[R] Weighted least squares
Adaikalavan Ramasamy
ramasamy at cancer.org.uk
Wed May 9 02:37:31 CEST 2007
http://en.wikipedia.org/wiki/Weighted_least_squares gives a formulaic
description of what you have said.
I believe the original poster has converted something like this
y x
0 1.1
0 2.2
0 2.2
0 2.2
1 3.3
1 3.3
2 4.4
...
into something like the following
y x freq
0 1.1 1
0 2.2 3
1 3.3 2
2 4.4 1
...
Now, the variance of means of each row in table above is ZERO because
the individual elements that comprise each row are identical. Therefore
your method of using inverse-variance will not work here.
Then is it valid then to use lm( y ~ x, weights=freq ) ?
Regards, Adai
S Ellison wrote:
> Hadley,
>
> You asked
>> .. what is the usual way to do a linear
>> regression when you have aggregated data?
>
> Least squares generally uses inverse variance weighting. For aggregated data fitted as mean values, you just need the variances for the _means_.
>
> So if you have individual means x_i and sd's s_i that arise from aggregated data with n_i observations in group i, the natural weighting is by inverse squared standard error of the mean. The appropriate weight for x_i would then be n_i/(s_i^2). In R, that's n/(s^2), as n and s would be vectors with the same length as x. If all the groups had the same variance, or nearly so, s is a scalar; if they have the same number of observations, n is a scalar.
>
> Of course, if they have the same variance and same number of observations, they all have the same weight and you needn't weight them at all: see previous posting!
>
> Steve E
>
>
>
> *******************************************************************
> This email and any attachments are confidential. Any use, co...{{dropped}}
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>
>
More information about the R-help
mailing list