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There is also the interesting interpretation of logistic regression as a latent choice/utility model, where unobserved variation in utility is modeled using the
by MidsizeBlowfish 10y ago
There is also the interesting interpretation of logistic regression as a latent choice/utility model, where unobserved variation in utility is modeled using the logistic distribution. In this interpretation, the sigmoid function arises as the CDF of the logistic distribution.
This interpretation is also nice as it shows the natural relationship between logistic and probit regression. Probit regression arises when the unobserved utility is modeled with a Gaussian distribution.
- thanatropism 10y agoIn this interpretation we expect decision-makers to be utility-maximizers - for example, as whether I buy or not Thing X; so, we expect Gumbel (an extreme value distribution) errors. But we're looking for Utility(1) minus Utility(0) (buying vs. not buying) and the difference between two Gumbels is a logistic. More detail: http://fisher.osu.edu/~schroeder.9/AMIS900/ch5.pdf http://fisher.osu.edu/~schroeder.9/AMIS900/ch5.pdf
- MidsizeBlowfish 10y agoAh, right you are! Thanks for correcting my mistake :)