I'm using lme4 and have a GLMM with a log link and gaussian variance structure. I would like to report my fixed effect estimates with their standard errors, as well as the standard deviation of my random effects on the response scale. The output from my model is on the link scale. Can I simply exponentiate the output, or do I need to do more?

# GLMM Analysis – How to Back Transform Standard Errors in a GLMM with a Log-Link Function

generalized linear modellink-functionmixed modelreporting

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## Best Answer

Standard errors do not transform. If uncertainty intervals on the link scale are symmetric (as they often approximately are), when you anti-log parameter estimates the uncertainty on the anti-logged scale will be asymmetric. You can anti-log the confidence limits but cannot get a standard error that is useful on the original scale because of the needed asymmetry.