{"id":1389,"date":"2015-01-22T02:00:01","date_gmt":"2015-01-22T09:00:01","guid":{"rendered":"http:\/\/www.mii.ucla.edu\/causality\/?p=1389"},"modified":"2015-01-22T02:00:01","modified_gmt":"2015-01-22T09:00:01","slug":"flowers-of-the-first-law-of-causal-inference-2","status":"publish","type":"post","link":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/2015\/01\/22\/flowers-of-the-first-law-of-causal-inference-2\/","title":{"rendered":"Flowers of the First Law of Causal Inference (2)"},"content":{"rendered":"<p><strong>Flower 2 &#8212; Conditioning on post-treatment variables<\/strong><\/p>\n<p>In this 2nd flower of the <a href=\"http:\/\/causality.cs.ucla.edu\/blog\/?p=1323\">First Law<\/a>, I share with readers interesting relationships among various ways of extracting information from post-treatment variables. These relationships came up in conversations with readers, students and curious colleagues, so I will present them in a question-answers format.<\/p>\n<p><strong>Question-1<\/strong><br \/>\nRule 2 of do-calculus does not distinguish post-treatment from pre-treatment variables. Thus, regardless of the nature of Z, it permits us to replace P (y|do(x), z) with P (y|x, z) whenever Z separates X from Y in a mutilated graph G<sub><span style=\"text-decoration: underline;\">X<\/span><\/sub> (i.e., the causal graph, from which arrows emanating from X are removed). How can this rule be correct, when we know that one should be careful about conditioning on a post treatment variables Z?<\/p>\n<p><strong>Example 1<\/strong> Consider the simple causal chain X \u2192 Y \u2192 Z. We know that if we condition on Z (as in case control studies) selected units cease to be representative of the population, and we cannot identify the causal effect of X on Y even when X is randomized. Applying Rule-2 however we get P (y|do(x), z) = P (y|x, z). (Since X and Y are separated in the mutilated graph X Y \u2192 Z). This tells us that the causal effect of X on Y IS identifiable conditioned on Z. Something must be wrong here.<\/p>\n<p><a title=\"r447-blog-version-rev1.pdf\" href=\"http:\/\/causality.cs.ucla.edu\/blog\/wp-content\/uploads\/2015\/02\/r447-blog-version_rev2.pdf\" target=\"_blank\">To read more, click here.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Flower 2 &#8212; Conditioning on post-treatment variables In this 2nd flower of the First Law, I share with readers interesting relationships among various ways of extracting information from post-treatment variables. These relationships came up in conversations with readers, students and curious colleagues, so I will present them in a question-answers format. Question-1 Rule 2 of [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,6,12,37],"tags":[],"class_list":["post-1389","post","type-post","status-publish","format-standard","hentry","category-back-door-criterion","category-counterfactual","category-do-calculus","category-structural-equations"],"_links":{"self":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=1389"}],"version-history":[{"count":0,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1389\/revisions"}],"wp:attachment":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=1389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=1389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=1389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}