscience"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>18}, "Computer Science"=>{"Computer Science"=>5}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>1}}, "reader_count_by_country"=>{"United States"=>3, "Brazil"=>2, "United Kingdom"=>2, "France"=>1, "Portugal"=>2, "Switzerland"=>1, "India"=>1}, "group_count"=>3}

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Figshare

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  • {"files"=>["https://ndownloader.figshare.com/files/773328"], "description"=>"<p><i>n<sub>ij</sub></i> denotes the number of objects that are common to clusters <i>A<sub>i</sub></i> and <i>B<sub>j</sub></i>.</p>", "links"=>[], "tags"=>["mathematics"], "article_id"=>443701, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Contingency_table_CT_/443701", "title"=>"Contingency table (<i>CT</i>).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-05-18 01:01:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/388521", "https://ndownloader.figshare.com/files/388603", "https://ndownloader.figshare.com/files/388665", "https://ndownloader.figshare.com/files/388710", "https://ndownloader.figshare.com/files/388746", "https://ndownloader.figshare.com/files/388792", "https://ndownloader.figshare.com/files/388843", "https://ndownloader.figshare.com/files/388886", "https://ndownloader.figshare.com/files/388931"], "description"=>"<div><p>Several research fields frequently deal with the analysis of diverse classification results of the same entities. This should imply an objective detection of overlaps and divergences between the formed clusters. The congruence between classifications can be quantified by clustering agreement measures, including pairwise agreement measures. Several measures have been proposed and the importance of obtaining confidence intervals for the point estimate in the comparison of these measures has been highlighted. A broad range of methods can be used for the estimation of confidence intervals. However, evidence is lacking about what are the appropriate methods for the calculation of confidence intervals for most clustering agreement measures. Here we evaluate the resampling techniques of bootstrap and jackknife for the calculation of the confidence intervals for clustering agreement measures. Contrary to what has been shown for some statistics, simulations showed that the jackknife performs better than the bootstrap at accurately estimating confidence intervals for pairwise agreement measures, especially when the agreement between partitions is low. The coverage of the jackknife confidence interval is robust to changes in cluster number and cluster size distribution.</p> </div>", "links"=>[], "tags"=>["jackknife", "bootstrap", "defining", "intervals", "pairwise", "measures"], "article_id"=>136724, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0019539.s001", "https://dx.doi.org/10.1371/journal.pone.0019539.s002", "https://dx.doi.org/10.1371/journal.pone.0019539.s003", "https://dx.doi.org/10.1371/journal.pone.0019539.s004", "https://dx.doi.org/10.1371/journal.pone.0019539.s005", "https://dx.doi.org/10.1371/journal.pone.0019539.s006", "https://dx.doi.org/10.1371/journal.pone.0019539.s007", "https://dx.doi.org/10.1371/journal.pone.0019539.s008", "https://dx.doi.org/10.1371/journal.pone.0019539.s009"], "stats"=>{"downloads"=>9, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Evaluation_of_Jackknife_and_Bootstrap_for_Defining_Confidence_Intervals_for_Pairwise_Agreement_Measures/136724", "title"=>"Evaluation of Jackknife and Bootstrap for Defining Confidence Intervals for Pairwise Agreement Measures", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2011-05-18 01:52:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/774025"], "description"=>"<p>Pairwise agreement measures.</p>", "links"=>[], "tags"=>["mathematics"], "article_id"=>444400, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.t001", "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pairwise_agreement_measures_/444400", "title"=>"Pairwise agreement measures.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-05-18 01:13:20"}
  • {"files"=>["https://ndownloader.figshare.com/files/773659"], "description"=>"<p>Rows refer to the methods by which the CIs were calculated. From top to the bottom: analytical formula, bootstrap percentile, bootstrap BC<i>a</i> method method and jackknife. Each dot represents a simulated population (PFT), with a particular set of parameters, and the average amplitude of the CIs for 1000 samples from the population (CTs). Symbols and colors represent changes in: dimensions of the simulated probability tables, corresponding to the number of clusters in each of the two classifications (left); exponent <i>alpha</i> of the Zipfian distribution determining the distribution of row cluster sizes of the simulated probability tables (middle); sample size or number of elements in the contingency tables (right).</p>", "links"=>[], "tags"=>["amplitudes", "intervals", "wallace"], "article_id"=>444028, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.g005", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_amplitudes_of_95_confidence_intervals_for_the_Wallace_coefficient_/444028", "title"=>"Average amplitudes of 95% confidence intervals for the Wallace coefficient.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-05-18 01:07:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/773911"], "description"=>"<p>Rows refer to the methods by which the CIs were calculated. From top to the bottom: bootstrap percentile method, bootstrap BC<i>a</i> method and jackknife. Each dot represents a simulated population (PFT), with a particular set of parameters, and the average amplitude of the CIs for 1000 samples from the population (CTs). Symbols and colors represent changes in: dimensions of the simulated probability tables, corresponding to the number of clusters in each of the two classifications (left); exponent <i>alpha</i> of the Zipfian distribution determining the distribution of row cluster sizes of the simulated probability tables (middle); sample size or number of elements in the contingency tables (right).</p>", "links"=>[], "tags"=>["amplitudes", "intervals", "adjusted"], "article_id"=>444277, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.g007", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_amplitudes_of_95_confidence_intervals_for_the_adjusted_Rand_/444277", "title"=>"Average amplitudes of 95% confidence intervals for the adjusted Rand.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-05-18 01:11:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/773782"], "description"=>"<p>Rows refer to the methods by which the CIs were calculated. From top to the bottom: bootstrap percentile method, bootstrap BC<i>a</i> method and jackknife. Each dot represents a simulated population (PFT), with a particular set of parameters, and 1000 samples from the population (CTs). Symbols and colors represent changes in: dimensions of the simulated probability tables, corresponding to the number of clusters in each of the two classifications (left); exponent <i>alpha</i> of the Zipfian distribution determining the distribution of row cluster sizes of the simulated probability tables (middle); sample size or number of elements in the contingency tables (right).</p>", "links"=>[], "tags"=>["intervals", "adjusted"], "article_id"=>444152, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.g006", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Coverages_of_95_confidence_intervals_for_adjusted_Rand_/444152", "title"=>"Coverages of 95% confidence intervals for adjusted Rand.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-05-18 01:09:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/773381"], "description"=>"<p><i>a</i>, <i>b</i>, <i>c</i> and <i>d</i> represent counts of unique entity pairs.</p>", "links"=>[], "tags"=>["mathematics"], "article_id"=>443756, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.g002", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mismatch_Matrix_/443756", "title"=>"Mismatch Matrix.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-05-18 01:02:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/773440"], "description"=>"<p>The parameters <i>R</i>, <i>C</i>, <i>alpha</i> and <i>beta</i> are used to generate a PFT, determining the number of rows, columns and the distribution of cluster size along rows and columns. The population parameter is calculated from the PFT. The sampling process is simulated generating 1000 CTs with <i>N</i> elements. The confidence interval is calculated for each one of the CTs. Finally, the coverage is calculated as the fraction of confidence intervals including the population estimate. An average amplitude of the 1000 CIs is also calculated.</p>", "links"=>[], "tags"=>["amplitude"], "article_id"=>443812, "categories"=>["Mathematics"], "users"=>["Ana Severiano", "João A. Carriço", "D. Ashley Robinson", "Mário Ramirez", "Francisco R. Pinto"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0019539.g003", "stats"=>{"downloads"=>9, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Method_used_to_calculate_the_coverage_and_average_amplitude_of_the_confidence_intervals_/443812", "title"=>"Method used to calculate the coverage and average amplitude of the confidence intervals.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-05-18 01:03:32"}

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Relative Metric

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