[R] proportional weights

Marco Inacio marcoigarapava at gmail.com
Wed Feb 5 22:40:04 CET 2014

Hello all, can help clarify something?

According to R's lm() doc:

> Non-NULL weights can be used to indicate that different observations
> have different variances (with the values in weights being inversely
> *proportional* to the variances); or equivalently, when the elements
> of weights are positive integers w_i, that each response y_i is the
> mean of w_i unit-weight observations (including the case that there
> are w_i observations equal to y_i and the data have been summarized).

Since the idea here is *proportion*, not equality, shouldn't the vectors 
of weights x, 2*x give the same result? And yet they don't, standard 
errors differs:

> > summary(lm(c(1,2,3,1,2,3)~c(1,2.1,2.9,1.1,2,3),weight=rep(1,6)))$sigma
> [1] 0.07108323
> > summary(lm(c(1,2,3,1,2,3)~c(1,2.1,2.9,1.1,2,3),weight=rep(2,6)))$sigma
> [1] 0.1005269

So what if I know a-priori, observation A has variance 2 times bigger 
than observation B? Both weights=c(1,2) and weights=c(2,4) (and so on) 
represent very well this knowledge, but we get different regression 
(since sigma is different).

Also, if we do the same thing with a glm() model, than we get a lot of 
other differences like in the deviance.

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