Graphical display of category scores from association models.
# S3 method for rc
plot(x, dim = c(1, 2),
what = c("both", "rows", "columns"), which = NULL,
mass = TRUE, luminosity = length(x$assoc$diagonal > 0),
conf.int = NA, replicates = FALSE,
coords = c("cartesian", "polar"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = c("blue", "red"), col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)# S3 method for rc.symm
plot(x, dim = c(1, 2), which = NULL,
mass = TRUE, luminosity = length(x$assoc$diagonal > 0),
conf.int = NA, replicates = FALSE,
coords = c("cartesian", "polar"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = "blue", col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
# S3 method for hmskew
plot(x, dim = c(1, 2),
what = c("skew-symmetric", "symmetric"), which = NULL,
mass = TRUE, luminosity = length(x$assoc.hmskew$diagonal > 0),
arrow = 45, conf.int = NA, replicates = FALSE,
coords = c("polar", "cartesian"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = "blue", col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
# S3 method for yrcskew
plot(x, dim = c(1, 2),
what = c("skew-symmetric", "symmetric"), which = NULL,
mass = TRUE, luminosity = length(x$assoc.yrcskew$diagonal > 0),
arrow = 45, conf.int = NA, replicates = FALSE,
coords = c("polar", "cartesian"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = "blue", col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
# S3 method for rcL
plot(x, dim = c(1, 2), layer = "average",
what = c("both", "rows", "columns"), which = NULL,
mass = TRUE, luminosity = length(x$assoc$diagonal > 0),
conf.int = NA, replicates = FALSE,
coords = c("cartesian", "polar"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = c("blue", "red"), col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
# S3 method for rcL.symm
plot(x, dim = c(1, 2), layer = "average",
which = NULL,
mass = TRUE, luminosity = length(x$assoc$diagonal > 0),
conf.int = NA, replicates = FALSE,
coords = c("cartesian", "polar"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = "blue", col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
# S3 method for hmskewL
plot(x, dim = c(1, 2), layer = "average",
what = c("skew-symmetric", "symmetric"), which = NULL,
mass = TRUE, luminosity = length(x$assoc.hmskew$diagonal > 0),
arrow=45, conf.int = NA, replicates = FALSE,
coords = c("polar", "cartesian"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = "blue", col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
# S3 method for assoc
plot(x, dim = c(1, 2), layer = 1,
what = c("both", "rows", "columns"), which = NULL,
mass = TRUE, luminosity = length(x$diagonal > 0),
arrow = NULL, conf.int = NA, replicates = FALSE,
coords = c("cartesian", "polar"), rev.axes = c(FALSE, FALSE),
cex = par("cex"), col = c("blue", "red"), col.conf.int = col, groups = NULL,
add = FALSE, type, xlim, ylim, asp, xlab, ylab, main, pch, font, ...)
an association model, or an object inheriting from class assoc.
numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical.
integer indicating which layer should be represented, or “average” or “average.rotate” when scores are homogeneous (see “Details” below).
for rc and assoc objects, whether points corresponding to rows, columns
or both should be plotted; for hmskew and yrcskew objects, what association
should be plotted.
an optional subset of points to be plotted, specified via a logical, integer or character
vector indexing the row or column component of the association object; if what = both,
a list of two such vectors, resp. for rows and columns.
whether the size of the point symbols should reflect on the mass of the categories;
this only makes sense when marginal weights were used when fitting the model. The precise
formula is that the pch of a symbol is equal to the pch argument, times the
weight of the category divided by average weight.
whether the luminosity of the symbols should vary according to the diagonal-specific
parameters (if diagonal = TRUE was passed when fitting the model); if TRUE,
hue and saturation of col are taken as a base, and value varies from 0 to 0.8
as a linear function of the diagonal parameter values.
Numeric value indicating the angle at which the polar coordinates system arrow should be plotted; use NULL for no arrow.
an integer between 0 and 1 giving the confidence level to use when drawing error bars/ellipses around the points (see “Details” below); by default nothing is plotted. Only possible if jackknife or bootstrap was enabled when fitting the model.
whether to plot points representing the values of the scores obtained for all of the jackknife of bootrap replicates, when applicable (see “Details” below).
whether to use a Cartesian or a polar coordinate system; the former makes sense when axes
offer an interpretation (like in RC(M) models), while the latter are more appropriate when
only the angle and distance to origin are of interest (like in hmskew models).
a numeric of length 1 or 2 indicating whether the sign of scores on the axes should be changed; as this sign is arbitrary in RC(M) models, changing it has no incidence on the results and may be more intuitive or consistent with other presentations.
a numeric vector indicating the size of the point symbols, recycled as necessary; the most common
choice is probably to pass only one value and use mass to make the size vary.
a vector indicating the color of the point symbols, recycled as necessary; as a special case, a
vector of length 2 can be passed, to indicate the color of row and column points, respectively.
See also luminosity.
a vector indicating the color of the confidence bars/ellipses, when these are plotted; see
col the format.
a vector indicating what symbol should be used for each point, recycled as necessary; groups will
use pch values 21, 24, 22, 23 and 25, in this order, cycling if needed. If not an integer,
the number of the factor level will be used.
whether to draw over an existing plot instead of creating a new one.
set to "n" to avoid actually plotting the points and labels; useful for customization based on the returned coordinates, see “Value” below.
numeric vector of length 2, giving the x coordinates range.
numeric vector of length 2, giving the y coordinates range.
the y/x aspect ratio, see plot.window.
a title for the x axis: see title. For RC(M) axes and Cartesian coordinates,
the default is “Dimension N (phi)”; it is empty in other cases where axes have no meaning.
a title for the y axis: see title. For RC(M) axes and Cartesian coordinates,
the default is “Dimension N (phi)”; it is empty in other cases where axes have no meaning.
an overall title for the plot: see title. If missing for RC(M)-L models, the name of
the plotted layer will be used.
a vector of plotting ‘character’, i.e., symbol to use for each point, recycled as necessary;
see points.
an integer vector indicating the font to use for each label, recycled as necessary;
see link{par}.
Further arguments passed to plot.
An invisible list with components row and col, two matrices containing the coordinates of the
plotted points (NULL when not plotted).
The functions documented here represent in a one- or two-dimensional space the category scores obtained from a log-multiplicative association model. They produce symmetric biplots in which the coordinates of points on both axes are the product of normalized scores and of the square root of the intrinsic association coefficient corresponding to each dimension: thus, row and column points share the same “unit” on all axes (Goodman, 1991, Appendix 2; Wong, 2010, eq. 2.38; Clogg & Shihadeh, 1994, p. 91-92). As a special case, models with only one dimension are presented as a dotchart of the scores.
Various convenience options are provided, with reasonable defaults for each model family. In particular,
you may find it necessary to adapt the cex, mass, luminosity and groups arguments
depending on the number of categories to be plotted and to their respective weights. When plotting a RC(2) model,
a polar coordinate system can be of substantive interest, allowing to interpret at a glance the distance to
origin as the general strength of the association for a category on both axes (a property that is lost for
higher-dimensional models).
Confidence bars/ellipses are computed from the scores' variances and covariances, based on the assumption that they are
follow a normal distribution, even if standard errors are computed using jackknife or bootstrap. When bootstrap (not
jackknife) was used, this normality assumption can be assessed visually using the replicates argument to check
whether points globally follow the shape of the ellipses. See se.assoc for details about checking the
validity of jackknife or bootstrap results.
When layer is set to “average” for models with layer effect and homogeneous scores, intrinsic association
coefficients are weighted across all layers. In addition, if layer is set to “average.rotate”, scores are
rotated so that axes of the plot are those with the highest variance; oblique axes represent the original dimensions
in the new space.
The plot.assoc function is called internally by all others, and may be leveraged for advanced use cases,
like plotting custom models that do not correspond stricly to the supported types.
For RC(M) models:
Goodman, L.A. (1991). Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data. J. of the Am. Stat. Association 86(416), 1085-1111.
Clogg, C.C., and Shihadeh, E.S. (1994). Statistical Models for Ordinal Variables. Sage: Advanced Quantitative Techniques in the Social Sciences (4).
Wong, R.S-K. (2010). Association models. Sage: Quantitative Applications in the Social Sciences (164).
For van der Heijden & Mooijaart models:
van der Heijden, P.G.M., and Mooijaart, A. (1995). Some new log bilinear models for the analysis of asymmetry in a square contingency table. Sociol. Methods and Research 24, 7-29.
# NOT RUN {
## Wong (2010), Figures 2.2 and 2.3 (p. 50-51)
data(gss8590)
# }
# NOT RUN {
model <- rc(margin.table(gss8590[,,c(2,4)], 1:2),
nd=2, weighting="none", se="jackknife")
plot(model, what="row", rev.axes=c(TRUE, FALSE), conf.int=0.95)
plot(model, what="col", rev.axes=c(TRUE, FALSE), conf.int=0.95)
# }
# NOT RUN {
## Wong (2010), Figures 4.1 and 4.2 (p. 108-109)
data(gss7590)
model <- rcL(gss7590, nd=2, weighting="none")
opar <- par(mfrow=c(2, 2))
for(i in 1:4)
plot(model, layer=i, what="rows", rev.axes=c(TRUE, FALSE),
main=rownames(model$assoc$phi)[i],
xlim=c(-1.2, 1.2), ylim=c(-1.2, 1.2))
par(mfrow=c(2, 2))
for(i in 1:4)
plot(model, layer=i, what="col", rev.axes=c(TRUE, FALSE),
main=rownames(model$assoc$phi)[i],
xlim=c(-1.4, 1.4), ylim=c(-1.2, 1.2))
par(opar)
## van der Heijden & Mooijaart (1995), Figure 1c (p. 23)
data(ocg1973)
# 5:1 is here to take "Farmers" as reference category (angle 0)
model <- hmskew(ocg1973[5:1, 5:1], weighting="uniform")
# Reproduce the plot from the original article
plot(model, coords="cartesian")
# Use a polar coordinates system, which makes more sense in this setting
plot(model)
# }
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