[R] weight in lm

[peter dalgaard]

> On 14 Aug 2017, at 10:13 , Troels Ring <tring at gvdnet.dk> wrote:
> 
> Dear friends - I hope you will accept a naive question on lm: R version 3.4.1, Windows 10
> 
> I have 204 "baskets" of three types corresponding to factor F, each of size from 2 to 33 containing measurements, and need to know if the standard deviation on the measurements  in each basket,sdd, is different across types, F. Plotting the observed sdd  versus the sizes from 2 to 33, called "k" , does show a decreasing spread as k increases towards 33.
> 
> I tried lm(sdd ~ F,weight=k) and got different results if omitting the weight argument but would it be the correct way to use sqrt(k) as weight instead?
> 

I doubt that there is a "correct" way, but theory says that if the baskets have the same SD and data are normally distributed, then the variance of the sample VARIANCE is proportional to 1/f = 1/(k-1). Weights in lm are inverse-variance, so the "natural" thing to do would seem to be to regress the square of sdd with weights (k-1).

(If the distribution is not normal, the variance of the sample variance is complicated by a term that involves both n and the excess kurtosis, whereas the variance of the sample SD is complicated in any case. All according to the gospel of St.Google.)

-pd


> Best wishes
> 
> Troels Ring
> Aalborg, Denmark
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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