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@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
>
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