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Maria Glymour and Sander Greenland introduces causal graph theory as a framework for reasoning from causal assumptions to statistical associations. The chapter explains basic definitions and assumptions, then develops preliminaries for causal graphs using potential-outcome (counterfactual) causation to distinguish causation from mere association. It formalizes statistical independence via conditional probability across strata, clarifying how unassociated variables relate to the lack of informative changes in outcomes across X levels, and sets up later rules and graphical reasoning.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/causal-diagrams-chapter-12-introduction-preliminaries-and-statistical-independence/665386/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/causal-diagrams-chapter-12-introduction-preliminaries-and-statistical-independence/665386.png","ImageObject",300,407,{"name":92,"@type":93},"gewufjwa","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the central purpose of causal diagrams in this chapter?","Question",{"text":112,"@type":113},"Causal diagrams provide a visual and logically grounded way to deduce the statistical associations implied by causal relations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the chapter distinguish causation from association?",{"text":117,"@type":113},"It uses the potential-outcome (counterfactual) concept of causation, where X affects Y only if intervening on X can change Y for at least one unit.",{"name":119,"@type":110,"acceptedAnswer":120},"What does statistical independence mean here?",{"text":121,"@type":113},"X and Y are statistically independent when the distribution of Y does not differ across strata defined by X, meaning knowing X gives no information about Y.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665386,1793302013,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},3985747882900,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Causal Diagrams  \nM. Maria Glymour and Sander Greenland  \nIntroduction 183  \nPreliminaries for Causal  \nGraphs 184  \nStatistical Independence 184  \nCausation and Association 185  \nCotlider Bias 185  \nSummary 186  \nGraphical Models 186  \nTerminology 186  \nRules Linking Absence of Open Paths to Statistical Independencies 187  \nAssumptions and Intwtions Underlying the Rules 190  \nGraphical Representation of Bias and its  \nControl 191  \nSufficient and Mnmally Sufficient Conditorung  \nSome Applications 194  \nWhy Conventional Rules for Confounding Are  \nNot Always Reliable 194  \nGraphical Analyses of Selection Bias 196 Bias from Intentional Se•ection 196  \nSurvivor Bias 198  \nResidual Confounding and Bias Quantification 198  \nBras from Use of Missing-Data Categories or Indicators 199  \nAdjusting for an Intermediate Does Not Necessarily Estimate a Direct Effect 200  \nInstrumental Variables 202  \nBias from Conditioning on a Descendant of the  \nOutcome 204  \nSelection Bias and Matchng in Case-Control Studies 205  \nSets 192  \nChoosing Conditioning Sets to Identify Causal Effects 192  \nConfounding and Selection Bias 192  \nHow Adjust•ng for Baseine Values Can Bias Ana!yses of Change 206  \nCaveats and Extensions 208  \nConclusion 209  \nINTRODUCTION  \nDiagrams of causal pathways have tong been used to visually summarize hypothetical relations among variables of interest. Modern causal diagrams, or causal graphs, were more recently devel oped from a mcrgerof graphical probability theory with path diagrams. The resulting theory provides a powerful yet intuitive device for deducing the statistical associations implied by causal relations. Conversely, given a set of observed statistical  relations. a researcher armed with causal graph theory  can systematically characterize all causal structures compatible with the observations. The theory  also provides a visual representation of key concepts in the more general theory or longitudinal causality or Robins ( 1997); see Chapter 21 for further discussion and references on the tatter topic.  \nThe graphical rules linking causal relations to statistical associations are grounded in mathe. matics. Hence, one way to think of causal diagrams is that they allow nonmathematicians to draw  logically sound conclusions about certain types of statistical relations. Learning the rules for reading statistical associations from causal diagrams may take a little time and practice. Once these rules  are mastered, though, they facilitate many tasks, such as understanding confounding and selection  \n183  \nIl •  \nbias, choosing covariates for adjustment and for regression analyses, understanding analyses of direct effects and instrumental-variable analyses, and assessing \"natural experiments.\" In particular, diagrams help researchers recognize and avoid common mistakes in causal analysis.  \nThis chapter begins with the basic definitions and assumptions used in causal graph theory. It then describes constnction of causal diagrams and the graphical separation rules linking the causal assumptions encoded in a diagram to the statistical relations implied by the diagram. The chapter concludes by presenting some examples of applications. Some readers may prefer to begin with the examples and refer back to the definitions and rules for causal diagrams as needed. The section on Graphical Models, however, is essential to understanding the examples. Full technical details of causal diagrams and their relation to causal inference can be found in Pearl (2000) and Spines et al. (2001), while Greenland and Pearl (2008) provide a short technical review. Less technical articles geared toward health scientists include Greenland et al. (1999a), Robins (2001 ), Greenland and Brumback (2002), Hernán et al. (2002), Jewell (2004), and Glymour (2006b) .  \nPRELIMINARIES FOR CAUSAL GRAPHS  \nConsider two variables X and Y for which we wish to represent a causal connection from X to Y, often phrased as \"X causes Y\" or \"X affects Y. \" Causal dia","cbCaibeGaBruXZwG","https://ap.wps.com/l/cbCaibeGaBruXZwG","pdf",431605,"English","# Introduction\n## Preliminaries for Causal Graphs\n## Statistical Independence\n## Causation and Association\n## Collider Bias\n## Summary\n## Graphical Models\n## Terminology\n## Rules Linking Absence of Open Paths to Statistical Independencies\n## Assumptions and Intentions Underlying the Rules","[{\"question\":\"What is the central purpose of causal diagrams in this chapter?\",\"answer\":\"Causal diagrams provide a visual and logically grounded way to deduce the statistical associations implied by causal relations.\"},{\"question\":\"How does the chapter distinguish causation from association?\",\"answer\":\"It uses the potential-outcome (counterfactual) concept of causation, where X affects Y only if intervening on X can change Y for at least one unit.\"},{\"question\":\"What does statistical independence mean here?\",\"answer\":\"X and Y are statistically independent when the distribution of Y does not differ across strata defined by X, meaning knowing X gives no information about Y.\"}]","Causal Diagrams - Chapter 12 - Introduction - Preliminaries and Statistical Independence | PDF",23]