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This is a very simple question. When I back transform log transformed coefficients it usually looks like this:

exp(interceptvalue) + exp(paramter1 coefficicent)

When I want to back transform the standard errors. Do I do the same thing? Or do I just have to backtransform it like this:

exp(paramter1 std.e)

I guess my question comes down to: Are standard errors in a generalized linear model output (in R) additive like the coefficient estimates?

kjetil b halvorsen
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Leo Ohyama
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    You cannot (at least not easily) backtransform standard errors, but you can backtransform confidence intervals. For an example see: http://stats.stackexchange.com/questions/241970/how-to-calculate-standard-errors-for-glms-fitted-values-by-hand-without-using/243333#243333 and then adapt the methods used there. – kjetil b halvorsen Dec 25 '16 at 22:56
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    Can you explain the type of model you're fitting? I am having trouble thinking of typical cases where your "exp(interceptvalue) + exp(paramter1 coefficicent)" would be a sensible thing to do – Glen_b Dec 26 '16 at 01:43
  • You can approximate the standard error of a function of the maximum likelihood estimator using [the Delta Method](https://en.wikipedia.org/wiki/Delta_method). Because coefficients in a GLM are typically estimated by maximum likelihood, this applies to your problem. – Linearity_Of_Expected_Value Dec 26 '16 at 00:51

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