MANOVA polynomial contrasts
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
> > > 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