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Is all in the title. I would like to know if there is any difference in terms of coefficients, residuals, p-values, but also conceptually.

conjugateprior
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JG11235
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  • The difference is in how the errors are modeled. You should look up the formulas. I'd guess there should be some duplicates here already. – Roland Mar 28 '15 at 14:56
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    In the first case, you assume that log(y) is normal given x (and that the mean of log(y) is a linear function of x), and in the second case you assume that y *itself* is normal given x (and the log of its mean is a linear function of x). These are two different models, and may potentially give very different answers. – Karl Ove Hufthammer Mar 28 '15 at 15:52
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    Just to add to @Roland’s comment: If you model log(y) ~ x, you assume that log(y) equals a linear function of x **plus** an error term (which is normally distributed). This means that y equals a (non-linear) function of x **times** an error term (which is log-normally distributed). – Karl Ove Hufthammer Mar 28 '15 at 15:55
  • @KarlOveHufthammer, your comments seem to have the makings of an answer (& I think a better answer than those at the other Q, including mine). Why not turn them into an official answer here before this gets closed? – gung - Reinstate Monica Mar 29 '15 at 01:29
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    Although none of them are close duplicates, you may get some benefit from [this question](http://stats.stackexchange.com/questions/67547/when-to-use-gamma-glms) or [this one](http://stats.stackexchange.com/questions/114046/multiplicative-error-and-additive-error-for-generalized-linear-model) and possibly even [this answer](http://stats.stackexchange.com/questions/67437/confusion-related-to-which-transformation-to-use/67505#67505) or [this question](http://stats.stackexchange.com/questions/72381/gamma-vs-lognormal-distributions) – Glen_b Mar 29 '15 at 09:31

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