Graphics Reference
In-Depth Information
In this chapter we consider mosaicplots, which were introduced by Hartigan and
Kleiner(
)asawayofvisualizing contingency tables. Named“mosaicplots” dueto
their resemblance to the art form, they consist of groups of rectangles that represent
the cells in a contingency table. Both the sizes and the positions of the rectangles are
relevant to mosaicplot interpretation, making them one of the more advanced plots
around.Withalittlepracticetheycanbecomeaninvaluabletoolintherepresentation
and exploration of multivariate categorical data.
In this chapter we will be discussing ways of constructing and interpreting mo-
saicplots, includingtheirconnection tologlinearmodels(Hofmann,
;heusand
Lauer,
; Friendly,
). In Sect.
.
we will be discussing ways of constructing
mosaicplots (Hofmann,
). Mosaic plots have the huge advantage of preserving
all of the information in multivariate contingency tables while simultaneously pro-
viding an overview of it. As the mosaicplot follows the hierarchy its corresponding
contingency table exactly, the order of the variables in the table is important. Select-
ing the “right,” or at least “good,” ordering is commonly found to be one of the main
di
culties first-time users experience with mosaicplots. We will discuss the effects
of changes in the order and provide recommendations about how to obtain “good
plots.”
Multivariate categorical modeling is usually done with loglinear models. It can be
shown(Hofmann,
;heusandLauer,
;Friendly,
)thatmosaicplots have
excellent mathematical propertieswhichenable the strengths ofinteraction effects to
be assessed visually and provide tools for checking residuals and modeling assump-
tions. We will discuss the relationship between mosaicplots and loglinear models in
Sect.
.
.
Close relatives of the mosaicplot, such as fluctuation diagrams and doubledecker
plots (Hofmann et al.,
), have also been found to be very useful in practice. We
are therefore going to have a look at those and other important variants of mosaic-
plotstooinSect.
.
.Allofthesevariants areessentially simplifications ofthedefault
mosaic construction. While some information is lost in the process, these plots place
additional emphasis on a specific aspect of the data.
Shneiderman (
) and trellis plots (Becker et al.,
) are generalizations of
two different aspects of mosaicplots. While trellis plots and mosaicplots share the
same structure, trellis plots are more flexible since numbers do not necessarily have
tobedisplayed asrectangles. Treemaps, on theother hand,always userectangles, but
are able to deal with more general partitions than mosaicplots. hese generalizations
do not come without losses, though. We will compare mosaicplots to these other
displaysinSect.
.
,andcommentonthestrengthsandweaknessesofeach.Sotware
implementations of mosaicplots arebecoming morefrequent. Animplementation in
R (Gentleman and Ihaka,
)was created by Emerson (
).Mosaic plots in JMP
(John Sall,
)have some limited interactive features. Fully interactive mosaicplots
(Hofmann,
) are implemented, e.g., in MANET (Unwin, Hawkins, Hofmann
and Siegl,
), Mondrian (heus,
) and KLIMT (Urbanek,
).
