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seen Sep 27 '13 at 17:28

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Sep
27
comment Intuition behind logistic regression
@AdamO, however you motivate logistic regression, it's still mathematically equivalent to a thresholded linear regression model where the errors have a logistic distribution. I agree that this assumption may be hard to test but it's there regardless of how you motivate the problem. I recall a previous answer on CV (I can't place it right now) that showed with a simulation study that trying to tell whether a logistic or probit model "fit better" was basically a coin flip, regardless of the true data generating model. I suspect logistic is more popular because of the convenient interpretation.
Sep
27
comment Logistic regression vs. estimating $\beta$ using linear regression and applying the inverse-logit function
I downvoted this because it doesn't answer the question.
Sep
27
comment Logistic regression vs. estimating $\beta$ using linear regression and applying the inverse-logit function
I think there's a minus sign missing in the exponent, because the inverse logit function (a.k.a. the logistic function) is $1/(1+e^{-x})$.
Sep
27
revised Logistic regression vs. estimating $\beta$ using linear regression and applying the inverse-logit function
changed the poor title
Sep
27
comment Usable estimators for parameters in Gumbel distribution
Just to add to what @Glen_b said, a common way of evaluating estimators is with the mean squared error(MSE). It's a fact that the MSE of an estimator $\hat \theta$ of a parameter $\theta$ can be written as $$ {\rm MSE}(\hat \theta) = {\rm bias}(\hat \theta)^2 + {\rm var}(\hat \theta) $$ So it's clear that a biased estimator can perform better than an unbiased estimator if its variance is lower. This is called the "bias variance tradeoff" and is part of the logic underlying regularized estimation (e.g. penalized maximum likelihood).
Sep
26
comment Intuition behind logistic regression
@AdamO, if the $\epsilon_i$ have a logistic distribution, then this describes logistic regression.
Sep
26
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