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It is an extremely common argument in sociology that the linear probability model (LPM) is bad for modeling binary outcomes because it can produce fitted probabilities smaller than 0 or larger than 1. This argument is commonly used to justify the use of logit (or probit). But the fact that LPM can produce impossible fitted values while logit cannot actually favors LPM. Here’s why.
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I again found myself pondering the meaning of the independence of irrelevant alternatives (IIA) assumption for multinomial logit models. The IIA assumption is often said to imply that given two options in the outcome, removing a third option would not change the relative probability of the first two options. This implication reads very counterfactual: under IIA, counterfactually designing a voting regime or a survey questionnaire excluding an option shouldn’t change the relative probability.
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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.