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.
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] 1.39204
> 1.39204-1.2596
[1] 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?
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]]
______________________________________________
R-help@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.
