[R] please help! what are the different using log-link function and log transformation?

[Bill.Venables at csiro.au]

The two commands you give below are certain to lead to very different results, because they are fitting very different models.

The first is a gaussian model for the response with a log link, and constant variance.

The second is a gaussian model for a log-transformed response and identity link.  On the original scale this model would imply a constant coefficient of variation and hence a variance proportional to the square of the mean, and not constant.

Your problem is not particularly an R issue, but a difficulty with understanding generalized linear models (and hence generalized additive models, which are based on them).

Bill Venables.
________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of pigpigmeow [glorykwok at hotmail.com]
Sent: 19 June 2011 17:39
To: r-help at r-project.org
Subject: [R] please help! what are the different using log-link function and log transformation?

I'm new R-programming user, I need to use gam function.

y <- gam(a ~ s(b), family = gaussian(link=log),  data)
y <- gam(log(a) ~ s(b), family = gaussian (link=identity), data)

why [do] these two command [give different] results?

I guess these two command results are same, but actally these two command
results are different, Why?

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