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href="#Scientific_malpractice_and_flawed_methodology"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Scientific malpractice and flawed methodology</span> </div> </a> <ul id="toc-Scientific_malpractice_and_flawed_methodology-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Branch of statistics concerned with inferring causal relationships between variables</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about methodological causal inference. For the philosophy behind causal inference, see <a href="/wiki/Causal_reasoning" title="Causal reasoning">Causal reasoning</a>.</div> <p><b>Causal inference</b> is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of <a href="/wiki/Association_(statistics)" class="mw-redirect" title="Association (statistics)">association</a> is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed.<sup id="cite_ref-Pearl_Journal_1-0" class="reference"><a href="#cite_note-Pearl_Journal-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Morgan_book_2-0" class="reference"><a href="#cite_note-Morgan_book-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The study of why things occur is called <i><a href="/wiki/Etiology" title="Etiology">etiology</a></i>, and can be described using the language of <a href="/wiki/Causal_notation" title="Causal notation">scientific causal notation</a>. Causal inference is said to provide the evidence of causality theorized by <a href="/wiki/Causal_reasoning" title="Causal reasoning">causal reasoning</a>. </p><p>Causal inference is widely studied across all sciences. Several innovations in the development and implementation of methodology designed to determine causality have proliferated in recent decades. Causal inference remains especially difficult where experimentation is difficult or impossible, which is common throughout most sciences. </p><p>The approaches to causal inference are broadly applicable across all types of scientific disciplines, and many methods of causal inference that were designed for certain disciplines have found use in other disciplines. This article outlines the basic process behind causal inference and details some of the more conventional tests used across different disciplines; however, this should not be mistaken as a suggestion that these methods apply only to those disciplines, merely that they are the most commonly used in that discipline. </p><p>Causal inference is difficult to perform and there is significant debate amongst scientists about the proper way to determine causality. Despite other innovations, there remain concerns of misattribution by scientists of correlative results as causal, of the usage of incorrect methodologies by scientists, and of deliberate manipulation by scientists of analytical results in order to obtain statistically significant estimates. Particular concern is raised in the use of regression models, especially linear regression models. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Inferring the <a href="/wiki/Cause" class="mw-redirect" title="Cause">cause</a> of something has been described as: </p> <ul><li>"...reason[ing] to the conclusion that something is, or is likely to be, the cause of something else".<sup id="cite_ref-EB_3-0" class="reference"><a href="#cite_note-EB-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>"Identification of the cause or causes of a phenomenon, by establishing covariation of cause and effect, a time-order relationship with the cause preceding the effect, and the elimination of plausible alternative causes."<sup id="cite_ref-psy_4-0" class="reference"><a href="#cite_note-psy-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Methodology">Methodology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=2" title="Edit section: Methodology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="General">General</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=3" title="Edit section: General"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Causality" title="Causality">Causality</a> and <a href="/wiki/Causal_analysis" title="Causal analysis">Causal analysis</a></div> <p>Causal inference is conducted via the study of systems where the measure of one variable is suspected to affect the measure of another. Causal inference is conducted with regard to the <a href="/wiki/Scientific_method" title="Scientific method">scientific method</a>. The first step of causal inference is to formulate a falsifiable <a href="/wiki/Null_hypothesis" title="Null hypothesis">null hypothesis</a>, which is subsequently <a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">tested with statistical methods</a>. Frequentist <a href="/wiki/Statistical_inference" title="Statistical inference">statistical inference</a> is the use of statistical methods to determine the probability that the data occur under the null hypothesis by chance; <a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a> is used to determine the effect of an independent variable.<sup id="cite_ref-:1_5-0" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Statistical inference is generally used to determine the difference between variations in the original data that are <a href="/wiki/Random_variation" class="mw-redirect" title="Random variation">random variation</a> or the effect of a well-specified causal mechanism. Notably, <a href="/wiki/Correlation_does_not_imply_causation" title="Correlation does not imply causation">correlation does not imply causation</a>, so the study of causality is as concerned with the study of potential causal mechanisms as it is with variation amongst the data.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2019)">citation needed</span></a></i>]</sup> A frequently sought after standard of causal inference is an experiment wherein treatment is randomly assigned but all other confounding factors are held constant. Most of the efforts in causal inference are in the attempt to replicate experimental conditions. </p><p>Epidemiological studies employ different <a href="/wiki/Epidemiological_method" title="Epidemiological method">epidemiological methods</a> of collecting and measuring evidence of risk factors and effect and different ways of measuring association between the two. Results of a 2020 review of methods for causal inference found that using existing literature for clinical training programs can be challenging. This is because published articles often assume an advanced technical background, they may be written from multiple statistical, epidemiological, computer science, or philosophical perspectives, methodological approaches continue to expand rapidly, and many aspects of causal inference receive limited coverage.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Common frameworks for causal inference include the <a href="/wiki/Causal_pie_model" title="Causal pie model">causal pie model</a> (component-cause), <a href="/wiki/Causal_model" title="Causal model">Pearl's structural causal model</a> (<a href="/wiki/Causal_model#Causal_diagram" title="Causal model">causal diagram</a> + <a href="/wiki/Causal_model#Do_calculus" title="Causal model">do-calculus</a>), <a href="/wiki/Structural_equation_modeling" title="Structural equation modeling">structural equation modeling</a>, and <a href="/wiki/Rubin_causal_model" title="Rubin causal model">Rubin causal model</a> (potential-outcome), which are often used in areas such as social sciences and epidemiology.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Experimental">Experimental</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=4" title="Edit section: Experimental"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Experiment" title="Experiment">Experiment</a></div> <p>Experimental verification of causal mechanisms is possible using experimental methods. The main motivation behind an experiment is to hold other experimental variables constant while purposefully manipulating the variable of interest. If the experiment produces statistically significant effects as a result of only the treatment variable being manipulated, there is grounds to believe that a causal effect can be assigned to the treatment variable, assuming that other standards for experimental design have been met. </p> <div class="mw-heading mw-heading4"><h4 id="Quasi-experimental">Quasi-experimental</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=5" title="Edit section: Quasi-experimental"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></div> <p>Quasi-experimental verification of causal mechanisms is conducted when traditional experimental methods are unavailable. This may be the result of prohibitive costs of conducting an experiment, or the inherent infeasibility of conducting an experiment, especially experiments that are concerned with large systems such as economies of electoral systems, or for treatments that are considered to present a danger to the well-being of test subjects. Quasi-experiments may also occur where information is withheld for legal reasons. </p> <div class="mw-heading mw-heading2"><h2 id="Approaches_in_epidemiology">Approaches in epidemiology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=6" title="Edit section: Approaches in epidemiology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Epidemiology" title="Epidemiology">Epidemiology</a> studies patterns of health and disease in defined populations of <a href="/wiki/Living_beings" class="mw-redirect" title="Living beings">living beings</a> in order to <a href="/wiki/Infer" class="mw-redirect" title="Infer">infer</a> causes and effects. An association between an exposure to a putative <a href="/wiki/Risk_factor" title="Risk factor">risk factor</a> and a disease may be suggestive of, but is not equivalent to causality because <a href="/wiki/Correlation_does_not_imply_causation" title="Correlation does not imply causation">correlation does not imply causation</a>. Historically, <a href="/wiki/Koch%27s_postulates" title="Koch's postulates">Koch's postulates</a> have been used since the 19th century to decide if a microorganism was the cause of a disease. In the 20th century the <a href="/wiki/Bradford_Hill_criteria" title="Bradford Hill criteria">Bradford Hill criteria</a>, described in 1965<sup id="cite_ref-bh65_8-0" class="reference"><a href="#cite_note-bh65-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> have been used to assess causality of variables outside microbiology, although even these criteria are not exclusive ways to determine causality. </p><p>In <a href="/wiki/Molecular_epidemiology" title="Molecular epidemiology">molecular epidemiology</a> the phenomena studied are on a <a href="/wiki/Molecular_biology" title="Molecular biology">molecular biology</a> level, including genetics, where <a href="/wiki/Biomarkers" class="mw-redirect" title="Biomarkers">biomarkers</a> are evidence of cause or effects. </p><p>A recent trend<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (August 2014)">when?</span></a></i>]</sup> is to identify evidence for influence of the exposure on <a href="/wiki/Molecular_pathology" title="Molecular pathology">molecular pathology</a> within diseased <a href="/wiki/Tissue_(biology)" title="Tissue (biology)">tissue</a> or cells, in the emerging interdisciplinary field of <a href="/wiki/Molecular_pathological_epidemiology" title="Molecular pathological epidemiology">molecular pathological epidemiology</a> (MPE).<sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Independent_sources" title="Wikipedia:Independent sources"><span title="This claim needs a reference to a independent, third-party source. (August 2014)">third-party source needed</span></a></i>]</sup> Linking the exposure to molecular pathologic signatures of the disease can help to assess causality. <sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Independent_sources" title="Wikipedia:Independent sources"><span title="This claim needs a reference to a independent, third-party source. (August 2014)">third-party source needed</span></a></i>]</sup> Considering the inherent nature of <a href="/wiki/Heterogeneity" class="mw-redirect" title="Heterogeneity">heterogeneity</a> of a given disease, the unique disease principle, disease phenotyping and subtyping are trends in biomedical and <a href="/wiki/Public_health" title="Public health">public health</a> sciences, exemplified as <a href="/wiki/Personalized_medicine" title="Personalized medicine">personalized medicine</a> and <a href="/wiki/Precision_medicine" class="mw-redirect" title="Precision medicine">precision medicine</a>.<sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Independent_sources" title="Wikipedia:Independent sources"><span title="This claim needs a reference to a independent, third-party source. (August 2014)">third-party source needed</span></a></i>]</sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Causal_Graph_Wikipedia.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Causal_Graph_Wikipedia.png/220px-Causal_Graph_Wikipedia.png" decoding="async" width="220" height="290" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/0d/Causal_Graph_Wikipedia.png 1.5x" data-file-width="251" data-file-height="331" /></a><figcaption>Causal graph where the hidden confounders <i>Z</i> have an effect on the observable variables <i>X</i>, the outcome <i>y</i> and the choice of treatment <i>t</i>. </figcaption></figure> <p>Causal Inference has also been used for treatment effect estimation. Assuming a set of observable patient symptoms(<i>X</i>) caused by a set of hidden causes(<i>Z</i>) we can choose to give or not a treatment <i>t</i>. The result of the giving or not giving the treatment is the effect estimation <i>y</i>. If the treatment is not guaranteed to have a positive effect then the decision whether the treatment should be applied or not depends firstly on expert knowledge that encompasses the causal connections. For novel diseases, this expert knowledge may not be available. As a result, we rely solely on past treatment outcomes to make decisions. A modified <a href="/wiki/Variational_autoencoder" title="Variational autoencoder">variational autoencoder</a> can be used to model the causal graph described above.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> While the above scenario could be modelled without the use of the hidden confounder(Z) we would lose the insight that the symptoms a patient together with other factors impacts both the treatment assignment and the outcome. </p> <div class="mw-heading mw-heading2"><h2 id="Approaches_in_computer_science">Approaches in computer science</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=7" title="Edit section: Approaches in computer science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Causal inference is an important concept in the field of <a href="/wiki/Causal_AI" title="Causal AI">causal artificial intelligence</a>. Determination of cause and effect from joint observational data for two time-independent variables, say X and Y, has been tackled using asymmetry between evidence for some model in the directions, X → Y and Y → X. The primary approaches are based on <a href="/wiki/Algorithmic_information_theory" title="Algorithmic information theory">Algorithmic information theory</a> models and noise models.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2019)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Noise_models">Noise models</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=8" title="Edit section: Noise models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Incorporate an independent noise term in the model to compare the evidences of the two directions. </p><p>Here are some of the noise models for the hypothesis Y → X with the noise E: </p> <ul><li>Additive noise:<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=F(X)+E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=F(X)+E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/607090f681310f4e2941debb587fc0e83a4edd11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.018ex; height:2.843ex;" alt="{\displaystyle Y=F(X)+E}"></span></li> <li>Linear noise:<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=pX+qE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mi>p</mi> <mi>X</mi> <mo>+</mo> <mi>q</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=pX+qE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e26806ed2eb9a1626947beff4e778ac96981c0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.707ex; height:2.509ex;" alt="{\displaystyle Y=pX+qE}"></span></li> <li>Post-nonlinear:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=G(F(X)+E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mi>G</mi> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=G(F(X)+E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c99799bd077636e31825d485fd68358fb898860f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.654ex; height:2.843ex;" alt="{\displaystyle Y=G(F(X)+E)}"></span></li> <li>Heteroskedastic noise: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=F(X)+E.G(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>E</mi> <mo>.</mo> <mi>G</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=F(X)+E.G(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d8a204e3ef1ad5b6a328fdb7a44db73c0fa0f0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.668ex; height:2.843ex;" alt="{\displaystyle Y=F(X)+E.G(X)}"></span></li> <li>Functional noise:<sup id="cite_ref-Mooij_13-0" class="reference"><a href="#cite_note-Mooij-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=F(X,E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=F(X,E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4af9bf7fc340679a0ca2f0ab0457e1caa2dfa3cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.211ex; height:2.843ex;" alt="{\displaystyle Y=F(X,E)}"></span></li></ul> <p>The common assumption in these models are: </p> <ul><li>There are no other causes of Y.</li> <li>X and E have no common causes.</li> <li>Distribution of cause is independent from causal mechanisms.</li></ul> <p>On an intuitive level, the idea is that the factorization of the joint distribution P(Cause, Effect) into P(Cause)*P(Effect | Cause) typically yields models of lower total complexity than the factorization into P(Effect)*P(Cause | Effect). Although the notion of "complexity" is intuitively appealing, it is not obvious how it should be precisely defined.<sup id="cite_ref-Mooij_13-1" class="reference"><a href="#cite_note-Mooij-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> A different family of methods attempt to discover causal "footprints" from large amounts of labeled data, and allow the prediction of more flexible causal relations.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Approaches_in_social_sciences">Approaches in social sciences</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=9" title="Edit section: Approaches in social sciences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Causality#Statistics_and_economics" title="Causality">Causality § Statistics and economics</a></div> <div class="mw-heading mw-heading3"><h3 id="Social_science">Social science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=10" title="Edit section: Social science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The social sciences in general have moved increasingly toward including quantitative frameworks for assessing causality. Much of this has been described as a means of providing greater rigor to social science methodology. Political science was significantly influenced by the publication of <a href="/wiki/Designing_Social_Inquiry" title="Designing Social Inquiry">Designing Social Inquiry</a>, by Gary King, Robert Keohane, and Sidney Verba, in 1994. King, Keohane, and Verba recommend that researchers apply both quantitative and qualitative methods and adopt the language of statistical inference to be clearer about their subjects of interest and units of analysis.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_16-0" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Proponents of quantitative methods have also increasingly adopted the <a href="/wiki/Rubin_causal_model" title="Rubin causal model">potential outcomes framework</a>, developed by <a href="/wiki/Donald_Rubin" title="Donald Rubin">Donald Rubin</a>, as a standard for inferring causality.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2019)">citation needed</span></a></i>]</sup> </p><p>While much of the emphasis remains on statistical inference in the potential outcomes framework, social science methodologists have developed new tools to conduct causal inference with both qualitative and quantitative methods, sometimes called a "mixed methods" approach.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Advocates of diverse methodological approaches argue that different methodologies are better suited to different subjects of study. Sociologist Herbert Smith and Political Scientists James Mahoney and Gary Goertz have cited the observation of Paul Holland, a statistician and author of the 1986 article "Statistics and Causal Inference", that statistical inference is most appropriate for assessing the "effects of causes" rather than the "causes of effects".<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Qualitative methodologists have argued that formalized models of causation, including <a href="/wiki/Process_tracing" title="Process tracing">process tracing</a> and <a href="/wiki/Fuzzy_set" title="Fuzzy set">fuzzy set</a> theory, provide opportunities to infer causation through the identification of critical factors within case studies or through a process of comparison among several case studies.<sup id="cite_ref-:0_16-1" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> These methodologies are also valuable for subjects in which a limited number of potential observations or the presence of confounding variables would limit the applicability of statistical inference.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2019)">citation needed</span></a></i>]</sup> </p><p>On longer timescales, <a href="/wiki/Persistence_studies" title="Persistence studies">persistence studies</a> uses causal inference to link historical events to later political, economic and social outcomes.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Economics_and_political_science">Economics and political science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=11" title="Edit section: Economics and political science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Economics" title="Economics">economic sciences</a> and <a href="/wiki/Political_science" title="Political science">political sciences</a> causal inference is often difficult, owing to the real world complexity of economic and political realities and the inability to recreate many large-scale phenomena within controlled experiments. Causal inference in the economic and political sciences continues to see improvement in methodology and rigor, due to the increased level of technology available to social scientists, the increase in the number of social scientists and research, and improvements to causal inference methodologies throughout social sciences.<sup id="cite_ref-:2_22-0" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Despite the difficulties inherent in determining causality in economic systems, several widely employed methods exist throughout those fields. </p> <div class="mw-heading mw-heading4"><h4 id="Theoretical_methods">Theoretical methods</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=12" title="Edit section: Theoretical methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Economists and political scientists can use theory (often studied in theory-driven econometrics) to estimate the magnitude of supposedly causal relationships in cases where they believe a causal relationship exists.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Theorists can presuppose a mechanism believed to be causal and describe the effects using data analysis to justify their proposed theory. For example, theorists can use logic to construct a model, such as theorizing that rain causes fluctuations in economic productivity but that the converse is not true.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> However, using purely theoretical claims that do not offer any predictive insights has been called "pre-scientific" because there is no ability to predict the impact of the supposed causal properties.<sup id="cite_ref-:1_5-1" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> It is worth reiterating that regression analysis in the social science does not inherently imply causality, as many phenomena may correlate in the short run or in particular datasets but demonstrate no correlation in other time periods or other datasets. Thus, the attribution of causality to correlative properties is premature absent a well defined and reasoned causal mechanism. </p> <div class="mw-heading mw-heading4"><h4 id="Instrumental_variables">Instrumental variables</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=13" title="Edit section: Instrumental variables"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Instrumental_variables" class="mw-redirect" title="Instrumental variables">instrumental variables</a> (IV) technique is a method of determining causality that involves the elimination of a correlation between one of a model's explanatory variables and the model's error term. This method presumes that if a model's error term moves similarly with the variation of another variable, then the model's error term is probably an effect of variation in that explanatory variable. The elimination of this correlation through the introduction of a new instrumental variable thus reduces the error present in the model as a whole.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Model_specification">Model specification</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=14" title="Edit section: Model specification"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Model specification is the act of selecting a model to be used in data analysis. Social scientists (and, indeed, all scientists) must determine the correct model to use because different models are good at estimating different relationships.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>Model specification can be useful in determining causality that is slow to emerge, where the effects of an action in one period are only felt in a later period. It is worth remembering that correlations only measure whether two variables have similar variance, not whether they affect one another in a particular direction; thus, one cannot determine the direction of a causal relation based on correlations only. Because causal acts are believed to precede causal effects, social scientists can use a model that looks specifically for the effect of one variable on another over a period of time. This leads to using the variables representing phenomena happening earlier as treatment effects, where econometric tests are used to look for later changes in data that are attributed to the effect of such treatment effects, where a meaningful difference in results following a meaningful difference in treatment effects may indicate causality between the treatment effects and the measured effects (e.g., Granger-causality tests). Such studies are examples of <a href="/wiki/Time_series" title="Time series">time-series analysis</a>.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Sensitivity_analysis">Sensitivity analysis</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=15" title="Edit section: Sensitivity analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Other variables, or regressors in regression analysis, are either included or not included across various implementations of the same model to ensure that different sources of variation can be studied more separately from one another. This is a form of sensitivity analysis: it is the study of how sensitive an implementation of a model is to the addition of one or more new variables.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>A chief motivating concern in the use of sensitivity analysis is the pursuit of discovering <a href="/wiki/Confounding_variable" class="mw-redirect" title="Confounding variable">confounding variables</a>. Confounding variables are variables that have a large impact on the results of a statistical test but are not the variable that causal inference is trying to study. Confounding variables may cause a regressor to appear to be significant in one implementation, but not in another. </p> <div class="mw-heading mw-heading5"><h5 id="Multicollinearity">Multicollinearity</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=16" title="Edit section: Multicollinearity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Another reason for the use of sensitivity analysis is to detect <a href="/wiki/Multicollinearity" title="Multicollinearity">multicollinearity</a>. Multicollinearity is the phenomenon where the correlation between two explanatory variables is very high. A high level of correlation between two such variables can dramatically affect the outcome of a statistical analysis, where small variations in highly correlated data can flip the effect of a variable from a positive direction to a negative direction, or vice versa. This is an inherent property of variance testing. Determining multicollinearity is useful in sensitivity analysis because the elimination of highly correlated variables in different model implementations can prevent the dramatic changes in results that result from the inclusion of such variables.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>However, there are limits to sensitivity analysis' ability to prevent the deleterious effects of multicollinearity, especially in the social sciences, where systems are complex. Because it is theoretically impossible to include or even measure all of the confounding factors in a sufficiently complex system, econometric models are susceptible to the common-cause fallacy, where causal effects are incorrectly attributed to the wrong variable because the correct variable was not captured in the original data. This is an example of the failure to account for a <a href="/wiki/Confounding" title="Confounding">lurking variable</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Design-based_econometrics">Design-based econometrics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=17" title="Edit section: Design-based econometrics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Recently, improved methodology in design-based econometrics has popularized the use of both natural experiments and quasi-experimental research designs to study the causal mechanisms that such experiments are believed to identify.<sup id="cite_ref-:3_31-0" class="reference"><a href="#cite_note-:3-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Malpractice_in_causal_inference">Malpractice in causal inference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=18" title="Edit section: Malpractice in causal inference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Despite the advancements in the development of methodologies used to determine causality, significant weaknesses in determining causality remain. These weaknesses can be attributed both to the inherent difficulty of determining causal relations in complex systems but also to cases of scientific malpractice. </p><p>Separate from the difficulties of causal inference, the perception that large numbers of scholars in the social sciences engage in non-scientific methodology exists among some large groups of social scientists. Criticism of economists and social scientists as passing off descriptive studies as causal studies are rife within those fields.<sup id="cite_ref-:1_5-2" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Scientific_malpractice_and_flawed_methodology">Scientific malpractice and flawed methodology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=19" title="Edit section: Scientific malpractice and flawed methodology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the sciences, especially in the social sciences, there is concern among scholars that scientific malpractice is widespread. As scientific study is a broad topic, there are theoretically limitless ways to have a causal inference undermined through no fault of a researcher. Nonetheless, there remain concerns among scientists that large numbers of researchers do not perform basic duties or practice sufficiently diverse methods in causal inference.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_22-1" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="This source is a defense of simple linear models, and does not seem to mention causal inference at all. (March 2021)">failed verification</span></a></i>]</sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>One prominent example of common non-causal methodology is the erroneous assumption of correlative properties as causal properties. There is no inherent causality in phenomena that correlate. Regression models are designed to measure variance within data relative to a theoretical model: there is nothing to suggest that data that presents high levels of covariance have any meaningful relationship (absent a proposed causal mechanism with predictive properties or a random assignment of treatment). The use of flawed methodology has been claimed to be widespread, with common examples of such malpractice being the overuse of correlative models, especially the overuse of regression models and particularly linear regression models.<sup id="cite_ref-:1_5-3" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The presupposition that two correlated phenomena are inherently related is a logical fallacy known as <a href="/wiki/Spurious_relationship" title="Spurious relationship">spurious correlation</a>. Some social scientists claim that widespread use of methodology that attributes causality to spurious correlations have been detrimental to the integrity of the social sciences, although improvements stemming from better methodologies have been noted.<sup id="cite_ref-:3_31-1" class="reference"><a href="#cite_note-:3-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>A potential effect of scientific studies that erroneously conflate correlation with causality is an increase in the number of scientific findings whose results are not reproducible by third parties. Such non-reproducibility is a logical consequence of findings that correlation only temporarily being overgeneralized into mechanisms that have no inherent relationship, where new data does not contain the previous, idiosyncratic correlations of the original data. Debates over the effect of malpractice versus the effect of the inherent difficulties of searching for causality are ongoing.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Critics of widely practiced methodologies argue that researchers have engaged statistical manipulation in order to publish articles that supposedly demonstrate evidence of causality but are actually examples of spurious correlation being touted as evidence of causality: such endeavors may be referred to as <a href="/wiki/Data_dredging" title="Data dredging">P hacking</a>.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> To prevent this, some have advocated that researchers preregister their research designs prior to conducting to their studies so that they do not inadvertently overemphasize a nonreproducible finding that was not the initial subject of inquiry but was found to be statistically significant during data analysis.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=20" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Causal_analysis" title="Causal analysis">Causal analysis</a></li> <li><a href="/wiki/Causal_model" title="Causal model">Causal model</a></li> <li><a href="/wiki/Granger_causality" title="Granger causality">Granger causality</a></li> <li><a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate statistics</a></li> <li><a href="/wiki/Partial_least_squares_regression" title="Partial least squares regression">Partial least squares regression</a></li> <li><a href="/wiki/Pathogenesis" title="Pathogenesis">Pathogenesis</a></li> <li><a href="/wiki/Pathology" title="Pathology">Pathology</a></li> <li><a href="/wiki/Probabilistic_causation" title="Probabilistic causation">Probabilistic causation</a></li> <li><a href="/wiki/Probabilistic_argumentation" title="Probabilistic argumentation">Probabilistic argumentation</a></li> <li><a href="/wiki/Probabilistic_logic" title="Probabilistic logic">Probabilistic logic</a></li> <li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></li> <li><a href="/wiki/Transfer_entropy" title="Transfer entropy">Transfer entropy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=21" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Pearl_Journal-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pearl_Journal_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFPearl2009" class="citation journal cs1">Pearl, Judea (1 January 2009). <a rel="nofollow" class="external text" href="http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf">"Causal inference in statistics: An overview"</a> <span class="cs1-format">(PDF)</span>. <i>Statistics Surveys</i>. <b>3</b>: 96–146. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1214%2F09-SS057">10.1214/09-SS057</a></span>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100806150433/http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 6 August 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">24 September</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Statistics+Surveys&rft.atitle=Causal+inference+in+statistics%3A+An+overview&rft.volume=3&rft.pages=96-146&rft.date=2009-01-01&rft_id=info%3Adoi%2F10.1214%2F09-SS057&rft.aulast=Pearl&rft.aufirst=Judea&rft_id=http%3A%2F%2Fftp.cs.ucla.edu%2Fpub%2Fstat_ser%2Fr350.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-Morgan_book-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Morgan_book_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorganWinship,_Chris2007" class="citation book cs1">Morgan, Stephen; Winship, Chris (2007). <i>Counterfactuals and Causal inference</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-67193-4" title="Special:BookSources/978-0-521-67193-4"><bdi>978-0-521-67193-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Counterfactuals+and+Causal+inference&rft.pub=Cambridge+University+Press&rft.date=2007&rft.isbn=978-0-521-67193-4&rft.aulast=Morgan&rft.aufirst=Stephen&rft.au=Winship%2C+Chris&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-EB-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-EB_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.britannica.com/EBchecked/topic/1442615/causal-inference">"causal inference"</a>. Encyclopædia Britannica, Inc. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150503062914/http://www.britannica.com/EBchecked/topic/1442615/causal-inference">Archived</a> from the original on 3 May 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">24 August</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=causal+inference&rft.pub=Encyclop%C3%A6dia+Britannica%2C+Inc.&rft_id=http%3A%2F%2Fwww.britannica.com%2FEBchecked%2Ftopic%2F1442615%2Fcausal-inference&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-psy-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-psy_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_ShaughnessyEugene_ZechmeisterJeanne_Zechmeister2000" class="citation book cs1">John Shaughnessy; Eugene Zechmeister; Jeanne Zechmeister (2000). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141015135541/http://www.mhhe.com/socscience/psychology/shaugh/ch01_concepts.html"><i>Research Methods in Psychology</i></a>. McGraw-Hill Humanities/Social Sciences/Languages. pp. Chapter 1 : Introduction. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0077825362" title="Special:BookSources/978-0077825362"><bdi>978-0077825362</bdi></a>. Archived from <a rel="nofollow" class="external text" href="http://www.mhhe.com/socscience/psychology/shaugh/ch01_concepts.html">the original</a> on 15 October 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">24 August</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Research+Methods+in+Psychology&rft.pages=Chapter+1+%3A+Introduction&rft.pub=McGraw-Hill+Humanities%2FSocial+Sciences%2FLanguages&rft.date=2000&rft.isbn=978-0077825362&rft.au=John+Shaughnessy&rft.au=Eugene+Zechmeister&rft.au=Jeanne+Zechmeister&rft_id=http%3A%2F%2Fwww.mhhe.com%2Fsocscience%2Fpsychology%2Fshaugh%2Fch01_concepts.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-:1-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:1_5-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchrodt2014" class="citation journal cs1">Schrodt, Philip A (1 March 2014). <a rel="nofollow" class="external text" href="https://doi.org/10.1177/0022343313499597">"Seven deadly sins of contemporary quantitative political analysis"</a>. <i>Journal of Peace Research</i>. <b>51</b> (2): 287–300. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0022343313499597">10.1177/0022343313499597</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-3433">0022-3433</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:197658213">197658213</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210815141548/https://journals.sagepub.com/doi/10.1177/0022343313499597">Archived</a> from the original on 15 August 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Peace+Research&rft.atitle=Seven+deadly+sins+of+contemporary+quantitative+political+analysis&rft.volume=51&rft.issue=2&rft.pages=287-300&rft.date=2014-03-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A197658213%23id-name%3DS2CID&rft.issn=0022-3433&rft_id=info%3Adoi%2F10.1177%2F0022343313499597&rft.aulast=Schrodt&rft.aufirst=Philip+A&rft_id=https%3A%2F%2Fdoi.org%2F10.1177%2F0022343313499597&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandsittelSrivastavaKropf2020" class="citation journal cs1">Landsittel, Douglas; Srivastava, Avantika; Kropf, Kristin (2020). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1097%2FQMH.0000000000000276">"A Narrative Review of Methods for Causal Inference and Associated Educational Resources"</a>. <i>Quality Management in Health Care</i>. <b>29</b> (4): 260–269. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1097%2FQMH.0000000000000276">10.1097/QMH.0000000000000276</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1063-8628">1063-8628</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/32991545">32991545</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:222146291">222146291</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210815141612/https://journals.lww.com/qmhcjournal/Abstract/2020/10000/A_Narrative_Review_of_Methods_for_Causal_Inference.12.aspx">Archived</a> from the original on 15 August 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">26 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Quality+Management+in+Health+Care&rft.atitle=A+Narrative+Review+of+Methods+for+Causal+Inference+and+Associated+Educational+Resources&rft.volume=29&rft.issue=4&rft.pages=260-269&rft.date=2020&rft.issn=1063-8628&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A222146291%23id-name%3DS2CID&rft_id=info%3Apmid%2F32991545&rft_id=info%3Adoi%2F10.1097%2FQMH.0000000000000276&rft.aulast=Landsittel&rft.aufirst=Douglas&rft.au=Srivastava%2C+Avantika&rft.au=Kropf%2C+Kristin&rft_id=https%3A%2F%2Fdx.doi.org%2F10.1097%252FQMH.0000000000000276&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenlandBrumback2002" class="citation journal cs1">Greenland, Sander; Brumback, Babette (October 2002). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fije%2F31.5.1030">"An overview of relations among causal modelling methods"</a>. <i>International Journal of Epidemiology</i>. <b>31</b> (5): 1030–1037. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fije%2F31.5.1030">10.1093/ije/31.5.1030</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1464-3685">1464-3685</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/12435780">12435780</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Epidemiology&rft.atitle=An+overview+of+relations+among+causal+modelling+methods&rft.volume=31&rft.issue=5&rft.pages=1030-1037&rft.date=2002-10&rft.issn=1464-3685&rft_id=info%3Apmid%2F12435780&rft_id=info%3Adoi%2F10.1093%2Fije%2F31.5.1030&rft.aulast=Greenland&rft.aufirst=Sander&rft.au=Brumback%2C+Babette&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fije%252F31.5.1030&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-bh65-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-bh65_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHill1965" class="citation journal cs1">Hill, Austin Bradford (1965). <a rel="nofollow" class="external text" href="http://www.edwardtufte.com/tufte/hill">"The Environment and Disease: Association or Causation?"</a>. <i><a href="/wiki/Proceedings_of_the_Royal_Society_of_Medicine" class="mw-redirect" title="Proceedings of the Royal Society of Medicine">Proceedings of the Royal Society of Medicine</a></i>. <b>58</b> (5): 295–300. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F003591576505800503">10.1177/003591576505800503</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898525">1898525</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/14283879">14283879</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210219104245/https://www.edwardtufte.com/tufte/hill">Archived</a> from the original on 19 February 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">25 February</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+of+Medicine&rft.atitle=The+Environment+and+Disease%3A+Association+or+Causation%3F&rft.volume=58&rft.issue=5&rft.pages=295-300&rft.date=1965&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1898525%23id-name%3DPMC&rft_id=info%3Apmid%2F14283879&rft_id=info%3Adoi%2F10.1177%2F003591576505800503&rft.aulast=Hill&rft.aufirst=Austin+Bradford&rft_id=http%3A%2F%2Fwww.edwardtufte.com%2Ftufte%2Fhill&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLouizosShalitMooijSontag2017" class="citation arxiv cs1">Louizos, Christos; Shalit, Uri; Mooij, Joris; Sontag, David; Zemel, Richard; Welling, Max (2017). "Causal Effect Inference with Deep Latent-Variable Models". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1705.08821">1705.08821</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/stat.ML">stat.ML</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Causal+Effect+Inference+with+Deep+Latent-Variable+Models&rft.date=2017&rft_id=info%3Aarxiv%2F1705.08821&rft.aulast=Louizos&rft.aufirst=Christos&rft.au=Shalit%2C+Uri&rft.au=Mooij%2C+Joris&rft.au=Sontag%2C+David&rft.au=Zemel%2C+Richard&rft.au=Welling%2C+Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Hoyer, Patrik O., et al. "<a rel="nofollow" class="external text" href="https://papers.nips.cc/paper/3548-nonlinear-causal-discovery-with-additive-noise-models.pdf">Nonlinear causal discovery with additive noise models</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201102052824/https://papers.nips.cc/paper/3548-nonlinear-causal-discovery-with-additive-noise-models.pdf">Archived</a> 2 November 2020 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>." NIPS. Vol. 21. 2008.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShimizu2011" class="citation journal cs1">Shimizu, Shohei; et al. (2011). <a rel="nofollow" class="external text" href="http://www.jmlr.org/papers/volume12/shimizu11a/shimizu11a.pdf">"DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model"</a> <span class="cs1-format">(PDF)</span>. <i>The Journal of Machine Learning Research</i>. <b>12</b>: 1225–1248. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1101.2489">1101.2489</a></span>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210723091227/https://www.jmlr.org/papers/volume12/shimizu11a/shimizu11a.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 23 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">27 July</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Machine+Learning+Research&rft.atitle=DirectLiNGAM%3A+A+direct+method+for+learning+a+linear+non-Gaussian+structural+equation+model&rft.volume=12&rft.pages=1225-1248&rft.date=2011&rft_id=info%3Aarxiv%2F1101.2489&rft.aulast=Shimizu&rft.aufirst=Shohei&rft_id=http%3A%2F%2Fwww.jmlr.org%2Fpapers%2Fvolume12%2Fshimizu11a%2Fshimizu11a.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Zhang, Kun, and Aapo Hyvärinen. "<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1205.2599">On the identifiability of the post-nonlinear causal model</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211019090447/https://arxiv.org/abs/1205.2599">Archived</a> 19 October 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>." Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. AUAI Press, 2009.</span> </li> <li id="cite_note-Mooij-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Mooij_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Mooij_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Mooij, Joris M., et al. "<a rel="nofollow" class="external text" href="http://papers.nips.cc/paper/4173-probabilistic-latent-variable-models-for-distinguishing-between-cause-and-effect.pdf">Probabilistic latent variable models for distinguishing between cause and effect</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200722165521/http://papers.nips.cc/paper/4173-probabilistic-latent-variable-models-for-distinguishing-between-cause-and-effect.pdf">Archived</a> 22 July 2020 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>." NIPS. 2010.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Lopez-Paz, David, et al. "<a rel="nofollow" class="external text" href="http://www.jmlr.org/proceedings/papers/v37/lopez-paz15.pdf">Towards a learning theory of cause-effect inference</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170313150048/http://www.jmlr.org/proceedings/papers/v37/lopez-paz15.pdf">Archived</a> 13 March 2017 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>" ICML. 2015</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKing2012" class="citation book cs1">King, Gary (2012). <i>Designing social inquiry : scientific inference in qualitative research</i>. Princeton Univ. Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0691034713" title="Special:BookSources/978-0691034713"><bdi>978-0691034713</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/754613241">754613241</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Designing+social+inquiry+%3A+scientific+inference+in+qualitative+research&rft.pub=Princeton+Univ.+Press&rft.date=2012&rft_id=info%3Aoclcnum%2F754613241&rft.isbn=978-0691034713&rft.aulast=King&rft.aufirst=Gary&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-:0-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMahoney2010" class="citation journal cs1">Mahoney, James (January 2010). "After KKV". <i>World Politics</i>. <b>62</b> (1): 120–147. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0043887109990220">10.1017/S0043887109990220</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/40646193">40646193</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:43923978">43923978</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=World+Politics&rft.atitle=After+KKV&rft.volume=62&rft.issue=1&rft.pages=120-147&rft.date=2010-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A43923978%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F40646193%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1017%2FS0043887109990220&rft.aulast=Mahoney&rft.aufirst=James&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCreswellClark2011" class="citation book cs1">Creswell, John W.; Clark, Vicki L. Plano (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YcdlPWPJRBcC"><i>Designing and Conducting Mixed Methods Research</i></a>. SAGE Publications. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781412975179" title="Special:BookSources/9781412975179"><bdi>9781412975179</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210721102124/https://books.google.com/books?id=YcdlPWPJRBcC">Archived</a> from the original on 21 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">23 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Designing+and+Conducting+Mixed+Methods+Research&rft.pub=SAGE+Publications&rft.date=2011&rft.isbn=9781412975179&rft.aulast=Creswell&rft.aufirst=John+W.&rft.au=Clark%2C+Vicki+L.+Plano&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DYcdlPWPJRBcC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSeawright2016" class="citation book cs1">Seawright, Jason (September 2016). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/books/multimethod-social-science/286C2742878FBCC6225E2F10D6095A0C"><i>Multi-Method Social Science by Jason Seawright</i></a>. Cambridge Core. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9781316160831">10.1017/CBO9781316160831</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781316160831" title="Special:BookSources/9781316160831"><bdi>9781316160831</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210721102124/https://www.cambridge.org/core/books/multimethod-social-science/286C2742878FBCC6225E2F10D6095A0C">Archived</a> from the original on 21 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">18 April</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Multi-Method+Social+Science+by+Jason+Seawright&rft.pub=Cambridge+Core&rft.date=2016-09&rft_id=info%3Adoi%2F10.1017%2FCBO9781316160831&rft.isbn=9781316160831&rft.aulast=Seawright&rft.aufirst=Jason&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fbooks%2Fmultimethod-social-science%2F286C2742878FBCC6225E2F10D6095A0C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith2014" class="citation journal cs1">Smith, Herbert L. (10 February 2014). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4251584">"Effects of Causes and Causes of Effects: Some Remarks from the Sociological Side"</a>. <i>Sociological Methods and Research</i>. <b>43</b> (3): 406–415. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0049124114521149">10.1177/0049124114521149</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4251584">4251584</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/25477697">25477697</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Sociological+Methods+and+Research&rft.atitle=Effects+of+Causes+and+Causes+of+Effects%3A+Some+Remarks+from+the+Sociological+Side&rft.volume=43&rft.issue=3&rft.pages=406-415&rft.date=2014-02-10&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4251584%23id-name%3DPMC&rft_id=info%3Apmid%2F25477697&rft_id=info%3Adoi%2F10.1177%2F0049124114521149&rft.aulast=Smith&rft.aufirst=Herbert+L.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4251584&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoertzMahoney2006" class="citation journal cs1">Goertz, Gary; Mahoney, James (2006). "A Tale of Two Cultures: Contrasting Quantitative and Qualitative Research". <i>Political Analysis</i>. <b>14</b> (3): 227–249. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fpan%2Fmpj017">10.1093/pan/mpj017</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1047-1987">1047-1987</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Political+Analysis&rft.atitle=A+Tale+of+Two+Cultures%3A+Contrasting+Quantitative+and+Qualitative+Research&rft.volume=14&rft.issue=3&rft.pages=227-249&rft.date=2006&rft_id=info%3Adoi%2F10.1093%2Fpan%2Fmpj017&rft.issn=1047-1987&rft.aulast=Goertz&rft.aufirst=Gary&rft.au=Mahoney%2C+James&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCironePepinsky2022" class="citation journal cs1">Cirone, Alexandra; Pepinsky, Thomas B. (2022). <a rel="nofollow" class="external text" href="https://www.annualreviews.org/doi/10.1146/annurev-polisci-051120-104325">"Historical Persistence"</a>. <i>Annual Review of Political Science</i>. <b>25</b> (1): 241–259. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev-polisci-051120-104325">10.1146/annurev-polisci-051120-104325</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1094-2939">1094-2939</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Political+Science&rft.atitle=Historical+Persistence&rft.volume=25&rft.issue=1&rft.pages=241-259&rft.date=2022&rft_id=info%3Adoi%2F10.1146%2Fannurev-polisci-051120-104325&rft.issn=1094-2939&rft.aulast=Cirone&rft.aufirst=Alexandra&rft.au=Pepinsky%2C+Thomas+B.&rft_id=https%3A%2F%2Fwww.annualreviews.org%2Fdoi%2F10.1146%2Fannurev-polisci-051120-104325&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-:2-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_22-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngristPischke2010" class="citation journal cs1">Angrist, Joshua D.; Pischke, Jörn-Steffen (June 2010). <a rel="nofollow" class="external text" href="https://doi.org/10.1257%2Fjep.24.2.3">"The Credibility Revolution in Empirical Economics: How Better Research Design Is Taking the Con out of Econometrics"</a>. <i>Journal of Economic Perspectives</i>. <b>24</b> (2): 3–30. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1257%2Fjep.24.2.3">10.1257/jep.24.2.3</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F54195">1721.1/54195</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0895-3309">0895-3309</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Perspectives&rft.atitle=The+Credibility+Revolution+in+Empirical+Economics%3A+How+Better+Research+Design+Is+Taking+the+Con+out+of+Econometrics&rft.volume=24&rft.issue=2&rft.pages=3-30&rft.date=2010-06&rft_id=info%3Ahdl%2F1721.1%2F54195&rft.issn=0895-3309&rft_id=info%3Adoi%2F10.1257%2Fjep.24.2.3&rft.aulast=Angrist&rft.aufirst=Joshua+D.&rft.au=Pischke%2C+J%C3%B6rn-Steffen&rft_id=https%3A%2F%2Fdoi.org%2F10.1257%252Fjep.24.2.3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUniversity" class="citation web cs1">University, Carnegie Mellon. <a rel="nofollow" class="external text" href="http://www.cmu.edu/dietrich/philosophy/research/areas/science-methodology/theory-of-causation.html">"Theory of Causation - Department of Philosophy - Dietrich College of Humanities and Social Sciences - Carnegie Mellon University"</a>. <i>www.cmu.edu</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210711195549/https://www.cmu.edu/dietrich/philosophy/research/areas/science-methodology/theory-of-causation.html">Archived</a> from the original on 11 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.cmu.edu&rft.atitle=Theory+of+Causation+-+Department+of+Philosophy+-+Dietrich+College+of+Humanities+and+Social+Sciences+-+Carnegie+Mellon+University&rft.aulast=University&rft.aufirst=Carnegie+Mellon&rft_id=http%3A%2F%2Fwww.cmu.edu%2Fdietrich%2Fphilosophy%2Fresearch%2Fareas%2Fscience-methodology%2Ftheory-of-causation.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSimon1977" class="citation book cs1">Simon, Herbert (1977). <i>Models of Discovery</i>. Dordrecht: Springer. p. 52.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Models+of+Discovery&rft.place=Dordrecht&rft.pages=52&rft.pub=Springer&rft.date=1977&rft.aulast=Simon&rft.aufirst=Herbert&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngristKrueger2001" class="citation journal cs1">Angrist, Joshua D.; Krueger, Alan B. (2001). <a rel="nofollow" class="external text" href="https://economics.mit.edu/files/18">"Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments"</a>. <i>Journal of Economic Perspectives</i>. <b>15</b> (4): 69–85. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1257%2Fjep.15.4.69">10.1257/jep.15.4.69</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F63775">1721.1/63775</a></span>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210506222157/http://economics.mit.edu/files/18">Archived</a> from the original on 6 May 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Perspectives&rft.atitle=Instrumental+Variables+and+the+Search+for+Identification%3A+From+Supply+and+Demand+to+Natural+Experiments&rft.volume=15&rft.issue=4&rft.pages=69-85&rft.date=2001&rft_id=info%3Ahdl%2F1721.1%2F63775&rft_id=info%3Adoi%2F10.1257%2Fjep.15.4.69&rft.aulast=Angrist&rft.aufirst=Joshua+D.&rft.au=Krueger%2C+Alan+B.&rft_id=https%3A%2F%2Feconomics.mit.edu%2Ffiles%2F18&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAllen1997" class="citation cs2">Allen, Michael Patrick, ed. (1997), <a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-0-585-25657-3_35">"Model specification in regression analysis"</a>, <i>Understanding Regression Analysis</i>, Boston, MA: Springer US, pp. 166–170, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-0-585-25657-3_35">10.1007/978-0-585-25657-3_35</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-585-25657-3" title="Special:BookSources/978-0-585-25657-3"><bdi>978-0-585-25657-3</bdi></a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210815141541/https://link.springer.com/chapter/10.1007%2F978-0-585-25657-3_35">archived</a> from the original on 15 August 2021<span class="reference-accessdate">, retrieved <span class="nowrap">16 February</span> 2021</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Understanding+Regression+Analysis&rft.atitle=Model+specification+in+regression+analysis&rft.pages=166-170&rft.date=1997&rft_id=info%3Adoi%2F10.1007%2F978-0-585-25657-3_35&rft.isbn=978-0-585-25657-3&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%2F978-0-585-25657-3_35&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaziarz2020" class="citation book cs1">Maziarz, Mariusz (2020). <i>The Philosophy of Causality in Economics: Causal Inferences and Policy Proposals</i>. New York: Routledge.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Philosophy+of+Causality+in+Economics%3A+Causal+Inferences+and+Policy+Proposals&rft.place=New+York&rft.pub=Routledge&rft.date=2020&rft.aulast=Maziarz&rft.aufirst=Mariusz&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSalciccioliCrutainKomorowskiMarshall2016" class="citation cs2">Salciccioli, Justin D.; Crutain, Yves; Komorowski, Matthieu; Marshall, Dominic C. (2016), MIT Critical Data (ed.), "Sensitivity Analysis and Model Validation", <i>Secondary Analysis of Electronic Health Records</i>, Cham: Springer International Publishing, pp. 263–271, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-43742-2_17">10.1007/978-3-319-43742-2_17</a></span>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-43742-2" title="Special:BookSources/978-3-319-43742-2"><bdi>978-3-319-43742-2</bdi></a>, <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/31314264">31314264</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Secondary+Analysis+of+Electronic+Health+Records&rft.atitle=Sensitivity+Analysis+and+Model+Validation&rft.pages=263-271&rft.date=2016&rft_id=info%3Apmid%2F31314264&rft_id=info%3Adoi%2F10.1007%2F978-3-319-43742-2_17&rft.isbn=978-3-319-43742-2&rft.aulast=Salciccioli&rft.aufirst=Justin+D.&rft.au=Crutain%2C+Yves&rft.au=Komorowski%2C+Matthieu&rft.au=Marshall%2C+Dominic+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIllowsky2013" class="citation web cs1">Illowsky, Barbara (2013). <a rel="nofollow" class="external text" href="https://openstax.org/details/introductory-statistics">"Introductory Statistics"</a>. <i>openstax.org</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170206081545/https://openstax.org/details/introductory-statistics">Archived</a> from the original on 6 February 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=openstax.org&rft.atitle=Introductory+Statistics&rft.date=2013&rft.aulast=Illowsky&rft.aufirst=Barbara&rft_id=https%3A%2F%2Fopenstax.org%2Fdetails%2Fintroductory-statistics&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenschen2018" class="citation journal cs1">Henschen, Tobias (2018). "The in-principle inconclusiveness of causal evidence in macroeconomics". <i>European Journal for Philosophy of Science</i>. <b>8</b> (3): 709–733. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs13194-018-0207-7">10.1007/s13194-018-0207-7</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:158264284">158264284</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+for+Philosophy+of+Science&rft.atitle=The+in-principle+inconclusiveness+of+causal+evidence+in+macroeconomics&rft.volume=8&rft.issue=3&rft.pages=709-733&rft.date=2018&rft_id=info%3Adoi%2F10.1007%2Fs13194-018-0207-7&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A158264284%23id-name%3DS2CID&rft.aulast=Henschen&rft.aufirst=Tobias&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-:3-31"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_31-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_31-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngrist_Joshua_&_Pischke_Jörn-Steffen2008" class="citation book cs1">Angrist Joshua & Pischke Jörn-Steffen (2008). <i>Mostly Harmless Econometrics: An Empiricist's Companion</i>. Princeton: Princeton University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mostly+Harmless+Econometrics%3A+An+Empiricist%27s+Companion&rft.place=Princeton&rft.pub=Princeton+University+Press&rft.date=2008&rft.au=Angrist+Joshua+%26+Pischke+J%C3%B6rn-Steffen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAchen2002" class="citation journal cs1">Achen, Christopher H. (June 2002). <a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.polisci.5.112801.080943">"Toward a new political methodology: Microfoundations and ART"</a>. <i>Annual Review of Political Science</i>. <b>5</b> (1): 423–450. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.polisci.5.112801.080943">10.1146/annurev.polisci.5.112801.080943</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1094-2939">1094-2939</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Political+Science&rft.atitle=Toward+a+new+political+methodology%3A+Microfoundations+and+ART&rft.volume=5&rft.issue=1&rft.pages=423-450&rft.date=2002-06&rft_id=info%3Adoi%2F10.1146%2Fannurev.polisci.5.112801.080943&rft.issn=1094-2939&rft.aulast=Achen&rft.aufirst=Christopher+H.&rft_id=https%3A%2F%2Fdoi.org%2F10.1146%252Fannurev.polisci.5.112801.080943&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDawes1979" class="citation journal cs1">Dawes, Robyn M. (1979). <a rel="nofollow" class="external text" href="https://psycnet.apa.org/record/1979-30170-001">"The robust beauty of improper linear models in decision making"</a>. <i>American Psychologist</i>. <b>34</b> (7): 571–582. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1037%2F0003-066X.34.7.571">10.1037/0003-066X.34.7.571</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210721125318/https://psycnet.apa.org/record/1979-30170-001">Archived</a> from the original on 21 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Psychologist&rft.atitle=The+robust+beauty+of+improper+linear+models+in+decision+making&rft.volume=34&rft.issue=7&rft.pages=571-582&rft.date=1979&rft_id=info%3Adoi%2F10.1037%2F0003-066X.34.7.571&rft.aulast=Dawes&rft.aufirst=Robyn+M.&rft_id=https%3A%2F%2Fpsycnet.apa.org%2Frecord%2F1979-30170-001&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVandenbrouckeBroadbentPearce2016" class="citation journal cs1">Vandenbroucke, Jan P; Broadbent, Alex; Pearce, Neil (December 2016). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5841832">"Causality and causal inference in epidemiology: the need for a pluralistic approach"</a>. <i>International Journal of Epidemiology</i>. <b>45</b> (6): 1776–1786. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fije%2Fdyv341">10.1093/ije/dyv341</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0300-5771">0300-5771</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5841832">5841832</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26800751">26800751</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Epidemiology&rft.atitle=Causality+and+causal+inference+in+epidemiology%3A+the+need+for+a+pluralistic+approach&rft.volume=45&rft.issue=6&rft.pages=1776-1786&rft.date=2016-12&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5841832%23id-name%3DPMC&rft.issn=0300-5771&rft_id=info%3Apmid%2F26800751&rft_id=info%3Adoi%2F10.1093%2Fije%2Fdyv341&rft.aulast=Vandenbroucke&rft.aufirst=Jan+P&rft.au=Broadbent%2C+Alex&rft.au=Pearce%2C+Neil&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5841832&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenland2017" class="citation journal cs1">Greenland, Sander (January 2017). <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28220361/">"For and Against Methodologies: Some Perspectives on Recent Causal and Statistical Inference Debates"</a>. <i>European Journal of Epidemiology</i>. <b>32</b> (1): 3–20. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10654-017-0230-6">10.1007/s10654-017-0230-6</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1573-7284">1573-7284</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28220361">28220361</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4574751">4574751</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210721125317/https://pubmed.ncbi.nlm.nih.gov/28220361/">Archived</a> from the original on 21 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+of+Epidemiology&rft.atitle=For+and+Against+Methodologies%3A+Some+Perspectives+on+Recent+Causal+and+Statistical+Inference+Debates&rft.volume=32&rft.issue=1&rft.pages=3-20&rft.date=2017-01&rft.issn=1573-7284&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4574751%23id-name%3DS2CID&rft_id=info%3Apmid%2F28220361&rft_id=info%3Adoi%2F10.1007%2Fs10654-017-0230-6&rft.aulast=Greenland&rft.aufirst=Sander&rft_id=https%3A%2F%2Fpubmed.ncbi.nlm.nih.gov%2F28220361%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDominus2017" class="citation news cs1">Dominus, Susan (18 October 2017). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2017/10/18/magazine/when-the-revolution-came-for-amy-cuddy.html">"When the Revolution Came for Amy Cuddy"</a>. <i>The New York Times</i>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0362-4331">0362-4331</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200103061226/https://www.nytimes.com/2017/10/18/magazine/when-the-revolution-came-for-amy-cuddy.html">Archived</a> from the original on 3 January 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">2 March</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=When+the+Revolution+Came+for+Amy+Cuddy&rft.date=2017-10-18&rft.issn=0362-4331&rft.aulast=Dominus&rft.aufirst=Susan&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2017%2F10%2F18%2Fmagazine%2Fwhen-the-revolution-came-for-amy-cuddy.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.americanscientist.org/article/the-statistical-crisis-in-science">"The Statistical Crisis in Science"</a>. <i>American Scientist</i>. 6 February 2017. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210813141330/https://www.americanscientist.org/article/the-statistical-crisis-in-science">Archived</a> from the original on 13 August 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">18 April</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=American+Scientist&rft.atitle=The+Statistical+Crisis+in+Science&rft.date=2017-02-06&rft_id=https%3A%2F%2Fwww.americanscientist.org%2Farticle%2Fthe-statistical-crisis-in-science&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=22" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="what_if" class="citation book cs1"><a href="/wiki/Miguel_Hern%C3%A1n" title="Miguel Hernán">Hernán, MA</a>; <a href="/wiki/James_Robins" title="James Robins">Robins, JM</a> (21 January 2020). <a rel="nofollow" class="external text" href="https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/"><i>Causal Inference: What If</i></a>. Barnsley: Boca Raton: Chapman & Hall/CRC.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Causal+Inference%3A+What+If&rft.place=Barnsley&rft.pub=Boca+Raton%3A+Chapman+%26+Hall%2FCRC&rft.date=2020-01-21&rft.aulast=Hern%C3%A1n&rft.aufirst=MA&rft.au=Robins%2C+JM&rft_id=https%3A%2F%2Fwww.hsph.harvard.edu%2Fmiguel-hernan%2Fcausal-inference-book%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACausal+inference" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Causal_inference&action=edit&section=23" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; 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