From: Ranjan Maitra <maitra_at_iastate.edu>

Date: Tue, 22 Mar 2011 19:36:10 -0500

Date: Tue, 22 Mar 2011 19:36:10 -0500

Dear John, Peter and others,

So, I now have a query at an even more elementary level and that is regarding my results from anova.mlm() not matching the car package's Manova(). Specifically, I have been trying the following out with regard to a simple one-way MANOVA setup. So, I try out the following using R:

- R code *******

morel <- read.table(file = "http://www.public.iastate.edu/~maitra/stat501/datasets/morel.dat", col.names = c("studentgroup", "aptitude", "mathematics", "language", "generalknowledge"))

morel[,1] <- as.factor(morel[,1])

fit <- anova.mlm(as.matrix(morel[,-1]) ~ morel[,1])

summary(fit, test="Wilks")

- providing the output ***

Df Wilks approx F num Df den Df Pr(>F) morel[, 1] 2 0.54345 6.7736 8 152 1.384e-07 *** Residuals 79 *** end of output

The above is correct, also by doing the calculations "by hand".

Then, I use the car package, following the help function on Anova() and do the following:

- R code ********

morel <- read.table(file = "http://www.public.iastate.edu/~maitra/stat501/datasets/morel.dat", col.names=c("studentgroup", "aptitude", "mathematics", "language", "generalknowledge"))

library(car)

fit1 <- Manova( lm( cbind(aptitude, mathematics, language, generalknowledge) ~ studentgroup , data = morel))
summary(fit1, test = "Wilks")

- providing the output *****

Type II MANOVA Tests:

Sum of squares and products for error:

aptitude mathematics language generalknowledge aptitude 78506.68 13976.5677 11041.9434 4330.1304 mathematics 13976.57 16040.3996 3979.9528 -416.4845 language 11041.94 3979.9528 6035.6132 -372.8491 generalknowledge 4330.13 -416.4845 -372.8491 7097.9562 ------------------------------------------

Term: studentgroup

Sum of squares and products for the hypothesis:

aptitude mathematics language generalknowledge aptitude 1129.7271 996.0542 237.54441 -880.4353 mathematics 996.0542 878.1980 209.43741 -776.2594 language 237.5444 209.4374 49.94777 -185.1266 generalknowledge -880.4353 -776.2594 -185.12655 686.1536 Multivariate Test: studentgroup Df test stat approx F num Df den Df Pr(>F) studentgroup 1 0.8620544 3.080378 4 77 0.020805 *

--- Signif. codes: 0 â€˜***â€™ 0.001 â€˜**â€™ 0.01 â€˜*â€™ 0.05 â€˜.â€™ 0.1 â€˜ â€™ 1 ***** end of output. Which is very different from the previous results. So what am I doing wrong here? Same issues arise with the other tests also (Pillai, Roy, Hotelling-Lawley, etc). Many thanks and best wishes, Ranjan On Sun, 20 Mar 2011 19:29:41 -0500 John Fox <jfox_at_mcmaster.ca> wrote:Received on Wed 23 Mar 2011 - 00:46:40 GMT

> Dear Peter and Ranjan,

>> In addition to Anova(), linearHypothesis() in the car package handles> multivariate linear models, including those for repeated measures.>> Best,> John>> --------------------------------> John Fox> Senator William McMaster> Professor of Social Statistics> Department of Sociology> McMaster University> Hamilton, Ontario, Canada> http://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 peter dalgaard> > Sent: March-20-11 6:50 PM> > To: Ranjan Maitra> > Cc: R-help> > Subject: Re: [R] manova question> >> >> > On Mar 20, 2011, at 21:05 , Ranjan Maitra wrote:> >> > > Dear friends,> > >> > > Sorry for this somewhat generically titled posting but I had a> > > question with using contrasts in a manova context. So here is my> > question:> > >> > > Suppose I am interested in doing inference on \beta in the case of the> > > model given by:> > >> > > Y = X %*% \beta + e> > >> > > where Y is a n x p matrix of observations, X is a n x m design matrix,> > > \beta is m x p matrix of parameters, and e is a normally-distributed> > > random matrix with mean zero and independent rows, each having> > > dispersion matrix given by \Sigma. Then, I know (I think) how to> > > perform MANOVA. Specifically, I use:> > >> > > fit <- manova(Y ~ X)> > >> > > and> > >> > > summary(fit) will allow me to perform appropriate inference on beta.> > >> > > Now, suppose I am interested in doing inference on C %*% \beta %*% M> > > (say testing whether this is equal to zero) with C and M being q x m> > > and p x r matrices, respectively (with q, r both being no more than> > > p), then can this be done using the manova object from the above? How?> > > If not, is there an efficient way to do this?> >> > Check out anova.mlm(), it does most of this sort of testing. Not quite> > the "C %*% ..." bit because the linear model code is not really built to> > handle linear constraints, but rather compare nested models, each> > specified using a set of betas. (So you usually test whether a subset of> > betas is zero).> >> > Also check out the "car" package. Its Anova() function does some similar> > stuff.> >> > If noone has done so already, I wouldn't think it to be very hard to> > implement the general case. Most of the bits are there already.> >> > --> > Peter Dalgaard> > Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000> > Frederiksberg, Denmark> > Phone: (+45)38153501> > Email: pd.mes_at_cbs.dk Priv: PDalgd_at_gmail.com> >> > ______________________________________________> > 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.>

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