
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.




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