{"id":1242,"date":"2025-01-29T09:18:24","date_gmt":"2025-01-29T14:18:24","guid":{"rendered":"https:\/\/ozer.gt\/log\/?p=1242"},"modified":"2025-02-16T16:34:26","modified_gmt":"2025-02-16T21:34:26","slug":"causal-effect-ordering-without-estimation","status":"publish","type":"post","link":"https:\/\/ozer.gt\/log\/2025\/01\/29\/causal-effect-ordering-without-estimation\/","title":{"rendered":"Causal effect ordering without estimation"},"content":{"rendered":"<p>[Click title for image]<\/p>\n<p>What if we could rank order causal effects without having to estimate them? A creative question, but would it work?<\/p>\n<p>Why would we want to rank rather than estimate at the first place? First, estimating causal effects is difficult and expensive. Also, in a case like the following, we may not need to estimate the effect: The decision to intervene has already been made (say, there will be a promotion). We want to maximize the return on the promotion.<\/p>\n<p>A missing piece, as I also discussed with one of the authors is the estimation of the financial impact, which usually precedes the decision to intervene (and how). Let&#8217;s skip this part for now and assume that an intervention (a specific promotion) has already been decided. So the conditional question we are answering is: Which of the customers should we target given the promotion? Can we decide this without estimating the causal effect for each customer?<\/p>\n<p>The paper explores two cases where causal effect ordering may be a viable solution:<\/p>\n<ul>\n<li><strong>Intervention data is not available.<\/strong> In other words, we only have predictions of the treatment effect, not a direct estimate as we would have in an experiment. Let&#8217;s say we only have predicted propensity scores for conversion.<\/li>\n<li><strong>Data on the actual outcome are not available, and we have to rely on a surrogate.<\/strong> Let&#8217;s say we can observe a customer&#8217;s short-term revenue, but that&#8217;s only a surrogate for the actual outcome we&#8217;re interested in: customer lifetime value.<\/li>\n<\/ul>\n<p>The authors use discrete choice modeling to show that in such cases where causal effect estimation is not feasible, causal effect ordering is possible if there exists a latent variable that satisfies the following two conditions:<\/p>\n<ol>\n<li><strong>Latent monotonicity:<\/strong> The latent variable is monotonically (positively or negatively) related to both the treatment effect and the outcome.<\/li>\n<li><strong>Full moderation:<\/strong> All (customer) features are informative only through the moderator.*<\/li>\n<\/ol>\n<p>That is, following the example in the opening slide, customer features (demographics, historical and behavioral purchase patterns&#8230;) are only relevant to the effect of the promotion and the customer&#8217;s decision to leave the company through, let&#8217;s say, the customer&#8217;s price sensitivity (a perfect mediation).<\/p>\n<p>Even with such strong assumptions, this looks like a useful and promising method. I came across this paper while attending a conference in December and finally found the time to take a look. Of course, there is more to the story. For example, what happens when you have multiple latent variables? If those latent variables are positively correlated, it shouldn&#8217;t be a problem, but what if they&#8217;re not? Also, the potentially different relationship between the latent variable and the outcome versus its surrogate is a concern. The authors address these boundary conditions and provide two decision trees in the paper that show when it is a good time to use causal effect ordering. Check it out <a href=\"https:\/\/arxiv.org\/abs\/2206.12532\">here<\/a>.<\/p>\n<p><em>* The latent variable is actually a moderator of the relationship between the treatment and the outcome. The authors show how it can also be defined as a mediator between the features and the outcome (and its surrogate) when the treatment is removed from the DAG. See Figure 10 in the paper.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[Click title for image] What if we could rank order causal effects without having to estimate them? A creative question, but would it work? Why would we want to rank rather than estimate at the first place? First, estimating causal effects is difficult and expensive. Also, in a case like the following, we may not [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1259,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"cybocfi_hide_featured_image":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1242","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/posts\/1242","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/comments?post=1242"}],"version-history":[{"count":19,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/posts\/1242\/revisions"}],"predecessor-version":[{"id":1469,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/posts\/1242\/revisions\/1469"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/media\/1259"}],"wp:attachment":[{"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/media?parent=1242"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/categories?post=1242"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ozer.gt\/log\/wp-json\/wp\/v2\/tags?post=1242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}