plot.assoc {logmult}

Plotting Scores from Association Models

Description

Graphical display of category scores from association models.

Usage

## S3 method for class '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 class '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 class '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 class '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 class '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 class '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 class '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 class '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, ...)

Arguments

x

an association model, or an object inheriting from class assoc.

dim

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.

layer

integer indicating which layer should be represented, or “average” or “average.rotate” when scores are homogeneous (see “Details” below).

what

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.

which

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.

mass

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.

luminosity

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.

arrow

Numeric value indicating the angle at which the polar coordinates system arrow should be plotted; use NULL for no arrow.

conf.int

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.

replicates

whether to plot points representing the values of the scores obtained for all of the jackknife of bootrap replicates, when applicable (see “Details” below).

coords

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).

rev.axes

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.

cex

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.

col

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.

col.conf.int

a vector indicating the color of the confidence bars/ellipses, when these are plotted; see col the format.

groups

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.

add

whether to draw over an existing plot instead of creating a new one.

type

set to "n" to avoid actually plotting the points and labels; useful for customization based on the returned coordinates, see “Value” below.

xlim

numeric vector of length 2, giving the x coordinates range.

ylim

numeric vector of length 2, giving the y coordinates range.

asp

the y/x aspect ratio, see plot.window.

xlab

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.

ylab

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.

main

an overall title for the plot: see title. If missing for RC(M)-L models, the name of the plotted layer will be used.

pch

a vector of plotting ‘character’, i.e., symbol to use for each point, recycled as necessary; see points.

font

an integer vector indicating the font to use for each label, recycled as necessary; see link{par}.

...

Further arguments passed to plot.

Details

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.

Value

An invisible list with components row and col, two matrices containing the coordinates of the plotted points (NULL when not plotted).

References

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.

See Also

rc, rcL, rcL.trans, hmskew, hmskewL, yrcskew

Examples

  ## 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)
  
## End(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)