[R] question about se of predicted glm values

[Berwin A Turlach]

G'day Jarrett,
> tapply(y,x,mean)
    a     b 
 1.00 25.58 
On Mon, 5 May 2008 20:21:26 -0700
Jarrett Byrnes <jebyrnes at ucdavis.edu> wrote:

> Hey, all.  I had a quick question about fitting new glm values and  
> then looking at the error around them.  I'm working with a glm using
> a Gamma distribution and a log link with two types of treatments.   
> However, when I then look at the predicted values for each category,
> I find for the one that is close to 0, 

And this does not surprise you, since with your data:

> tapply(y,x,mean)
    a     b 
 1.00 25.58 

So wouldn't you expect one predicted value to be close to 1 instead of
zero?

> the error (using se.fit=T with predicted) actually makes it overlap
> 0.  This is not possible, as non-0 values have no meaning.
> 
> Am I missing something in the interpretation?  

Yes. :)

For GLMs, predict returns by default the predicted values on the linear
predictor scale, not on the response scale.  Negative values for the
linear predictor are, of course, possible and may have meaning.

Look closely at the pictures that you have created.  In the first one,
for x=b, the values are around 30, in the picture with the fitted value
the prediction for x=b is around 3; clearly another scale (namely the
scale of the linear predictor).

> #get predicted values and their error
> a.fit<-predict(my.glm, data.frame(x="a"), se.fit=T)
> b.fit<-predict(my.glm, data.frame(x="b"), se.fit=T)

Try: 

a.fit<-predict(my.glm, data.frame(x="a"), se.fit=T, type="response")
b.fit<-predict(my.glm, data.frame(x="b"), se.fit=T, type="response")

Hope this helps.

Best wishes,

	Berwin

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