Re: [R] type I and type III sums of squares

[Thomas W Blackwell]

Paul  -

Your question is best answered by a textbook reference, because
that will supply all the context needed to fully answer your
question.  A good, basic reference is:

George W. Snedecor and William G. Cochran (1980)
Statistical Methods, 7th edition.  Iowa State Univ. Press.
ISBN: 0-8138-1560-6; LC:  QA 276.12 .S591 1980

(I have the Taubman copy already checked out - others in the
Science Library.)  A more advanced reference is:

George A. Milliken and Dallas E. Johnson (1984)
Analysis of messy data (2 vols.)  Van Nostrand Reinhold, NY
ISBN: 0-534-02713-x;  LC:  QA 279 .M481 1984

(Science library only, more recent edition in Public Health library.)

The terms type I and type III are specific to SAS software.
Their precise definitions are given in the SAS documentation.
I don't have a copy handy.  George Milliken was a contributor
to the SAS software, so his definitions will coincide with SAS's.

HTH  -  tom blackwell  -  program in bioinformatics and department
of human genetics  -  u michigan medical school  -  ann arbor  -

On Mon, 18 Aug 2003, Paul Litvak wrote:

 I have been digging around in the FAQ's and online looking for an answer
 to my questions, and perhaps someone here can help me.

 For a statistical experiment, I need to run 3,000,000 ANOVAs, which is
 taking me a very long time. As a result, I have recoded my analyses in
 C. However, I cannot find the formula to calculate either the type I or
 type III sums of squares (in the case of my model, the two are
 equivalent). I know that the formula must be in the R source code, as
 they are able to calculate it, but I am not sure where. Does anyone know
 where I can find the explicit procedure for calculating this? A
 mathematical formula or the source code would be equally helpful. I am
 aware of the formula in matrix algebra, but is there a formulation that
 does not use matrix algebra?

 thanks very much in advance,
 Paul Litvak
 Department of Human Genetics
 University of Michigan

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RE: [R] type I and type III sums of squares

[Liaw, Andy]

Not knowing any more details about your experiment and data, we can only
speculate.  If the reason (or part of the reason) that you need to run ANOVA
3 million times is that you have that many responses collected from the same
experiment (or several experiments, but not 3 million different
experiments), you should be able to do the ANOVA computation in R very
efficiently.  E.g., assuming you actually have one experiment with 3m
responses, you can compute the hat matrix once and apply it to the response
matrix, rather than computing the same hat matrix 3M times.

Just a thought.  HTH.

Andy

 -Original Message-
 From: Paul Litvak [mailto:[EMAIL PROTECTED] 
 Sent: Monday, August 18, 2003 2:18 PM
 To: [EMAIL PROTECTED]
 Subject: [R] type I and type III sums of squares
 
 
 Hello-
 
 I have been digging around in the FAQ's and online looking 
 for an answer 
 to my questions, and perhaps someone here can help me.
 
 For a statistical experiment, I need to run 3,000,000 ANOVAs, 
 which is 
 taking me a very long time. As a result, I have recoded my 
 analyses in 
 C. However, I cannot find the formula to calculate either the 
 type I or 
 type III sums of squares (in the case of my model, the two are 
 equivalent). I know that the formula must be in the R source code, as 
 they are able to calculate it, but I am not sure where. Does 
 anyone know 
 where I can find the explicit procedure for calculating this? A 
 mathematical formula or the source code would be equally 
 helpful. I am 
 aware of the formula in matrix algebra, but is there a 
 formulation that 
 does not use matrix algebra?
 
 thanks very much in advance,
 Paul Litvak
 Department of Human Genetics
 University of Michigan
 
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