Peter Dalgaard <p.dalgaard <at> biostat.ku.dk> writes: > > The point is that R (as well as almost all other mainstream statistical > software) assumes that a "weight" means that the variance of the > corresponding observation is the general variance divided by the weight > factor. The general variance is still determined from the residuals, and > if they are zero to machine precision, well, there you go. I suspect you > get closer to the mark with glm, which allows you to assume that the > dispersion is known: > > > summary(glm(y~x,family="gaussian"),dispersion=0.3^2) > > or > > > summary(glm(y~x,family="gaussian",weights=1/error^2),dispersion=1) >
Excellent; any of these commands provide Std. Errors which now coincide with my naive expectation: though the data fall perfectly in a straight line, since they have some associated "uncertainties" (only) in the response variables (homoskedasticity), the estimated coefficients should have some kind of nonvanishing "uncertainties" as well, should they not?? Now, forgive me, but I did not get the explanation for the distinct meanings of Std. Error when calling simply summary(lm(y~x,weights=1/error^2), which I had done before, and your suggested calls; could you rephrase and dwell a little bit more upon this point. What does the option dispersion exactly mean? Also, could you suggest some specific reference for me to read about this? I have your excellent book "Introductory statistics with R", 1st edition, but was not able (perhaps I have missed some point) to find this kind of distinction there... Does this theme is specifically what statisticians call really generalized linear models (glm) as opposed to (ordinary) linear models? If so, which good references could you please suggest?? I thought of the following books and would feel much obliged should you give me your impressions about them, if any, or about any other relevant references at all: 1) Faraway, "Linear models with R" 2) Faraway, "Extending the linear model with R: generalized linear..." 3) Fox, "An R and S-Plus companion.." 4) Uusipaikka, "Confidence intervals in generalized linear regression models" Thank you very much!! ______________________________________________ R-help@r-project.org 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.
