analysis of data with observation weights

Dear Peter and Michal,

I was under the impression that the weights argument in lm specifies 
inverse-variance weights, but that the weights argument in glm specifies 
case weights. Inverse-variance weights, which produce a WLS solution, are 
inappropriate for Michal's problem. I checked and now see that the weights 
arguments for both lm and glm are inverse-variance weights, so the 
procedure that I suggested was incorrect.

Sorry,
  John

Michal Bojanowski <bojaniss at poczta.onet.pl> writes:

I'm gettin the same coefficients, but different standard errors. I 

guess this is

what you had in mind.

I guess I need a book on WLS... Thank you for the answer anyway.

Thomas Lumley once did a brief but very good writeup on the various
kinds of weighting. I forget whether it was for one of the open
mailing lists or in connection with a discussion in R-core.

One thing I remember from it was the need to distinguish between the
various reasons for weighting. The one used in lm/glm is based on the
idea that some measurements are more precise than others and therefore
deserve more weight, so basically the weight is the inverse variance
of an observation. However, you might want to weight observations
differently even if their variance is the same, e.g. to obtain a
method that is stable against differences in population structure,
even if the model is slightly wrong. (Some rather subtle issues are
involved here and I'm not sure I'm representing them adequately.)

-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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