Hi,

I have a few questions about glht() and the interpretation of output from
Tukey's in multcomp package for lme() model.
The main issue is that I noticed that a plot that I produced with code
letters seem to contradict the graph itself.  I provide data and code
below.  I end with my questions.

A few things about data set.  "LMA.vcp" is continuous response variable.
 "Canopy.position.vcp" is independent categorical variable and
"Leaf.height.vcp" is independent covariate.
"plots.vcp" and "tree.vcp" are random effects.


> data.vcp ##data-set##
LMA.vcp Canopy.position.vcp Leaf.height.vcp plots.vcp tree.vcp
1     96.8              BOTTOM            14.5         2        1
2    104.4              BOTTOM            14.7         2        2
3     95.0              BOTTOM            14.7         2        3
4    105.5              BOTTOM            17.4         4        1
5    105.1              BOTTOM            17.6         4        2
6     94.2              BOTTOM            12.6        11        1
7     85.1              BOTTOM            13.0        11        2
8    101.6              BOTTOM            13.5        11        3
9     95.8              BOTTOM            14.0        12        4
10    91.8              BOTTOM            14.7        12        5
11   101.8              BOTTOM            16.7        17        5
12   108.7              BOTTOM            16.9        17        6
13    83.5              BOTTOM            14.5        19        6
14    86.7              BOTTOM            14.7        19        7
15    88.5              BOTTOM            13.1        21        4
16   103.9              BOTTOM            13.0        21        5
17    98.2              BOTTOM            13.7        21        6
18   121.5              BOTTOM            17.1        23        3
19   112.6              BOTTOM            16.7        23        4
20    93.0              BOTTOM            13.1        28        7
21    84.6              BOTTOM            12.1        28        8
22    86.6              BOTTOM            14.3        29        8
23   108.3              BOTTOM            17.0        31        7
24    78.1              BOTTOM            17.4        31        8
25   100.0              MIDDLE            16.7         2        1
26    99.8              MIDDLE            16.6         2        2
27    82.8              MIDDLE            16.7         2        3
28   103.2              MIDDLE            19.4         4        1
29   104.7              MIDDLE            19.9         4        2
30    80.7              MIDDLE            14.9        11        1
31    87.8              MIDDLE            15.0        11        2
32    88.1              MIDDLE            15.6        11        3
33    85.0              MIDDLE            16.4        12        4
34    98.9              MIDDLE            17.0        12        5
35    69.4              MIDDLE            19.1        17        5
36   106.6              MIDDLE            18.9        17        6
37    96.8              MIDDLE            16.6        19        6
38    96.3              MIDDLE            16.7        19        7
39    83.3              MIDDLE            15.2        21        4
40    96.1              MIDDLE            15.3        21        5
41    91.2              MIDDLE            15.6        21        6
42   118.9              MIDDLE            19.2        23        3
43   111.6              MIDDLE            18.6        23        4
44    88.6              MIDDLE            15.2        28        7
45    96.0              MIDDLE            14.4        28        8
46    92.2              MIDDLE            16.3        29        8
47   114.9              MIDDLE            19.1        31        7
48   106.1              MIDDLE            19.3        31        8
49    95.4                 TOP            18.9         2        1
50    92.9                 TOP            18.4         2        2
51    93.4                 TOP            18.7         2        3
52    90.3                 TOP            21.4         4        1
53    89.8                 TOP            22.2         4        2
54    82.8                 TOP            17.2        11        1
55    75.2                 TOP            17.0        11        2
56    85.4                 TOP            17.7        11        3
57    99.9                 TOP            18.8        12        4
58    90.4                 TOP            19.3        12        5
59    93.5                 TOP            21.4        17        5
60    98.7                 TOP            20.9        17        6
61    85.5                 TOP            18.7        19        6
62    97.7                 TOP            18.7        19        7
63    72.2                 TOP            17.3        21        4
64    93.8                 TOP            17.5        21        5
65    79.2                 TOP            17.4        21        6
66   118.3                 TOP            21.3        23        3
67   101.6                 TOP            20.5        23        4
68    83.9                 TOP            17.3        28        7
69    85.7                 TOP            16.7        28        8
70    94.4                 TOP            18.3        29        8
71   117.0                 TOP            21.2        31        7
72   101.1                 TOP            21.2        31        8

##Model##

>modelVCP1<-lme(LMA.vcp~Canopy.position.vcp+Leaf.height.vcp,random=~1 |
plots.vcp/tree.vcp,data=data.vcp,na.action=na.omit)  ##lme model##
>modelVCP1_glht<-glht(modelVCP1,linfct=mcp(Canopy.position.vcp="Tukey"))
>summary(modelVCP1_glht) ##summary output of Tukey's test##

 *Simultaneous Tests for General Linear Hypotheses*
*
*
*Multiple Comparisons of Means: Tukey Contrasts*
*
*
*
*
*Fit: lme.formula(fixed = LMA.vcp ~ Canopy.position.vcp + Leaf.height.vcp, *
*    data = data.vcp, random = ~1 | plots.vcp/tree.vcp, na.action = na.omit)
*
*
*
*Linear Hypotheses:*
*                     Estimate Std. Error z value Pr(>|z|)    *
*MIDDLE - BOTTOM == 0   -8.926      2.777  -3.214  0.00383 ** *
*TOP - BOTTOM == 0     -19.817      4.080  -4.857  < 0.001 ****
*TOP - MIDDLE == 0     -10.891      2.769  -3.934  < 0.001 ****
*---*
*Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 *
*(Adjusted p values reported -- single-step method)*
*
*
*
*
Based on the output it appears that the mean (LMA) is greatest at the
bottom and lowest at the bottom.  However, when I receive the code letters
(a,b,c, etc) from
line and from a graph, the output suggests otherwise.

>modelVCP1_glht_cld<-cld(modelVCP1_glht,level=0.05,decreasing=FALSE)
>modelVCP1_glht_cld
>old.par<-par(mai=c(1,1,1.25,1))
>plot(modelVCP1_glht_cld,col=c("yellow","red","blue"))
>par(old.par)



First Question:
As you can see, the code letters in the boxplot graph seem to contradict
the plot itself as well as the Tukey output that I displayed above.
Can anyone explain why this may be happening?

Second Question:
Are the estimate values in the output the difference between the mean of
one level and another level?

Third Question:
If results from the Tukey's test are reported, does one typically report
the difference between levels or the means with code letters?  If so, how
are the means extracted from
the model "modelVCP1_glht"?

Thanks!

-- 
Adam P. Coble
Ph.D. Student
Michigan Technological University
School of Forest Resources and Environmental Science
Houghton, MI  49931

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