I have a question about the interpretation difference between log link of GLM and log transformation of LM. I know that log transformation is for target variable but log link is for mean .But related with the interpretation of the model seems they are similar ? both need e^coefficent to measure the influence of the target variable? The question may be convert to if we want to get 1) estimation of Y or 2)the interpretation of coefficient, how these two affect the result ?
I have some clue that:
- For the interpretation of coefficient : using mean to measure the impact ? so for the log of LM, nothing changing with normal distribution , so u=p0+p1x. For log link will be u=e^(po+p1x)
- For the estimation of y, using signal function and estimator of p to get y.For log transform y=e^(po+p1x), for log link is only depend on the which exponential family choose.
But I am not very clear why using mean to moniter the impact of coefficient. I originally thought is same as the estimation of y. So I am confused there