R help - Oct 2007 - In a SLR, Why Does the Hat Matrix Depend on the Weights?

I understand that the hat matrix is a function of the predictor variable
alone. So, in the following example why do the values on the diagonal of the
hat matrix change when I go from an unweighted fit to a weighted fit? Is the
function hatvalues giving me something other than what I think it is?

 

library(ISwR)

data(thuesen)

attach(thuesen)

 

fit <- lm(short.velocity ~ blood.glucose)

summary(fit)

hatvalues(fit)

 

W <- 1/blood.glucose

fit.w <- lm(short.velocity ~ blood.glucose,weights=W)

summary(fit.w)

hatvalues(fit.w)

 

Thanks for the help.

 

Tom

 


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Because it does. I should have looked ahead a few chapters in the book
before I asked the question. However, I can't seem to reproduce the values
of the hat matrix given by R for the weighted fit example I gave. Any
suggestions (other than looking ahead a few more chapters)?

 

Tom

 


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Tom La Bone wrote:
> I understand that the hat matrix is a function of the predictor variable
> alone. So, in the following example why do the values on the diagonal of
the
> hat matrix change when I go from an unweighted fit to a weighted fit? Is
the
> function hatvalues giving me something other than what I think it is?
>
>  
>   
It's a bit difficult to know what you might be thinking.

The formula for the hat matrix is X inv(X'WX) X'W and I have some 
difficulty seeing how you might expect that _not_ to depend on W....

(I suspect that whatever source you used intended to say that the hat 
matrix does not depend on the observations, with no thought given to the 
possibility of a weighted analysis.)
> library(ISwR)
>
> data(thuesen)
>
> attach(thuesen)
>
>  
>
> fit <- lm(short.velocity ~ blood.glucose)
>
> summary(fit)
>
> hatvalues(fit)
>
>  
>
> W <- 1/blood.glucose
>
> fit.w <- lm(short.velocity ~ blood.glucose,weights=W)
>
> summary(fit.w)
>
> hatvalues(fit.w)
>
>  
>
> Thanks for the help.
>
>  
>
> Tom
>
>  
>
>
> 	[[alternative HTML version deleted]]
>
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>   

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