[S] MANOVAs and ANOVAs with repeated measures (summary)

Gabriel Baud-Bovy (baudbovy@fpshp1.unige.ch)
Fri, 13 Feb 98 15:23:23 +0100


Tuesday, I posted a question regarding MANOVA with repeated measures
designs (see below). I received one answer suggesting to
do the computations myself (see below) and several requests for
a summary. If I get more info, I'll update this summary.

I would like to know also if SPLUS can compute the Huynh-Feldt (Box)
and the Greenhouse-Geisser adjustements in the case of repeated measures
analysis with an ANOVA (these are useful when the sphericity condition
is not satisfied) (see Hays, 1988, 4th ed, chapter 13.23, p. 524).

Thank you for the help,

Gabriel Baud-Bovy

Response from Rick Bilonick:

Return-Path: <rab@nauticom.net>
Date: Tue, 10 Feb 98 10:58:17
From: Rick Bilonick <rab@nauticom.net>
Subject: Re: [S] MANOVA with splus (repeated measures)
To: Gabriel Baud-Bovy <baudbovy@fpshp1.unige.ch>
Reply-To: Rick Bilonick <rab@nauticom.net>
Priority: Normal

>From my experience, I would recommend
doing the matrix computations directly
rather than using the S-Plus functions.
The problem is not so much S-Plus but any
very complicated canned procedure in any
package. There is rarely enough
information to know exactly what you are
getting. (Usually there are so many
possible variations.)

When you set up the matrices you end up
knowing exactly which hypotheses you are
testing.

Although I imagine most people will balk
at doing this(!), most of the multivariate
computations are not that difficult when
using matrix computations.

ORIGINAL MESSAGE

>Date: Tue, 10 Feb 1998 16:30:31
>To: s-news
>From: Gabriel Baud-Bovy <baudbovy@fpshp1.unige.ch>
>Subject: MANOVA with splus (repeated measures)
>
>Hello,
>
>I do have a problem in replicating the MANOVA analyses published
>in statistical books with SPLUS 3.4 (UNIX version). For example, I would
>like to have the exact procedure to follow to get the correct
>results (F values) in the two following examples:
>
>1) Repeated measure design in Stevens (1992) "Applied Multivariate
> statistics for the social science", p.442-453
>2) Doubly multivariate design in Tabachnick and Fidel (1996) "Using
> multivariate statistics", p.476-483.
>
>Questions:
>
>1) Can somebody show me how to perform these analysis (see below for the
> data)?
>2) Where can I find information, examples of MANOVA analysis with
> repeated measures done with SPLUS?
>
>Gabriel Baud-Bovy
>
>------------------------------------------------------------------------
>EXAMPLE 1: Stevens (1992) Applied Multivariate statistics for the social
>science, p.442-453
>
>DESIGN: single group repeated measure
>
>One fixed factor: drug
>One random factor: su
>
>DATA
>
>fname<-list(drug=1:4,su=1:5)
>data<-fac.design(c(4,5),factor.names=fname,replications=1)
>data<-data[order(data$drug,data$su),]
>data$obs<-
>c(30,14,24,38,26,
>28,18,20,34,28,
>16,10,18,20,14,
>34,22,30,44,30)
>
>RESULTS (see Table 13.3)
>
> Multivariate Tests of Significance
>
>Test name Value Exact F Hyp. DF Err. DF P
>Pillais .97707 28.412 3 2 0.34
>Hottelings 42.618 28.412 3 2 0.34
>Wilks .02293 28.412 3 2 0.34
>Roys .97707
>
> PROBLEM:
>
> I don't know how to get these results
>
>---------------------------------------------------------------------
>EXAMPLE 2: Tabachnick and Fidel (1996) Using multivariate statistics,
>p.476-483.
>
>DESIGN Doubly multivariate design
>
>Between subject independent variables: cbw
>Within subject independent variables: month
>Dependent variables: wtloss, esteem
>
>DATA
>
>d1<- c(4,4,4,3,5,6,6,5,5,3,4,5,
> 6,5,7,6,3,5,4,4,6,7,4,7,
> 8,3,7,4,9,2,3,6,6,9,7,8)
>d2<- c(3,4,3,2,3,5,5,4,4,3,2,2,
> 3,4,6,4,2,5,3,2,5,6,3,4,
> 4,6,7,7,7,4,5,5,6,5,9,6)
>d3<- c(3,3,1,1,2,4,4,1,1,2,2,1,
> 2,1,3,2,1,4,1,1,3,4,2,3,
> 2,3,4,1,3,1,1,2,3,2,4,1)
>d4<-10+c(4,3,7,1,6,7,7,3,4,4,6,5,
> 2,3,7,6,6,3,2,2,7,9,5,6,
> 6,9,5,6,3,6,3,5,5,6,6,7)
>d5<-10+c(3,4,2,1,5,8,6,5,4,5,6,3,
> 1,4,1,5,7,1,1,1,6,9,5,4,
> 2,9,1,2,2,3,3,2,3,4,6,7)
>d6<-10+c(5,7,6,2,4,8,9,5,5,3,1,6,
> 4,5,8,8,5,5,4,1,9,9,5,8,
> 6,6,9,8,7,7,6,8,8,7,9,7)
>tabach<-cbind.data.frame( su=rep( paste("s",as.character(1:36), sep=""), 3),
> cbw=rep( rep( c("ctl","diet","diex"),rep(12,3) ),
3 ),
> month=rep(1:3,rep(36,3)),
> wtloss=c(d1,d2,d3), esteem=c(d4,d5,d6) )
>tabach$month<-factor(tabach$month)
>
>RESULTS (in the book):
>
>Between subject variable cbw: Wilks = 0.773 F(4,64)=2.2 p=0.0791
>Within subject variable month:
> doubly multivariate analysis: Wilks = ? F(4,30)= 59.23 p=0.0
> sinlgy multivariate analysis: Wilks = 0.1987 F(4,130)=40.40 p=0.0
>
>PROBLEM:
>
>The following command produce only some of the results
>
>tmp_manova(cbind(wtloss,esteem) ~ cbw*month + Error(su/month), data=tabach)
>summary(tmp,test="wilk")
>
>I cannot get the doubly multivariate analysis.

-------------------------------------------------------------
Gabriel Baud-Bovy baudbovy@fpshp1.unige.ch
Université de Genève, FAPSE tel. +41 22 705 97 67
9, route de Drize fax +41 22 300 14 82
1227 Carouge, Switzerland home tel. +41 22 320 21 38
-------------------------------------------------------------

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