{"id":634,"date":"2018-06-04T08:30:00","date_gmt":"2018-06-04T12:30:00","guid":{"rendered":"http:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/?p=634"},"modified":"2018-06-03T18:07:20","modified_gmt":"2018-06-03T22:07:20","slug":"causal-inference-in-ecology-the-rubin-causal-model-part-2","status":"publish","type":"post","link":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/blog\/2018\/06\/04\/causal-inference-in-ecology-the-rubin-causal-model-part-2\/","title":{"rendered":"Causal inference in ecology – The Rubin causal model (part 2)"},"content":{"rendered":"

Causal inference in ecology – links to the series<\/a><\/p>\n

Last week<\/a> I described a straightforward example of why inferring a causal relationship from an observed association can be problematic. The authors of the study on the \u201cScully effect<\/a>\u201d are mostly pretty careful to write things like \u201cregular viewers of The X-Files<\/em> have far more positive beliefs about STEM than other women in the sample\u201d rather than claiming that viewing of the X Files<\/em> caused<\/strong><\/em> women to have more positive beliefs about STEM. In the end, though, they can\u2019t help themselves:<\/p>\n

The findings of this study confirm what previous research has established, that entertainment media is influential in shaping life choices.<\/p><\/blockquote>\n

As I pointed out last time, in order to make that claim from these data, we\u2019d need to know that there wasn\u2019t already a difference between women in the sample that caused women with positive beliefs about STEM to watch the X Files<\/strong><\/em> more often than other women.<\/p>\n

So let\u2019s suppose that in addition to asking women in their sample (a) whether they had watched the X Files<\/strong><\/em> and (b) whether they had a positive beliefs about STEM they had also asked them (c) how many courses in science and math they took during junior high and high school. Then a statistical model describing the data they collected would look like this:<\/p>\n\\(y_i = \\alpha_{treat[i]} + \\beta x_i \\\\\\)\n

where yi<\/sub><\/em> is a measure of positive belief for individual i<\/em>,1<\/a><\/sup> \u03b1treat[i]<\/sub><\/em> is an indicator variable that denotes whether or not the individual was part of the treatment (watching the X Files<\/strong><\/em> ),2<\/a><\/sup> \u03b2<\/em> is a regression coefficient indicating the amount that taking once science or math course affects the measure of positive belief, and xi<\/sub><\/em>; is the number of science or math courses that individual i<\/em> took. If \u03b1t<\/sub><\/em> > \u03b1c<\/sub><\/em>;, then we have some evidence that watching the X Files<\/strong><\/em> causally contributes to more positive impressions of stem in women.3<\/a><\/sup><\/p>\n

This approach only works, though, if the range in number of science courses taken by the two groups of women is roughly the same. If all of the women who watched the X Files<\/strong><\/em> took more science courses than any of the women who didn\u2019t, we couldn\u2019t tell whether the difference in their positive impressions was due to watching the X Files<\/strong><\/em> or to taking more science courses (or to the personality traits that caused them to take more science courses).<\/p>\n

That\u2019s the basic idea behind the Rubin causal model: Identify all of the factors that might reasonably influence the outcome of interest, include those factors in an analysis of covariance (or something similar), and infer a causal effect of the difference between two groups if there\u2019s an effect of the grouping variable after controlling for all of the other factors and<\/strong><\/em> if the groups broadly overlap on other potential causal factors. The degree to which you can be confident in your causal inference depends (a) on how well you\u2019ve done at identifying and measuring plausible causal factors and (b) how closely your two groups are matched on those other causal factors. Matching here plays the same conceptual role as randomization in a controlled experiment<\/a>.<\/p>\n

    \n
  1. Where I assume that larger values correspond to more positive beliefs. ↩<\/a><\/li>\n
  2. Notice that the subscript on \u03b1 will only take two values. I\u2019ll denote them \u03b1c<\/sub> and \u03b1t<\/sub> for \u201ccontrol\u201d and \u201ctreatment\u201d, respectively. ↩<\/a><\/li>\n
  3. Provided we\u2019re willing to extrapolate from our sample to women in general, or at least to women in the US. ↩<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Causal inference in ecology – links to the series Last week I described a straightforward example of why inferring a causal relationship from an observed association can be problematic. The… Read more ><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-634","post","type-post","status-publish","format-standard","hentry","category-statistics"],"_links":{"self":[{"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/posts\/634","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/comments?post=634"}],"version-history":[{"count":3,"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/posts\/634\/revisions"}],"predecessor-version":[{"id":636,"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/posts\/634\/revisions\/636"}],"wp:attachment":[{"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/media?parent=634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/categories?post=634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/darwin.eeb.uconn.edu\/uncommon-ground\/wp-json\/wp\/v2\/tags?post=634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}