Back transforming standard errors in a GLMM with a log-link

Question

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?

It may help to read [Back-transformation of regression coefficients](https://stats.stackexchange.com/q/27067/7290). — gung - Reinstate Monica, Mar 03 '22 at 21:03

score 3 · Accepted Answer · answered Mar 03 '22 at 12:30

3

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.

answered Mar 03 '22 at 12:30

Frank Harrell

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Thanks for your response! Can I anti-log the SD of my random effects though? Would that be meaningful? – teeniv Mar 03 '22 at 12:48
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No! Please read my answer again. – Frank Harrell Mar 03 '22 at 13:05

Back transforming standard errors in a GLMM with a log-link

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