On Fri, Jan 22, 2010 at 3:33 PM, Dennis Murphy <djmu...@gmail.com> wrote: > Hi: > > On Thu, Jan 21, 2010 at 1:06 PM, Peng Yu <pengyu...@gmail.com> wrote: >> >> On Thu, Jan 21, 2010 at 2:41 PM, Dennis Murphy <djmu...@gmail.com> wrote: >> > Hi: >> > >> > On Thu, Jan 21, 2010 at 12:29 PM, Peng Yu <pengyu...@gmail.com> wrote: >> >> >> >> On Thu, Jan 21, 2010 at 2:16 PM, Dennis Murphy <djmu...@gmail.com> >> >> wrote: >> >> > Hi: >> >> > >> >> > This paper was a prelude to his first book 'Exact Statistical Methods >> >> > for >> >> > Data Analysis'. >> >> > He uses what is called a generalized p-value approach to inference, >> >> > and >> >> > for >> >> > the >> >> > book he wrote commercial software. AFAIK, no R package implements his >> >> > methodology. The 'conventional' approach to unequal variance in ANOVA >> >> > is >> >> > to use generalized least squares, whose implementation is found in >> >> > gls() >> >> > in >> >> > the nlme package. >> >> >> >> There are quite a few references on ?gls. Which one is the most >> >> introductory material that I should start with, if I want to >> >> understand the method? >> > >> > GLS is a standard technique in linear model theory. It is well >> > documented. >> > Any good book on linear statistical models should have a discussion on >> > it. >> > (Probably Wikipedia, too). If unequal >> > variance is the only issue (meaning independent observations), the >> > technique >> > is called weighted least squares (WLS). GLS is more general in that it >> > can >> > be applied to correlated observations. Assuming the variances are known >> > (a big if), it is easy to convert from WLS to ordinary least squares - >> > divide all >> > the responses by the group standard deviation to which it belongs. The >> > transformation in GLS (again, assuming variances known) involves a >> > matrix >> > transformation (Cholesky, when appropriate). When the variances are >> > unknown, >> > as they usually are, the estimation problem is a lot messier and one >> > needs >> > to resort to approximations. >> >> Would you please recommend a good book to me? > > Here are a couple: if you haven't been exposed to the matrix approach to > regression, > these will be over your head, but it's necessary to develop GLS: > > (1) Ravishanker & Dey: A First Course in Linear Model Theory. GLS starts on > p. 122 > (2) Myers: Classical and Modern Regression with Applications. See Chapter 7. > > There are a number of other good books that discuss GLS, but these are > pretty > good. Myers is on a lower mathematical level than R & D.
Is gls() with only two factor levels the same as t.test() with var.equal=F? >> >> Do you have any simple explanation that may help me understand what is >> >> the difference between the method in 'Exact Statistical Methods for >> >> Data Analysis' and the method in gls()? >> > >> > No. They're quite different approaches. Weerahandi's is conditional; >> > GLS is unconditional. >> >> Would you please elaborate what you mean by "conditional" and >> "unconditional"? > > Conditional means given the observed data; unconditional means over all > potential > sets of data (of the same size, from the same population) that could be > observed. > These are two different forms of inference. > > Take the simple linear regression of Y on X. Regression analysis aims to > estimate > the conditional mean E(Y|x); i.e., we treat the observed x's as fixed and Y > as random. > If we didn't make this assumption, then X would also be a random variable > and > we would have what is called 'errors in variables' regression, where the > objective > is to estimate E(Y), among other things. This topic arises more often in > econometrics. > > HTH, > Dennis >> >> > Dennis >> >> >> >> > HTH, >> >> > Dennis >> >> > >> >> > On Thu, Jan 21, 2010 at 12:03 PM, Peng Yu <pengyu...@gmail.com> >> >> > wrote: >> >> >> >> >> >> I found this paper on ANOVA on unequal error variance. Has this be >> >> >> incorporated to any R package? Is there any textbook that discuss >> >> >> the >> >> >> problem of ANOVA on unequal error variance in general? >> >> >> >> >> >> http://www.jstor.org/stable/2532947?cookieSet=1 >> >> >> >> >> >> ______________________________________________ >> >> >> 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. >> >> > >> >> > >> >> >> >> ______________________________________________ >> >> 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. >> > >> > > > ______________________________________________ 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.