# [R] car::linearHypothesis Sum of Sqaures Error?

John Jay Wiley Jr. jwileyjr at syr.edu
Tue Oct 9 15:16:37 CEST 2012

```John,

The data are balanced; I double-checked. I believe the contrasts are orthogonal. Sum of squares in summary(aov) with the contrasts split out add to the main effect. I am still unsure of where the error is for the sum of squares calculation.

I have written some code with a parallel model structure that may help (see below).

Can linearHypothesis return type II tests? It seems to only return type III with no option to set 'type'.

Cheers,
John

y<-runif(36,0,100)
block<-factor(rep(c("A","B","C"),each=12))
a<-factor(rep(c("A","B"),times=3,each=6))
b<-factor(rep(c("A","B"),times=6,each=3))
c<-factor(rep(c("A","B","C"),times=12,each=1))
covar<-0.6*y+rnorm(36,10,25)
data<-data.frame(y,block,a,b,c,covar)

c_contrasts<-matrix(c(-1,2,-1,1,0,-1),3,2)
dimnames(c_contrasts)<-list(levels(data\$c),c("B vs. A&C","A vs. C"))
contrasts(data\$c)<-c_contrasts

model<-lm(y~block+a*b*c+covar,data=data)
summary.aov(model,split=list(c=list("B vs. A&C"=1,"A vs. C"=2)))
#Sum of squares add here, but factorial ANCOVA non-orthogonal in type I SS

Anova(model,type=2)
Anova(model,type=3)
linearHypothesis(model,c("cB vs. A&C","cA vs. C"))
#Anova and linear hypothesis produce equal sum of squares for c main effect in type III
linearHypothesis(model,"cB vs. A&C")
linearHypothesis(model,"cA vs. C")
#Sum of squares of the individual contrasts do not add to the main effect of c

John J. Wiley, Jr.
PhD Candidate
State University of New York
College of Environmental Science and Forestry
Department of Environmental and Forest Biology
460 Illick Hall
Syracuse, NY 13210
315.470.4825 (office)
740.590.6121 (cell)

________________________________________
From: John Fox [jfox at mcmaster.ca]
Sent: Tuesday, October 09, 2012 7:15 AM
To: John Jay Wiley Jr.
Cc: r-help at r-project.org
Subject: Re: [R] car::linearHypothesis Sum of Sqaures Error?

Dear John

On Tue, 9 Oct 2012 02:07:07 +0000
"John Jay Wiley Jr." <jwileyjr at syr.edu> wrote:
> I am working with a RCB 2x2x3 ANCOVA, and I have noticed a difference in the calculation of sum of squares in a Type III calculation.

For type III tests, you should use contrasts that are orthogonal in the row basis of the design. Perhaps you've done that (by setting the contrasts for the factors directly), but I suspect not. Why not just use type II tests? They're hard to screw up.

As well, I assume that the variables that enter additively are the covariates. If not, and a covariate is involved in the interaction, the type III tests aren't sensible unless the 0 point of the covariate is where you want to test a "main effect" or lower-order interaction.

>
> Anova output is a follows:
>
> > Anova(aov(MSOIL~Forest+Burn*Thin*Moisture+ROCK,data=env3l),type=3)
> Anova Table (Type III tests)
>
> Response: MSOIL
>                     Sum Sq Df F value    Pr(>F)
> (Intercept)        22.3682  1 53.2141 3.499e-07 ***
> Forest              1.0954  2  1.3029   0.29282
> Burn                2.6926  1  6.4058   0.01943 *
> Thin                0.0494  1  0.1176   0.73503
> Moisture            1.2597  2  1.4984   0.24644
> ROCK                2.1908  1  5.2119   0.03296 *
> Burn:Thin           0.2002  1  0.4764   0.49763
> Burn:Moisture       1.0612  2  1.2623   0.30360
> Thin:Moisture       1.6590  2  1.9734   0.16392
> Burn:Thin:Moisture  1.1175  2  1.3292   0.28605
> Residuals           8.8272 21
>
>
> However, I would like to calculate some a priori contrasts within the Moisture factor as follows:
>
> Transect_moisture_contrasts<-matrix(c(-1,2,-1,1,0,-1),3,2)
> dimnames(Transect_moisture_contrasts)<-list(levels(env\$Moisture),c("I vs. X&M","X vs. M"))
> contrasts(env\$Moisture)<-Transect_moisture_contrasts
> > contrasts(env3l\$Moisture)
>   I vs. X&M X vs. M
> X        -1       1
> I         2       0
> M        -1      -1
>
>
> soilmodel<-lm(MSOIL~Forest+Burn*Thin*Moisture+ROCK,data=env3l)
> > linearHypothesis(soilmodel,"MoistureI vs. X&M")
> Linear hypothesis test
>
> Hypothesis:
> MoistureI vs. X&M = 0
>
> Model 1: restricted model
> Model 2: MSOIL ~ Forest + Burn * Thin * Moisture + ROCK
>
>   Res.Df    RSS Df Sum of Sq      F Pr(>F)
> 1     22 9.4106
> 2     21 8.8272  1   0.58333 1.3877  0.252
> > linearHypothesis(soilmodel,"MoistureX vs. M")
> Linear hypothesis test
>
> Hypothesis:
> MoistureX vs. M = 0
>
> Model 1: restricted model
> Model 2: MSOIL ~ Forest + Burn * Thin * Moisture + ROCK
>
>   Res.Df    RSS Df Sum of Sq      F Pr(>F)
> 1     22 9.6359
> 2     21 8.8272  1   0.80871 1.9239   0.18
>
> The sum of squares for these two contrasts do not add up to the sum of squares of the main effect Moisture
> > .80871+.58333
>  1.39204
> > 1.39204-1.2596
>  0.13244
>
> Checking them together produces the correct sum of squares for the main effect
> > linearHypothesis(soilmodel,c("MoistureI vs. X&M","MoistureX vs. M"))
> Linear hypothesis test
>
> Hypothesis:
> MoistureI vs. X&M = 0
> MoistureX vs. M = 0
>
> Model 1: restricted model
> Model 2: MSOIL ~ Forest + Burn * Thin * Moisture + ROCK
>
>   Res.Df     RSS Df Sum of Sq      F Pr(>F)
> 1     23 10.0869
> 2     21  8.8272  2    1.2596 1.4984 0.2464
>
>
> So my question is:
> Should the sum of squares for the two contrasts add to the main effect here?

Only if the data are balanced.

I hope this helps,
John

------------------------------------------------
John Fox
Sen. William McMaster Prof. of Social Statistics
Department of Sociology
McMaster University
http://socserv.mcmaster.ca/jfox/

> If they should, maybe we can figure out why mine do not.
>
> Thanks in advance for any assistance.
>
> Cheers,
> John
>
>
> John J. Wiley, Jr.
> PhD Candidate
> State University of New York
> College of Environmental Science and Forestry
> Department of Environmental and Forest Biology
> 460 Illick Hall
> Syracuse, NY 13210
> 315.470.4825 (office)
> 740.590.6121 (cell)
>
>       [[alternative HTML version deleted]]
>
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