{"id":48,"date":"2010-11-01T01:28:48","date_gmt":"2010-11-01T05:28:48","guid":{"rendered":"https:\/\/cyrussamii.com\/?p=48"},"modified":"2010-11-03T13:23:28","modified_gmt":"2010-11-03T17:23:28","slug":"superpopulations-and-inference-with-all-the-data","status":"publish","type":"post","link":"https:\/\/cyrussamii.com\/?p=48","title":{"rendered":"Superpopulations and inference with &#8220;all the data&#8221;"},"content":{"rendered":"<p>Doug [Rivers, I presume?] added a nice comment on superpopulation versus (sampling) design-based approaches to inference in regression modeling (<a href=\"http:\/\/www.stat.columbia.edu\/~cook\/movabletype\/archives\/2009\/07\/how_does_statis.html#comment-1090876\">link<\/a>).  The comment is to a post on Andy Gelman&#8217;s blog from over a year ago about what to do when one is trying to fit regressions to data on the &#8220;full population.&#8221;<\/p>\n<p>One comment: Doug suggests that &#8220;the definition of the regression parameters is arbitrary (why not LAD or some other estimator applied to the population?) and it&#8217;s not obvious how to interpret the parameters.&#8221; \u00a0My reading of Goldberger (<a href=\"http:\/\/www.amazon.com\/Course-Econometrics-Arthur-S-Goldberger\/dp\/0674175441\">reference<\/a>) and Angrist and Pischke (<a href=\"http:\/\/press.princeton.edu\/titles\/8769.html\">reference<\/a>) suggests that OLS is well motivated, based on the best linear approximation criterion. \u00a0Going beyond the trivial case of a binary predictor variable (for which OLS is a convenient way to calculate mean differences), with a continuous predictor, linear approximation is an easy-to-interpret summary of the predictor&#8217;s relationship to the outcome variable. \u00a0 Along similar lines, logistic regression is well motivated as the maximum entropy estimator of a relationship to a binary outcome. \u00a0So I am not sure that it is all that arbitrary.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Doug [Rivers, I presume?] added a nice comment on superpopulation versus (sampling) design-based approaches to inference in regression modeling (link). The comment is to a post on Andy Gelman&#8217;s blog from over a year ago about what to do when one is trying to fit regressions to data on the &#8220;full population.&#8221; One comment: Doug &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/cyrussamii.com\/?p=48\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Superpopulations and inference with &#8220;all the data&#8221;&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-48","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=48"}],"version-history":[{"count":6,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts\/48\/revisions"}],"predecessor-version":[{"id":52,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=\/wp\/v2\/posts\/48\/revisions\/52"}],"wp:attachment":[{"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cyrussamii.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}