[R] Anova unequal variance

[Peng Yu]

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
>> >>
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>> >
>> >
>>
>> ______________________________________________
>> 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.
>
>