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] 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?
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 Hamilton, Ontario, Canada 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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