[R] MANOVA polynomial contrasts

jesse.fox at sympatico.ca jesse.fox at sympatico.ca
Mon Jul 30 16:28:25 CEST 2012 

Dear GMM,

> -----Original Message-----
> From: Manzoni, GianMauro [mailto:gm.manzoni at auxologico.it]
> Sent: July-30-12 9:49 AM
> To: John Fox
> Cc: r-help at r-project.org; Greg Snow
> Subject: Re: [R] MANOVA polynomial contrasts
> 
> Dear Prof. John Fox,
> thus all I should do to test quadratic and cubic effects is to change the
second
> argument of the linearHypothesis() function, right?
> So, for testing the cubic effect:
> >  linearHypothesis (mod, "f.C")

Yes, but wouldn't it have been faster simply to try it? Also see
?linearHypothesis.

> 
> Is there a chapter or paragragh about contrasts in your book "An R
> companion for applied regression"?

There are discussions of contrasts and of linear hypotheses about
coefficients, though not in the context of *multivariate* linear models;
that's the subject of an on-line appendix, at <
http://socserv.socsci.mcmaster.ca/jfox/Books/Companion/appendix/Appendix-Mul
tivariate-Linear-Models.pdf>.

Best,
 John

> 
> Best regards,
> GMM
> 
> 2012/7/30 John Fox <jfox at mcmaster.ca>
> 
> 
> 	Dear Gian Mauro,
> 
> 
> 	On Mon, 30 Jul 2012 14:44:44 +0200
> 	 "Manzoni, GianMauro" <gm.manzoni at auxologico.it> wrote:
> 	> Dear Prof. John Fox,
> 	> thank you very much for your suggestions.
> 	> However, I still do not know how to use the contrasts after
> generating them.
> 	> Once I generate the matrix with the polynomial contrasts, what are
> the
> 	> following steps toward the statistical test?
> 
> 
> 	Here's a contrived example, which uses the Anova() and
> linearHypothesis() functions in the car package:
> 
> 	----- snip ------
> 
> 	> Y <- matrix(rnorm(300), 100, 3)
> 	> colnames(Y) <- c("y1", "y2", "y3")
> 	> f <- ordered(sample(letters[1:4], 100, replace=TRUE))
> 	> (mod <- lm(Y ~ f))
> 
> 	Call:
> 	lm(formula = Y ~ f)
> 
> 	Coefficients:
> 	             y1        y2        y3
> 	(Intercept)   0.06514  -0.01683  -0.13787
> 	f.L          -0.37837   0.18309   0.29736
> 	f.Q          -0.02102  -0.39894   0.08455
> 	f.C           0.05898   0.09358  -0.17634
> 
> 	> Anova(mod)
> 
> 	Type II MANOVA Tests: Pillai test statistic
> 	  Df test stat approx F num Df den Df Pr(>F)
> 	f  3   0.11395   1.2634      9    288 0.2566
> 
> 	> linearHypothesis(mod, "f.L")
> 
> 	Sum of squares and products for the hypothesis:
> 	          y1        y2        y3
> 	y1  3.607260 -1.745560 -2.834953
> 	y2 -1.745560  0.844680  1.371839
> 	y3 -2.834953  1.371839  2.227995
> 
> 	Sum of squares and products for error:
> 	          y1        y2        y3
> 	y1 86.343376 -8.054928 -3.711756
> 	y2 -8.054928 95.473020  2.429151
> 	y3 -3.711756  2.429151 89.593163
> 
> 	Multivariate Tests:
> 	                 Df test stat approx F num Df den Df   Pr(>F)
> 	Pillai            1 0.0648520 2.172951      3     94 0.096362 .
> 	Wilks             1 0.9351480 2.172951      3     94 0.096362 .
> 	Hotelling-Lawley  1 0.0693495 2.172951      3     94 0.096362 .
> 	Roy               1 0.0693495 2.172951      3     94 0.096362 .
> 	---
> 	Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> 	----- snip ------
> 
> 	You could do similar tests for the quadratic and cubic contrasts.
> 
> 	I hope this helps,
> 
> 	 John
> 
> 	------------------------------------------------
> 	John Fox
> 	Sen. William McMaster Prof. of Social Statistics
> 	Department of Sociology
> 	McMaster University
> 	Hamilton, Ontario, Canada
> 	http://socserv.mcmaster.ca/jfox/
> 
> 	>
> 	> A whole example would be very useful.
> 	>
> 	> Thank you very much in advance!
> 	>
> 	> Best regards,
> 	> Gian Mauro Manzoni
> 	>
> 	>
> 	>
> 	> 2012/7/25 John Fox <jfox at mcmaster.ca>
> 	>
> 	> > Dear Gian,
> 	> >
> 	> > How contrasts are created by default is controlled by the
> contrasts option:
> 	> >
> 	> > > getOption("contrasts")
> 	> >         unordered           ordered
> 	> > "contr.treatment"      "contr.poly"
> 	> >
> 	> > So, unless you've changed this option, contr.poly() will be used
to
> 	> > generate orthogonal polynomial contrasts for an ordered factor,
> and you
> 	> > therefore need do nothing special to get this result. For
example:
> 	> >
> 	> > > (f <- ordered(sample(letters[1:3], 10, replace=TRUE)))
> 	> >  [1] c c a a c c b c a c
> 	> > Levels: a < b < c
> 	> >
> 	> > > round(contrasts(f), 4)
> 	> >           .L      .Q
> 	> > [1,] -0.7071  0.4082
> 	> > [2,]  0.0000 -0.8165
> 	> > [3,]  0.7071  0.4082
> 	> >
> 	> > For more information, see section 11 on statistical models in
the
> manual
> 	> > "An Introduction to R," which is part of the standard R
> distribution, and
> 	> > in particular sections 11.1 and 11.1.1.
> 	> >
> 	> > I hope that this clarifies the issue.
> 	> >
> 	> > Best,
> 	> >  John
> 	> >
> 	> > ------------------------------------------------
> 	> > John Fox
> 	> > Sen. William McMaster Prof. of Social Statistics
> 	> > Department of Sociology
> 	> > McMaster University
> 	> > Hamilton, Ontario, Canada
> 	> > http://socserv.mcmaster.ca/jfox/
> 	> >
> 	> > On Wed, 25 Jul 2012 11:58:30 +0200
> 	> >  "Manzoni, GianMauro" <gm.manzoni at auxologico.it> wrote:
> 	> > > Dear Greg Snow,
> 	> > > thank you very much for your suggestions. However, I need an
> example in
> 	> > > order to understand fully.
> 	> > > I was told that, given the ordinal factor, I do not need to
specify
> the
> 	> > > contr.poly function because R does it automatically.
> 	> > > However, I don not know if I have to add an argument into the
> 	> > manova/anova
> 	> > > function or something else.
> 	> > > Please write me an illustrative example.
> 	> > > Many thanks.
> 	> > >
> 	> > > Best regards,
> 	> > > Gian Mauro Manzoni
> 	> > >
> 	> > > 2012/7/25 Greg Snow <538280 at gmail.com>
> 	> > >
> 	> > > > You should not need to write them yourself. Look at the
> contr.poly
> 	> > > > function along with the C function (Note uppercase C) or the
> contrasts
> 	> > > > function.
> 	> > > >
> 	> > > >
> 	> > > > On Monday, July 23, 2012, Manzoni, GianMauro wrote:
> 	> > > >
> 	> > > >> Dear all,
> 	> > > >> I am quite new to R and I am having trouble writing the
> polynomial
> 	> > > >> contrasts for an ordinal factor in MANOVA.
> 	> > > >> # I have a model such as this
> 	> > > >> fit<-manova(cbind(Y1,Y2,Y3)~Groups,data=Events) # where
> groups is an
> 	> > > >> ordinal factor with 4 levels
> 	> > > >> # how to set polynomial contrasts for the "Groups" factor ?
> 	> > > >>
> 	> > > >> Thank you very much in advance for any help!
> 	> > > >>
> 	> > > >> Best regards,
> 	> > > >> Mauro
> 	> > > >>
> 	> > > >> --
> 	> > > >> Dr. Gian Mauro Manzoni
> 	> > > >> PhD, PsyD
> 	> > > >> Psychology Research Laboratory
> 	> > > >> San Giuseppe Hospital
> 	> > > >> Istituto Auxologico Italiano
> 	> > > >> Verbania - Italy
> 	> > > >> e-mail: gm.manzoni at auxologico.it
> 	> > > >> cell. phone +39 338 4451207 <tel:%2B39%20338%204451207>
> 	> > > >> Tel. +39 0323 514278 <tel:%2B39%200323%20514278>
> 	> > > >>
> 	> > > >>         [[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.
> 	> > > >>
> 	> > > >
> 	> > > >
> 	> > > > --
> 	> > > > Gregory (Greg) L. Snow Ph.D.
> 	> > > > 538280 at gmail.com
> 	> > > >
> 	> > >
> 	> > >
> 	> > >
> 	> > > --
> 	> > > Dr. Gian Mauro Manzoni
> 	> > > PhD, PsyD
> 	> > > Psychology Research Laboratory
> 	> > > San Giuseppe Hospital
> 	> > > Istituto Auxologico Italiano
> 	> > > Verbania - Italy
> 	> > > e-mail: gm.manzoni at auxologico.it
> 	> > > cell. phone +39 338 4451207 <tel:%2B39%20338%204451207>
> 	> > > Tel. +39 0323 514278 <tel:%2B39%200323%20514278>
> 	> > >
> 	> > >       [[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.
> 	> >
> 	> >
> 	> >
> 	>
> 	>
> 	> --
> 	> Dr. Gian Mauro Manzoni
> 	> PhD, PsyD
> 	> Psychology Research Laboratory
> 	> San Giuseppe Hospital
> 	> Istituto Auxologico Italiano
> 	> Verbania - Italy
> 	> e-mail: gm.manzoni at auxologico.it
> 	> cell. phone +39 338 4451207 <tel:%2B39%20338%204451207>
> 	> Tel. +39 0323 514278 <tel:%2B39%200323%20514278>
> 
> 
> 
> 
> 
> --
> Dr. Gian Mauro Manzoni
> PhD, PsyD
> Psychology Research Laboratory
> San Giuseppe Hospital
> Istituto Auxologico Italiano
> Verbania - Italy
> e-mail: gm.manzoni at auxologico.it
> cell. phone +39 338 4451207
> Tel. +39 0323 514278

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