# [R] proportional weights

Göran Broström goran.brostrom at umu.se
Thu Feb 6 09:27:22 CET 2014

```On 05/02/14 22:40, Marco Inacio wrote:
> 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
>>  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
>>  0.1005269

The weights are in fact case weights, i.e., a weight of 2 is the same as
including the corresponding item twice. I agree that the documentation
is no wonder of clarity in this respect.

Btw, note that, in your example, (0.1005269 / 0.07108323)^2 = 2, your
constant weight.

Göran Broström
>
>
> 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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