[R] multiple comparison of interaction of ANCOVA
Jinsong Zhao
jszhao at yeah.net
Sun Dec 11 13:15:12 CET 2011
Hi there,
The following data is obtained from a long-term experiments.
> mydata <- read.table(textConnection("
+ y year Trt
+ 9.37 1993 A
+ 8.21 1995 A
+ 8.11 1999 A
+ 7.22 2007 A
+ 7.81 2010 A
+ 10.85 1993 B
+ 12.83 1995 B
+ 13.21 1999 B
+ 13.70 2007 B
+ 15.15 2010 B
+ 5.69 1993 C
+ 5.76 1995 C
+ 6.39 1999 C
+ 5.73 2007 C
+ 5.55 2010 C"), header = TRUE)
> closeAllConnections()
The experiments is designed without replication, thus I have to use
ANCOVA or linear mixed effect model to analyze the data. In the model,
variable year is coded as a continuous variable, and Trt is factor variable.
> mydata.aov <- aov(y~Trt*year, mydata)
> anova(mydata.aov)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
Trt 2 140.106 70.053 197.9581 3.639e-08 ***
year 1 0.610 0.610 1.7246 0.221600
Trt:year 2 8.804 4.402 12.4387 0.002567 **
Residuals 9 3.185 0.354
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
As you have seen, the interaction effect is significant. I hope to use
TukeyHSD() or glht() to do multiple comparison on Trt:year. However, for
variable year is not a factor, they all give error messages.
I try to follow the demo("MMC.WoodEnergy") in HH package, as follwoing:
> library(HH)
> mca.1993 <- mcalinfct(mydata.aov, "Trt")
> non.zero <- mca.1993[,5:6] != 0
> mca.1993[,5:6][non.zero] <- 1993 * sign(mca.1993[,5:6][non.zero])
> summary(glht(mydata.aov, linfct=mca.1993))
Simultaneous Tests for General Linear Hypotheses
Fit: aov(formula = y ~ Trt * year, data = mydata)
Linear Hypotheses:
Estimate Std. Error t value Pr(>|t|)
B - A == 0 2.8779 0.5801 4.961 0.00215 **
C - A == 0 -2.8845 0.5801 -4.972 0.00191 **
C - B == 0 -5.7624 0.5801 -9.933 < 0.001 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)
It can give comparison between levels of Trt within one year, e.g., 1993.
Is it possible to do multiple comparison for the following pairs:
A.1995 - A.1993
B.1995 - A.1993
C.1995 - A.1993
Any suggestions or comments will be really appreciated. Thanks in advance!
Regards,
Jinsong
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