multiple comparison of interaction of ANCOVA

Thank you for you use of HH.
I think the right graph for this data is the much simpler ancova function
library(HH)

ancova(y ~ year * Trt, data=mydata)
where we see that the three treatments have totally different slopes.

The WoodEnergy example doesn't apply here.  The WoodEnergy example
illustrates
a way of finding differences among treatments for a fixed value of the
covariate when the
slopes are similar.

Rich
On Sun, Dec 11, 2011 at 7:15 AM, Jinsong Zhao <jszhao at yeah.net
<mailto:jszhao at yeah.net>> wrote:

    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