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gjm comments on Even if you have a nail, not all hammers are the same - Less Wrong
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Credit should go to Andrew Gelman, who also points out (in his book with Jennifer Hill on hierarchical modeling) that the logistic regression coefficients do have a straightforward interpretation, at least when the probabilities are not too close to the extremes. (I'd have to look it up.)
I don't have Gelman's book, but: logistic regression says p = 1 / (1 + exp(-z)) where z is a linear combination of 1 and the independent variables. But then z is just the "log odds", log(p/(1-p)); you can think of the coefficient of 1 as being the log prior odds ratio and the other coefficients as being the amount of evidence you get for X over not-X per unit change in each independent variable.