R help - Feb 2005 - cook's distance in weighted regression

I have a puzzle as to how R is computing Cook's distance in weighted linear
regression.

In 
this case cook's distance should be given not  as in OLS case by

h_ii*r_i^2/(1-hii)^2 divided by k*s^2                                    (1)
(where  r is plain unadjusted residual, k is number of parameters in model,
etc. )

but rather by 

w_ii*h_ii*r_i^2/(1-hii)^2 divided by k*s^2,                            (2)

i.e. has the weight in there. Apart from the division this is sum of
weighted squares of differences 

yhat_j - yhat_j[i]. (That is, it is the weighted sum of squares of fits
minus fits with ith point deleted.)

However, a little experimentation in R, using ls.diag(fit)$cooks, suggests
that in weighted case R gives (1) times some constant. Does anybody know how
that constant is calculated?  What is the rationale for
using equation (1) (times a constant) in the weighted case anyway?  
Thanks.




	[[alternative HTML version deleted]]

Dear Alan,

You can use the (generic) cooks.distance function in R, which uses the
weighted residuals. See ?cooks.distance, and stats:::cooks.distance.lm for
the function definition (i.e., the method for a linear model).

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
> Dorfman, Alan - BLS
> Sent: Friday, February 11, 2005 11:08 AM
> To: 'r-help at stat.math.ethz.ch'
> Subject: [R] cook's distance in weighted regression
> 
> 
> I have a puzzle as to how R is computing Cook's distance in 
> weighted linear regression.
> 
> In
> this case cook's distance should be given not  as in OLS case by
> 
> h_ii*r_i^2/(1-hii)^2 divided by k*s^2                         
>            (1)
> (where  r is plain unadjusted residual, k is number of 
> parameters in model, etc. )
> 
> but rather by 
> 
> w_ii*h_ii*r_i^2/(1-hii)^2 divided by k*s^2,                   
>          (2)
> 
> i.e. has the weight in there. Apart from the division this is 
> sum of weighted squares of differences 
> 
> yhat_j - yhat_j[i]. (That is, it is the weighted sum of 
> squares of fits minus fits with ith point deleted.)
> 
> However, a little experimentation in R, using 
> ls.diag(fit)$cooks, suggests that in weighted case R gives 
> (1) times some constant. Does anybody know how that constant 
> is calculated?  What is the rationale for using equation (1) 
> (times a constant) in the weighted case anyway?  
> Thanks.
> 
> 
> 
> 
> 	[[alternative HTML version deleted]]
> 
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