The problem is not that you are new to R. This is a conceptual issue.

Let y be the response variable and let {x_i} be a set of predictors. Your first model (identity response and log-link) is saying that 

y=f(x_1)f(x_2)...f(x_n) + e, e~Normal(0,sigma)

i.e. this is an additive observation-error model with constant variance.

Your second model (log-response and identity link) is saying that
 
y=f(x_1)f(x_2)...f(x_n)u, u=exp(e), e~Normal(0,sigma)

i.e. this a multiplicative observation-error model with variance proportional to the mean.

Plot the data versus response and visually examine whether you have heteroscedasticity. If this is true, use your second model, otherwise use the first one.

One key to understand these kind of dichotomies is to realize that statistical models are composed of a process part and an observation part. In your models the process part is deterministic and multiplicative but after that, you still have two choices, make the random observation part additive (your first model) or multiplicative (your second model).

Needless to say (but I am saying it anyways) these two models will give different results, at the very least because one assumes constant variance (your first model) whereas the other assumes a variance proportional to the mean.

In my experience with multiplicative process models, the random observation part shall usually be multiplicative as well because of heteroscedasticity.

HTH

Rubén

-----------------------------------------

Rubén H. Roa-Ureta, Ph. D.
AZTI Tecnalia, Txatxarramendi Ugartea z/g,
Sukarrieta, Bizkaia, SPAIN

-----Original Message-----
From: r-help-bounces@r-project.org on behalf of pigpigmeow
Sent: Sun 6/19/2011 9:39 AM
To: r-help@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(loga~s(b), family =gaussian (link=identity),data)
why these two command results are different?
I guess these two command results are same, but actally these two command
results are different, Why?

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