mmc: MMC (Mean-mean Multiple Comparisons) plots.

In HH: Statistical Analysis and Data Display: Heiberger and Holland

MMC (Mean–mean Multiple Comparisons) plots.

Description

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, ...)


## Default S3 method:
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 for lmat in R is to use the transpose of the linfct component produced by glht. Required for user-specified contrasts.
lmat.rows	rows in lmat for the focus 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 as mmc(my.aov, factorA="Tukey", `interaction_average`=TRUE, `covariate_average`=TRUE) With TRUE, TRUE, multcomp::glht always gives the same result as the S-Plus multcomp function. Without the TRUE, TRUE, multcomp::glht gives a different answer when there are interactions or covariates in the model. See glht.
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. Each column must sum to zero. See catalystm.lmat in the Examples section for an example. The focus.lmat matrix is multiplied by the lmat from the none component to create the lmat for the user-specified contrasts. Display the hibrido.lmat and maiz2.lmat in the maiz example below to see what is happening.
linfct	In R, see glht.
...	other arguments. alternative and base are frequently used with glht.
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 all contrasts to positive.
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 glht in R. S-Plus multicomp uses the argument bounds for this concept.
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 when lmat is specified. This argument is called crit.point with multicomp in S-Plus and calpha when used with glht and confint in R. In R, with a large number of levels for the focus factor, calpha should be specified. See notes below for discussion of the timing issues and the examples for an illustration how to use calpha.
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" components mca, 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 glht. MMC plots in S-Plus are constructed by multicomp.mmc based on the S-Plus multicomp. The MMC plot is the same in both systems. The details of getting the plot differ.

Function mmc calls glht and confint.glht. 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 lattice-based function, is recommended. mmcplot, chooses better default values for it arguments and is better coordinated with the tiebreaker plot.

The older plot.mmc.multicomp, built on base graphics, chooses sensible defaults for its many arguments, but they still often need manual adjustment. The examples show several types of adjustments. We have changed the centering and scaling to avoid overprinting of label information. By default the significant contrasts are shown in a more intense color than the nonsignificant contrasts. We have an option to reduce the color intensity of the isomeans grid.

Author(s)

Richard M. Heiberger <[e-mail]>

References

Heiberger, Richard M. and Holland, Burt (2015). Statistical Analysis and Data Display: An Intermediate Course with Examples in R. Second Edition. Springer-Verlag, New York. https://link.springer.com/book/10.1007/978-1-4939-2122-5

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

mmcplot, plot.mmc.multicomp, as.multicomp

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

## Not run: 
## 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

## End(Not run)

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")


## Not run: 
## 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\nof the two levels in the contrasts")

tmp.dunnett.mmc

## End(Not run)

## Not run: 
## 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")

## End(Not run)

## Not run: 
## 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")

## End(Not run)

HH documentation built on Aug. 9, 2022, 5:08 p.m.