This question already has an answer here:
I asked this question before, but maybe on the wrong audience at math.stackexchange.com. So, sorry for the redundancy.
I sat up a mixed-effects linear model with the dependent variable log-transformed (in order to get it normal distributed and as it is common with this kind of data in scientific publications).
log10(y) ~ = 0 + var1:var2 + var1:var2:cov1 + var1:var2:cov2
var1 and var2 define the treatments, and cov1 and cov1 are numerical covariables (regressors). I'm working with
lme() in R btw.
All fixed effects are significant and a consequent multiple comparisons of means (
glht()) works also: Detection of significant differences of different treatments. Now I wonder how to interpret the model estimates quantitatively, i.e. the intercepts per treatment compared by
The answer of Nworno on Linear mixed effect model interpretation with log transformed dependent variable says:
Regarding the interpretation of the intercept, it's a bit more complicated to translate it clearly, because it's related to the Region random effect. Here you have a random effect on the intercept, hence its value depends on the value of the categorical Region variable. The value -1.112047 showed in your output is the intercept value for the base value of the Region variable (i.e. Region category encoded as 0). In any case, there is no need for the intercept to be equal to the mean of the reponse variable, intercept is simply the expected value of your response variable when all other [in]dependent variables are equal to zero.
Independent covariables on zero makes no sense in my case. Therefore I standardized them to their respective mean. So ´glht()´ compares the log10 of the measured factor (the dependent variable) when the independent covariables are on their mean value, right?
Then my question is, regardless if mean-levels of the independent variables are to be expected in reality, are the back-transformed intercepts per treatment (
10^intercept) valid values in the initial unit? Are there mathematical restrictions or can I interpret those back-transformed values as the model predictions at the specific level of independent variables?
Hopefully this edit specified my question. Otherwise I'm open to further suggestions. Thanks in advance.