mmc
MMC (Mean--mean Multiple Comparisons) plots.
Constructs a "mmc.multicomp"
object from the formula and
other arguments. The constructed object must be explicitly plotted
with the mmcplot
function.
Usage
mmc(model, ...) ## R
## S3 method for class 'glht':
mmc(model, ...)
## S3 method for class 'default':
mmc(model, ## lm object
linfct=NULL,
focus=
if (is.null(linfct))
{
if (length(model$contrasts)==1) names(model$contrasts)
else stop("focus or linfct must be specified.")
}
else
{
if (is.null(names(linfct)))
stop("focus must be specified.")
else names(linfct)
},
focus.lmat,
ylabel=deparse(terms(model)[[2]]),
lmat=if (missing(focus.lmat)) {
t(linfct)
} else {
lmatContrast(t(none.glht$linfct), focus.lmat)
},
lmat.rows=lmatRows(model, focus),
lmat.scale.abs2=TRUE,
estimate.sign=1,
order.contrasts=TRUE,
level=.95,
calpha=NULL,
alternative = c("two.sided", "less", "greater"),
...
)
multicomp.mmc(x, ## S-Plus
focus=dimnames(attr(x$terms,"factors"))[[2]][1],
comparisons="mca",
lmat,
lmat.rows=lmatRows(x, focus),
lmat.scale.abs2=TRUE,
ry,
plot=TRUE,
crit.point,
iso.name=TRUE,
estimate.sign=1,
x.offset=0,
order.contrasts=TRUE,
main,
main2,
focus.lmat,
...)
## S3 method for class 'mmc.multicomp':
[(x, ..., drop = TRUE)
Arguments
- model
"aov"
object in"lm"
method.- ylabel
- name of the response variable.
- lmat
- contrast matrix as in the S-Plus
multicomp
. The convention forlmat
in R is to use the transpose of thelinfct
component produced byglht
. Required for user-specified contrasts. - lmat.rows
- rows in
lmat
for thefocus
factor. - focus
- define the factor to compute contrasts of.
In R this argument often can be used to simplify the call.
The statement
mmc(my.aov, focus="factorA")
is interpreted asmmc(my.aov, factorA="Tukey", `interaction_average`=TRUE, `covariate_av
- focus.lmat
- R only. Contrast matrix used in the user-specified
comparisons of the
focus
factor. This is the matrix the user constructs. Row names must include all levels of the factor. Column names are the names the user assigns to the contrasts. - linfct
- In R, see#ifndef S-Plus
glht
. #endif #ifdef S-Plusmulticomp
. #endif - ...
- other arguments.
alternative
andbase
are frequently used withglht
. - comparisons
- argument to
multicomp
- lmat.scale.abs2
- logical, scale the contrasts in the columns of
lmat
to make the sum of the absolute values of each column equal 2. - estimate.sign
- numeric. If
0
, leave contrasts in the default lexicographic direction. If positive, force all contrasts to positive, reversing their names if needed (if contrast A-B is negative, reverse it to B-A). If negative, the force al - order.contrasts
- sort the contrasts in the (
mca
,none
,lmat
) components by height on the MMC plot. This will place the contrasts in the multicomp plots in the same order as in the MMC plot. - alternative
- Direction of alternative hypothesis.
See#ifndef S-Plus
glht
#endif #ifdef S-Plusglht
#endif in R. S-Plusmulticomp
uses the argumentbounds
- level
- Confidence level. Defaults to 0.95.
- crit.point, calpha
- critical value for the tests. The value from the
specified
multicomp
method is used for the user-specified contrasts whenlmat
is specified. This argument is calledcrit.point
withmulticomp
- plot
- logical, display the plot if
TRUE
. - ry, iso.name, x.offset, main, main2
- arguments to
plot.mmc.multicomp
. - x, drop
- See
"["
.
Details
By default, if lmat
is not specified, we plot the isomeans grid
and the pairwise comparisons for the focus
factor. By default,
we plot the specified contrasts if the lmat
is specified.
Each contrast is plotted at a height which is the weighted average of
the means being compared. The weights are scaled to the sum of their
absolute values equals 2.
We get the right contrasts automatically if the aov is oneway. If we
specify an lmat for oneway it must have a leading row of 0.
For any more complex design, we must study the lmat
from the mca
component of the result to see how to construct the lmat
(with the
extra rows as needed) and how to specify the lmat.rows
corresponding to the rows for the focus factor.
mmc
in R works from either an "glht"
object or an
"aov"
object. multicomp.mmc
in S-Plus works from an
"aov"
object.
Value
- An
"mmc.multicomp"
object contains either the first two or all three of the"multicomp"
componentsmca
,none
,lmat
described here. Each"multicomp"
component in R also contains a"glht"
object. mca Object containing the pairwise comparisons. none Object comparing each mean to 0. lmat Object for the contrasts specified in the lmat
argument."[.mmc.multicomp"
is a subscript method.
Note
The multiple comparisons calculations in R and S-Plus use
completely different functions.
MMC plots in R are constructed by mmc
based on#ifndef S-Plus
glht
.
#endif
#ifdef S-Plus
glht
.
#endif
MMC plots in S-Plus are constructed by
multicomp.mmc
based on the S-Plus#ifndef S-Plus
multicomp
.
#endif
#ifdef S-Plus
multicomp
.
#endif
The MMC plot is the same in both systems. The details of getting the
plot differ.
Function mmc
calls#ifndef S-Plus
glht
and confint.glht
.
#endif
#ifdef S-Plus
glht
and confint.glht
.
#endif
With a large number of levels
for the focus factor, the confint
function is exceedingly slow
(80 minutes for 30 levels on 1.5GHz Windows XP). Therefore,
always specify calpha
to reduce the time to under a second for
the same example.
There are two plotting functions for MMC plots. mmcplot
, the
newer mmcplot
,
chooses better default values for it arguments and is better coordinated
with the tiebreaker plot.
The older
plot.mmc.multicomp
, built on
References
Heiberger, Richard M. and Holland, Burt (2004b). Statistical Analysis and Data Display: An Intermediate Course with Examples in S-Plus, R, and SAS. Springer Texts in Statistics. Springer. ISBN 0-387-40270-5. Heiberger, Richard M. and Holland, Burt (2006). "Mean--mean multiple comparison displays for families of linear contrasts." Journal of Computational and Graphical Statistics, 15:937--955. Hsu, J. and Peruggia, M. (1994). "Graphical representations of Tukey's multiple comparison method." Journal of Computational and Graphical Statistics, 3:143--161.
See Also
Examples
## Use mmc with R.
## Use multicomp.mmc with S-Plus.
## data and ANOVA
## catalystm example
data(catalystm)
bwplot(concent ~ catalyst, data=catalystm,
scales=list(cex=1.5),
ylab=list("concentration", cex=1.5),
xlab=list("catalyst",cex=1.5))
catalystm1.aov <- aov(concent ~ catalyst, data=catalystm)
summary(catalystm1.aov)
catalystm.mca <-
glht(catalystm1.aov, linfct = mcp(catalyst = "Tukey"))
confint(catalystm.mca)
plot(catalystm.mca) ## multcomp plot
mmcplot(catalystm.mca, focus="catalyst") ## HH plot
## pairwise comparisons
catalystm.mmc <-
mmc(catalystm1.aov, focus="catalyst")
catalystm.mmc
## these three statements are identical for a one-way aov
mmc(catalystm1.aov) ## simplest
mmc(catalystm1.aov, focus="catalyst") ## generalizes to higher-order designs
mmc(catalystm1.aov, linfct = mcp(catalyst = "Tukey")) ## glht arguments
mmcplot(catalystm.mmc, style="both")
## User-Specified Contrasts
## Row names must include all levels of the factor.
## Column names are the names the user assigns to the contrasts.
## Each column must sum to zero.
catalystm.lmat <- cbind("AB-D" =c( 1, 1, 0,-2),
"A-B" =c( 1,-1, 0, 0),
"ABD-C"=c( 1, 1,-3, 1))
dimnames(catalystm.lmat)[[1]] <- levels(catalystm$catalyst)
catalystm.lmat
catalystm.mmc <-
mmc(catalystm1.aov,
linfct = mcp(catalyst = "Tukey"),
focus.lmat=catalystm.lmat)
catalystm.mmc
mmcplot(catalystm.mmc, style="both", type="lmat")
## Dunnett's test
## weightloss example
data(weightloss)
bwplot(loss ~ group, data=weightloss,
scales=list(cex=1.5),
ylab=list("Weight Loss", cex=1.5),
xlab=list("group",cex=1.5))
weightloss.aov <- aov(loss ~ group, data=weightloss)
summary(weightloss.aov)
group.count <- table(weightloss$group)
tmp.dunnett <-
glht(weightloss.aov,
linfct=mcp(group=contrMat(group.count, base=4)),
alternative="greater")
mmcplot(tmp.dunnett, main="contrasts in alphabetical order", focus="group")
tmp.dunnett.mmc <-
mmc(weightloss.aov,
linfct=mcp(group=contrMat(group.count, base=4)),
alternative="greater")
mmcplot(tmp.dunnett.mmc,
main="contrasts ordered by average value of the means
of the two levels in the contrasts")
tmp.dunnett.mmc
## two-way ANOVA
## display example
data(display)
interaction2wt(time ~ emergenc * panel.ordered, data=display)
displayf.aov <- aov(time ~ emergenc * panel, data=display)
anova(displayf.aov)
## multiple comparisons
## MMC plot
displayf.mmc <- mmc(displayf.aov, focus="panel")
displayf.mmc
## same thing using glht argument list
displayf.mmc <-
mmc(displayf.aov,
linfct=mcp(panel="Tukey", `interaction_average`=TRUE, `covariate_average`=TRUE))
mmcplot(displayf.mmc)
panel.lmat <- cbind("3-12"=c(-1,-1,2),
"1-2"=c( 1,-1,0))
dimnames(panel.lmat)[[1]] <- levels(display$panel)
panel.lmat
displayf.mmc <-
mmc(displayf.aov, focus="panel", focus.lmat=panel.lmat)
## same thing using glht argument list
displayf.mmc <-
mmc(displayf.aov,
linfct=mcp(panel="Tukey", `interaction_average`=TRUE, `covariate_average`=TRUE),
focus.lmat=panel.lmat)
mmcplot(displayf.mmc, type="lmat")
## split plot design with tiebreaker plot
##
## This example is based on the query by Tomas Goicoa to R-news
## http://article.gmane.org/gmane.comp.lang.r.general/76275/match=goicoa
## It is a split plot similar to the one in HH Section 14.2 based on
## Yates 1937 example. I am using the Goicoa example here because its
## MMC plot requires a tiebreaker plot.
data(maiz)
interaction2wt(yield ~ hibrido+nitrogeno+bloque, data=maiz,
par.strip.text=list(cex=.7))
interaction2wt(yield ~ hibrido+nitrogeno, data=maiz)
maiz.aov <- aov(yield ~ nitrogeno*hibrido + Error(bloque/nitrogeno), data=maiz)
summary(maiz.aov)
summary(maiz.aov,
split=list(hibrido=list(P3732=1, Mol17=2, A632=3, LH74=4)))
try(glht(maiz.aov, linfct=mcp(hibrido="Tukey"))) ## can't use 'aovlist' objects in glht
## R glht() requires aov, not aovlist
maiz2.aov <- aov(terms(yield ~ bloque*nitrogeno + hibrido/nitrogeno,
keep.order=TRUE),
data=maiz)
summary(maiz2.aov)
## There are many ties in the group means.
## These are easily seen in the MMC plot, where the two clusters
## c("P3747", "P3732", "LH74") and c("Mol17", "A632")
## are evident from the top three contrasts including zero and the
## bottom contrast including zero. The significant contrasts are the
## ones comparing hybrids in the top group of three to ones in the
## bottom group of two.
## We have two graphical responses to the ties.
## 1. We constructed the tiebreaker plot.
## 2. We construct a set of orthogonal contrasts to illustrate
## the clusters.
## pairwise contrasts with tiebreakers.
maiz2.mmc <- mmc(maiz2.aov,
linfct=mcp(hibrido="Tukey", interaction_average=TRUE))
mmcplot(maiz2.mmc, style="both") ## MMC and Tiebreaker
## orthogonal contrasts
## user-specified contrasts
hibrido.lmat <- cbind("PPL-MA" =c(2, 2,-3,-3, 2),
"PP-L" =c(1, 1, 0, 0,-2),
"P47-P32"=c(1,-1, 0, 0, 0),
"M-A" =c(0, 0, 1,-1, 0))
dimnames(hibrido.lmat)[[1]] <- levels(maiz$hibrido)
hibrido.lmat
maiz2.mmc <-
mmc(maiz2.aov, focus="hibrido", focus.lmat=hibrido.lmat)
maiz2.mmc
## same thing using glht argument list
maiz2.mmc <-
mmc(maiz2.aov, linfct=mcp(hibrido="Tukey",
`interaction_average`=TRUE), focus.lmat=hibrido.lmat)
mmcplot(maiz2.mmc, style="both", type="lmat")