Back transforming log data

Question

I have a dataset with biomass, dbh, height, wood density, site, and species. As data were not normally distributed, I converted biomass, dbh and wd using the log() function. Then I developed a linear mixed model using the lmer() function in R Studio. I kept biomass as the response variable and the remaining other parameters as the fixed and random effects as shown below:

lmer(B~D + H + WD +(1|species) + (1|site)

Now, the problem I am facing is how to back-transform the model in order to calculate the bias and correction factor. In linear regression, we can back-transform by using exp(), but in my case, I don't have any idea. I went into lots of tutorials but these tutorials cannot solve my problem. Additionally, how do I perform train/test splits and cross-validation on my lmer model using caret()?

This is the first time I am developing a model and I am not from a statistics background. Can anyone please help me out?

Answer 1

Welcome to the site.

First, linear models don't require that the data be normally distributed. Some models make assumptions about the error and, since we can't know the error, we look at the residuals.

Second, even if the residuals aren't normally distributed, these days, there are models that make fewer assumptions. Some of these are old, but computer intensive and didn't become practical until there were fast computers.

So, don't transform the data unless you have a substantive reason for doing so. That is, do it when you want to look at variables multiplicatively rather than additively (this often happens with variables related to money).

There are a bunch of nonlinear mixed models. Without knowing more about your goals, I'm not sure which is best, but one possibility is a quantile model, which is available in R with the lqmm package.