# Interpret model estimates after log transformation

I sat up a mixed-effects linear model with the dependent variable log-transformed (in oder to get it normal distributed and as ist is common with this kind of data in other publications). All fixed affects are significant and a consequent multiple comparissons of means works also great (significant differences of log10 values of different treatments). Now I wonder how to interpret the model estimates quantitatively. It seems not correct to just re-transform the estimates. Although the results are in the regular range and the means are in the same order as with untransformed values. [Only related topic I found is this][1] but I'm not sure if it is applicable to my case. The formula I use is:

log10(y) ~ = 0 + var1:var2 + var1:var2:cov1 + var1:var2:cov2


I'm working with R btw. Thanks for any help.

• This is a major problem as you noticed in my answer in the linked page. The key problem is that you measure $y$ and not $\log_{10}(y)$; so, if the errors are not very samll, you can face serious dangers. Can't you afford a nonlinear regression since you already have good (or at least reasonable) estimates of the parameters ? It would be much safer. – Claude Leibovici Apr 11 at 8:42
• @Claude: Thanks for your answer. I specified my question here: stats.stackexchange.com/questions/402415/…. If you would be so kind and have a look :) – Clem Snide Apr 12 at 7:23
• @Claude: How to set up a nonlinear regression on basis of my pre-work? – Clem Snide Apr 12 at 7:23
• No idea ! I am not a statistician ... even if I have some experience with data fitting. This expalins my comment. Just a stupid question : can you write $y=10^{xxx}$ ? – Claude Leibovici Apr 12 at 7:30