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I recently found myself reading the large methodological literature on logit models in sociology again. And I think I may have found a way to more intuivtively explain certain things about logit models. I’ll try some ideas here to see if they make sense to people.
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It has been commonly argued in sociology that odds ratio—as a measure of association between categorical variables—is appealing, because of its “margin-free” property. This has always baffled me, so I decided to articulate my bafflement here as a sanity check.
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Inverse probability weighting (IPW) is a popular tool for estimating the average treatment effect (ATE) of a binary variable under the conditional ignorability assumption. There are multiple variants of IPW. Particularly, I used to be intrigued by the relationship between the so-called Horvitz–Thompson (HT) estimator and the Weighted Least Squares (WLS) estimator, both of which implement IPW.