[R] Post-hoc after Anova() car package using linear.hypothesis() in a Repeated Measure Analysis

[John Fox]

Dear Alejandro,

If I understand correctly what you want (that is, pairwise multivariate
tests among the groups), you could do the following tests (some output
suppressed):

> linear.hypothesis(diversitylm.ok, c("(Intercept)=CategoryM"), 
+     idata=idata.df, idesign=~Season, iterms="Season")

 Response transformation matrix:
         Season1 Season2
dLluvias       1       0
dNortes        0       1
dSecas        -1      -1

Sum of squares and products for the hypothesis:
           Season1    Season2
Season1 0.03447365 0.04897023
Season2 0.04897023 0.06956279

Sum of squares and products for error:
           Season1   Season2
Season1 0.07481798 0.1463547
Season2 0.14635470 0.3945622

Multivariate Tests: 
                 Df test stat  approx F num Df den Df  Pr(>F)
Pillai            1 0.3557184 1.3802911      2      5 0.33319
Wilks             1 0.6442816 1.3802911      2      5 0.33319
Hotelling-Lawley  1 0.5521164 1.3802911      2      5 0.33319
Roy               1 0.5521164 1.3802911      2      5 0.33319

> linear.hypothesis(diversitylm.ok, c("(Intercept)=CategoryI"), 
+     idata=idata.df, idesign=~Season, iterms="Season")

. . .

Multivariate Tests: 
                 Df test stat approx F num Df den Df   Pr(>F)  
Pillai            1  0.712033 6.181560      2      5 0.044500 *

. . .

> linear.hypothesis(diversitylm.ok, c("CategoryI=CategoryM"), 
+     idata=idata.df, idesign=~Season, iterms="Season")

. . .

Multivariate Tests: 
                 Df test stat approx F num Df den Df  Pr(>F)  
Pillai            1  0.716616 6.321937      2      5 0.04275 *

. . .

The Bonferroni adjustment is to multiply each p-value by 3 (the number of
tests); it should be conservative in this context, and so there should be
better approaches for multivariate pairwise comparisons.

Regards,
 John

--------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
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 "Alejandro 
> Luis Collantes Chávez-Costa"
> Sent: Thursday, September 27, 2007 1:45 PM
> To: r-help at r-project.org
> Subject: [R] Post-hoc after Anova() car package using 
> linear.hypothesis() in a Repeated Measure Analysis
> 
> R masters:
> 
> I need your help to figure out how can I perform Post-hoc 
> test after “Anova()” “car package” using 
> “linear.hypothesis()” in a Repeated Measure Analysis.
> 
> I performed a Repeated Measures Analysis to test the effect 
> of Category, Season and their Interaction on some ecological 
> properties using “Anova()” from “car package”.
> I find some significant effect and now I would like to know 
> where the differences are. In order to perform these Within, 
> Between and within-between post hoc’s Professor John Fox 
> recommend me to use “linear.hypothesis()” and a Bonferonni 
> adjustment of the p-values.
> 
> After a couple of weeks of work, I can not figure out how to 
> do that. I am very sorry, I did my best but I am not 
> statistician and I can not find examples to understand how 
> can I use linear.hypothesis() in post hoc test.
> 
> There are someone who can help me?
> 
> P.D.  (I am very thankful to Professor Richard Heiberger who 
> give me advices about the use of “glht.mmc()” with the 
> “calpha” argument).
> 
> 
> For those who can help me, I am posting some extra 
> information about my case and my attempts:
> 
> The experiment design was as follow: 1 between subjects 
> (fixed factor with 3 levels) and 1 within subjects (fixed 
> factor with 3 levels). Between subjects are nine plots 
> grouped into 3 age category (tree plot for each age category 
> “T”, “I”, “M”), and Within category are 3 season of the year  
> "llu”, “nor”, “sec" (equidistant in the time scale). The data set is:
> 
> lludiversity	nordiversity	secdiversity	Plot	
> Category	Season
> 1.96601	2.10215	2.17984	07A	T	llu
> 1.73697	1.96866	1.99766	10B	T	llu
> 1.87122	1.92848	2.2673	10C	T	llu
> 2.06851	1.98455	2.43838	15B	I	llu
> 2.17905	2.49451	2.25759	15C	I	llu
> 2.2572	2.16882	2.58295	17A	I	llu
> 1.99913	2.43767	2.29582	60A	M	llu
> 2.12738	2.64161	2.5385	60B	M	llu
> 2.22421	2.42401	2.5385	60C	M	llu
> 
> To test the effect of Category, Season and their Interaction 
> on some ecological properties I use the following code:
> 
> rm(list=ls(all=TRUE))
> library(lattice);
> library(Matrix);
> library(car);
> setwd(“c:/R help/”);
> diversity.tbl <- read.table("diversity.txt", header=TRUE); 
> Season <- factor(c("Lluvias","Nortes","Secas"), 
> levels=c("Lluvias","Nortes","Secas"));
> idata.df <- data.frame(Season) # Within “plot”; Plot <- 
> diversity.tbl[,4]; Category <- factor(diversity.tbl[,5], 
> levels=c("T", "I", "M")) #Between “plot”; dLluvias <- 
> diversity.tbl[,1]; dNortes <- diversity.tbl[,2]; dSecas <- 
> diversity.tbl[,3]; datalm.df <- data.frame(Plot, Category, 
> dLluvias, dNortes, dSecas); diversitylm.ok <- 
> lm(cbind(dLluvias, dNortes, dSecas) ~ Category, 
> data=datalm.df); diversityav.ok <- Anova(diversitylm.ok, 
> idata=idata.df, type="II", idesign=~Season); 
> summary(diversityav.ok, multivariate=FALSE); diversityav.ok
> 
> To try perform post hoc test I did:
> linear.hypothesis(diversitylm.ok, c("(Intercept)=CategoryM"), 
> idata=idata.df, idesign=~Season, iterms="Season"); #To 
> contrast Intercept (Category T) and Category M
> 
> 
> Alejandro Collantes Chávez-Costa
> Universidad de Quintana Roo, Unidad Cozumel
> 
> http://www.cozumel.uqroo.mx
>