I analyzed some data using Proc Mixed and one of my outcome variables
was log transformed, while the predictor and other two outcome
variables were not. How do I interpret this data in light of the log
transformed variable? Any suggestions or references would be greatly
I suppose You can interpret it the same as varibales without log transformed.
Because log transformed is monotonous increasing, that means the value of this variable is larger and log transformed of this variable is also larger.
The target of log transformed of the variable Maybe is to make distribution of variable to approach Normal distribution which can fit the model better.
did you find any reference? I am also interested in this point. This is a problem that from time to time I find and I never managed to solve.
As far as I know, when you model log transformed data, you are modeling the geometric mean instead of the standard mean. Moreover, the effects in this context are interpreted as multiplicative effects rather than additive, e,g:
If we want to study the effect on Y of a new treatment with the model:
log(y) = a + b * x
where x is an indicator variable where x=1 for the experimental treatment and x=0 for the placebo, then exp(b) is equal to the relative change!!
exp(b) = exp(a+b)/exp(a) = [expected value for the treatment] / [expected value for the placebo].
Many books explain the good properties of the log-transformation for variance homogenization, normalization of the data, etc, but it is quite frustating that then they do not explain how to interpret the data. Maybe is too obvious?
Another interesting property: the back-transformation of a mean log is the median (not the mean) of the original scale. And, as stated in the other reply, the EFFECTS in a model fitted to log data are used to obtain relative changes (say, of treatment).
Interpretation of the back-transformed value as a median requires that the residuals of the log-transformed response have a symmetric distribution. The residuals do not have to be normally distributed, just symmetric.
It should be noted that any transformation which achieves a symmetric distribution for the residuals will result in a back-transformed estimate which is interpretable as the median, assuming that the back-transformation is applied to an estimate of the mean. The mean of the log-transformed (or square-root transformed, or inverse, or ...) data is an estimate of the 50th percentile of the transformed response as long as the transformed data are symmetric. Back-transforming the 50th percentile of the transformed response will result in an estimate of the 50th percentile on the original scale.