[R] Nested ANOVA with covariate using Type III sums of squares

[John Fox]

Dear Anita and Joris,

Please see <https://stat.ethz.ch/pipermail/r-help/2010-March/230280.html>,
posted to r-help in March.

Regards,
 John

--------------------------------
John Fox
Senator William McMaster 
  Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Anita Narwani
> Sent: June-03-10 8:49 PM
> To: Joris Meys
> Cc: r-help at r-project.org
> Subject: Re: [R] Nested ANOVA with covariate using Type III sums of
squares
> 
> Yes I understood the strangeness of removing a main effect without
> interactions that contain it because I did this during my efforts using
> model simplification. I had checked out the link you sent a couple of days
> ago. It was useful. So does Type II SS remove both the factor and any
> interactions containing it when comparing models? i.e. to test for the
main
> effect of B you compare A + B + A:B against A?
> 
> On Thu, Jun 3, 2010 at 4:59 PM, Joris Meys <jorismeys at gmail.com> wrote:
> 
> > Hi Anita,
> >
> > I have to correct myself too, I've been rambling a bit. Off course you
> > don't delete the variable out of the interaction term when you test the
> main
> > effect. What I said earlier didn't really make any sense.
> >
> > That testing a main effect without removing the interaction term is has
a
> > tricky interpretation. By removing a main effect you test full model  A
+ B
> > + A:B against the model A + A:B.  If you remove the main effect "Zoop"
for
> > example, you basically nest Zoop within Diversity and test whether
that's
> > not worse than the full model. This explains it very well:
> >
> > https://stat.ethz.ch/pipermail/r-help/2010-March/230280.html
> >
> > I'd go for type II, but you're free to test any hypothesis you want.
> >
> > Cheers
> > Joris
> >
> >
> >
> > On Thu, Jun 3, 2010 at 9:59 PM, Anita Narwani
> <anitanarwani at gmail.com>wrote:
> >
> >> Thanks for your response Joris.
> >>
> >> I was aware of the potential for aliasing, although I thought that this
> >> was only a problem when you have missing cell means. It was interesting
to
> >> read the vehement argument regarding the Type III sums of squares, and
> >> although I knew that there were different positions on the topic, I had
no
> >> idea how divisive it was. Nevertheless, Type III SS are generally
> >> recommended by statistical texts in ecology for my type of experimental
> >> design. Interestingly, despite the aliasing, SPSS has no problems
> >> calculating Type III SS for this data set. This is simply because I am
> >> entering a co-variate, which causes non-orthogonality. I would be
happier
> >> using R and the default Type I SS, which are the same as the Type III
SS
> >> anyway when I omit the co-variate of Mean.richness, except that these
> >> results are very sensitive to the order in which I add the variables
into
> >> the model when I do enter the co-variate. I understand that the order
is
> >> very important relates back to the scientific hypothesis, but I am
equally
> >> interested in the main effects of Zoop, Diversity, and the nested
effect
> of
> >> Phyto, so entering either of these variables before the other does not
> make
> >> sense from an ecological perspective, and because the results do
change,
> the
> >> order cannot be ignored from a statistical perspective.
> >> Finally, I have tried using the Type II SS and received similar
warnings.
> >>
> >> Do you have a recommendations?
> >> Anita.
> >>
> >
> >
> >
> > --
> > Joris Meys
> > Statistical Consultant
> >
> >
> > Ghent University
> > Faculty of Bioscience Engineering
> > Department of Applied mathematics, biometrics and process control
> >
> > Coupure Links 653
> > B-9000 Gent
> >
> > tel : +32 9 264 59 87
> > Joris.Meys at Ugent.be
> > -------------------------------
> > Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php
> >
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> 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.