In this paper titled "CHOOSING AMONG GENERALIZED LINEAR MODELS APPLIED TO MEDICAL DATA" the authors write:
In a generalized linear model, the mean is transformed, by the link function, instead of transforming the response itself. The two methods of transformation can lead to quite different results; for example, the mean of log-transformed responses is not the same as the logarithm of the mean response. In general, the former cannot easily be transformed to a mean response. Thus, transforming the mean often allows the results to be more easily interpreted, especially in that mean parameters remain on the same scale as the measured responses.
It appears they advise the fitting of a generalized linear model (GLM) with log link instead of a linear model (LM) with log-transformed response. I do not grasp the advantages of this approach, and it seems quite unusual to me.
My response variable looks log-normally distributed. I get similar results in terms of the coefficients and their standard errors with either approach.
Still I wonder: If a variable has a log-normal distribution, isn't the mean of the log-transformed variable preferable over the log of the mean untransformed variable, as the mean is the natural summary of a normal distribution, and the log-transformed variable is normally distributed, whereas the variable itself is not?