Back transform log-transformed results (CI, SE, Estimates)

[Jolien]

Hello everybody,

I am running into problems back transforming my results.

I made 1 LM and 3 LME models in which my dependent variable (blood ketone bodies concentration) was log transformed due to the positieve skew. The final model therefore looked like this:

KFPlma4 = Ketone bodies as dependent outcome variable
KFPlma4 = Random effects Farm (F) and Parity (P)
KFPlma4 = Linear mixed model
KFPlma4 = All significant found independent variables (behaviours, mean daily eating time blabla) nr 4 based on AIC scores.

The results that i have thus far are as followed. I thought i had to include both the log transformed as well as the back transformed results for confidence interval, SE and estimates. However, as i back transform the results by 10^(original result) the relation between my CI and SE are way off. Before back transforming, they are normal?

I am transforming in excel, but i think i am doing something wrong.. Can somebody help me?

Help is very much appreciated!

Thanks in advance!

[arthur.t]

log() in R is actually the natural log, so you need exp() to inverse transform.

[Jolien]

Hi Arthur!

Thanks a lot, i now see that it isnt clear but i actually did that. But the balance between still log-transformed results is good, the balance between the back transformed results isn't.... That's the problem at the moment i guesss...

[arthur.t]

OK. Another idea. You can't inverse trans. the SE or CI width and then add/subtract that to the inverse trans mean. That violates the math properties of the logarithm. Instead, you have to inverse trans. individually the upper and lower CI.

[arthur.t]

@Jolien

Hi Arthur!

Thanks a lot, i now see that it isnt clear but i actually did that. But the balance between still log-transformed results is good, the balance between the back transformed results isn't.... That's the problem at the moment i guesss...

I do think you're doing a 10^ instead of an exp based on what you typed in original post and the numbers in your screenshot.

[Jolien]

Hey Arthur!

Thanks again for your help! Wow, yes i am doing a 10^, i thought that was the way to back transform. But i now understand i need to use the exp?

However, i am a beginner, so if you could help me be sure i'm doing this right, i would be so grateful!

For every model, i ask for confint(modelname) and summary(modelname)
Can i just individually put, for example, the lower limit of the Eating -3 CI in the exp?

So for the new back transformed results, can i just type into R studio the log transformed results? Like below:

If by individually trans. the upper and lower CI you mean: individually calculate by means of exp(), i did already do that with the (apparently wrongly used) 10^

By means of this screenshot, do you think i am doing this correctly?

Hope you can help me!

Thanks alot in advance (really, like massive thanks)