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
>
>
>
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