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
On Thu, Jan 21, 2010 at 2:16 PM, Dennis Murphy <djmuser at 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? 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()?> HTH, > Dennis > > On Thu, Jan 21, 2010 at 12:03 PM, Peng Yu <pengyu.ut at 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 at 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. > >
On Thu, Jan 21, 2010 at 2:41 PM, Dennis Murphy <djmuser at gmail.com> wrote:> Hi: > > On Thu, Jan 21, 2010 at 12:29 PM, Peng Yu <pengyu.ut at gmail.com> wrote: >> >> On Thu, Jan 21, 2010 at 2:16 PM, Dennis Murphy <djmuser at 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?>> 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"?> Dennis >> >> > HTH, >> > Dennis >> > >> > On Thu, Jan 21, 2010 at 12:03 PM, Peng Yu <pengyu.ut at 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 at 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 at 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. > >
On Fri, Jan 22, 2010 at 3:33 PM, Dennis Murphy <djmuser at gmail.com> wrote:> Hi: > > On Thu, Jan 21, 2010 at 1:06 PM, Peng Yu <pengyu.ut at gmail.com> wrote: >> >> On Thu, Jan 21, 2010 at 2:41 PM, Dennis Murphy <djmuser at gmail.com> wrote: >> > Hi: >> > >> > On Thu, Jan 21, 2010 at 12:29 PM, Peng Yu <pengyu.ut at gmail.com> wrote: >> >> >> >> On Thu, Jan 21, 2010 at 2:16 PM, Dennis Murphy <djmuser at 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.ut at 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 at 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 at 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. >> > >> > > >