assoc {vcd} | R Documentation

## Extended Association Plots

### Description

Produce an association plot indicating deviations from a specified independence model in a possibly high-dimensional contingency table.

### Usage

    ## Default S3 method:
    assoc(x, row_vars = NULL, col_vars = NULL, compress = TRUE,
      xlim = NULL, ylim = NULL,
      spacing = spacing_conditional(sp = 0), spacing_args = list(),
      split_vertical = NULL, keep_aspect_ratio = FALSE, residuals_type = "Pearson",
      xscale = 0.9, yspace = unit(0.5, "lines"), main = NULL, sub = NULL,
      ..., gp_axis = gpar(lty = 3))
    ## S3 method for class 'formula':
    assoc(formula, data = NULL, subset, na.action, ...,
      main = NULL, sub = NULL)

### Arguments

`x` | a contingency table in array form with optional category labels specified in the `dimnames(x)` attribute, or an object inheriting from the `"ftable"` class (such as `"structable"` objects).
`row_vars` | a vector of integers giving the indices, or a character vector giving the names of the variables to be used for the rows of the association plot.
`col_vars` | a vector of integers giving the indices, or a character vector giving the names of the variables to be used for the columns of the association plot.
`compress` | logical; if `FALSE`, the space between the rows (columns) are chosen such that the total heights (widths) of the rows (columns) are all equal. If `TRUE`, the space between rows and columns is fixed and hence the plot is more “compressed”.
`xlim` | a 2 x k matrix of doubles, k number of total columns of the plot. The columns of `xlim` correspond to the columns of the association plot, the rows describe the column ranges (minimums in the first row, maximums in the second row). If `xlim` is `NULL`, the ranges are determined from the residuals according to `compress` (if `TRUE`: widest range from each column, if `FALSE`: from the whole association plot matrix).
`ylim` | a 2 x k matrix of doubles, k number of total rows of the plot. The columns of `ylim` correspond to the rows of the association plot, the rows describe the column ranges (minimums in the first row, maximums in the second row). If `ylim` is `NULL`, the ranges are determined from the residuals according to `compress` (if `TRUE`: widest range from each row, if `FALSE`: from the whole association plot matrix).
`spacing` | a spacing object, a spacing function, or a corresponding generating function (see `strucplot` for more information). The default is the spacing-generating function `spacing_conditional` that is (by default) called with the argument list `spacing_args` (see `spacings` for more details).
`spacing_args` | list of arguments for the spacing-generating function, if specified (see `strucplot` for more information).
`split_vertical` | vector of logicals of length k, where k is the number of margins of `x` (default: `FALSE`). Values are recycled as needed. A `TRUE` component indicates that the corresponding dimension is folded into the columns, `FALSE` folds the dimension into the rows.
`keep_aspect_ratio` | logical indicating whether the aspect ratio should be fixed or not.
`residuals_type` | a character string indicating the type of residuals to be computed. Currently, only Pearson residuals are supported.
`xscale` | scale factor resizing the tile's width, thus adding additional space between the tiles.
`yspace` | object of class `"unit"` specifying additional space separating the rows.
`gp_axis` | object of class `"gpar"` specifying the visual aspects of the tiles' baseline.
`formula` | a formula object with both left and right hand sides specifying the column and row variables of the flat table.
`data` | a data frame, list or environment containing the variables to be cross-tabulated, or a contingency table (see below).
`subset` | an optional vector specifying a subset of observations to be used. Ignored if `data` is a contingency table.
`na.action` | a function which indicates what should happen when the data contain `NA`s. Ignored if `data` is a contingency table.
`main, sub` | either a logical, or a character string used for plotting the main (sub) title. If logical and `TRUE`, the name of the `data` object is used.
`...` | other parameters passed to `strucplot`

### Details

Association plots have been suggested by Cohen (1980) and extended by Friendly (1992) and provide a means for visualizing the residuals of an independence model for a contingency table.

`assoc` is a generic function and currently has a default method and a formula interface. Both are high-level interfaces to the `strucplot` function, and produce (extended) association plots. Most of the functionality is described there, such as specification of the independence model, labeling, legend, spacing, shading, and other graphical parameters.

For a contingency table, the signed contribution to Pearson's chi^2 for cell {ij... k} is

d_{ij...k} = (f_{ij...k} - e_{ij...k}) / sqrt(e_{ij...k})

where f_{ij...k} and e_{ij...k} are the observed and expected counts corresponding to the cell. In the association plot, each cell is represented by a rectangle that has (signed) height proportional to d_{ij...k} and width proportional to sqrt(e_{ij...k}), so that the area of the box is proportional to the difference in observed and expected frequencies. The rectangles in each row are positioned relative to a baseline indicating independence (d_{ij...k} = 0). If the observed frequency of a cell is greater than the expected one, the box rises above the baseline, and falls below otherwise.

Additionally, the residuals can be colored depending on a specified shading scheme (see Meyer et al., 2003). Package vcd offers a range of residual-based shadings (see the shadings help page). Some of them allow, e.g., the visualization of test statistics.

Unlike the `assocplot` function in the graphics package, this function allows the visualization of contingency tables with more than two dimensions. Similar to the construction of ‘flat’ tables (like objects of class `"ftable"` or `"structable"`), the dimensions are folded into rows and columns.

The layout is very flexible: the specification of shading, labeling, spacing, and legend is modularized (see `strucplot` for details).

### Value

The `"structable"` visualized is returned invisibly.

### Author(s)

David Meyer David.Meyer@R-project.org

### References

A. Cohen (1980), On the graphical display of the significant components in a two-way contingency table. Communications in Statistics—Theory and Methods, A9, 1025–1041.

M. Friendly (1992), Graphical methods for categorical data. SAS User Group International Conference Proceedings, 17, 190–200. http://www.math.yorku.ca/SCS/sugi/sugi17-paper.html

D. Meyer, A. Zeileis, K. Hornik (2003), Visualizing independence using extended association plots. Proceedings of the 3rd International Workshop on Distributed Statistical Computing, K. Hornik, F. Leisch, A. Zeileis (eds.), ISSN 1609-395X. http://www.ci.tuwien.ac.at/Conferences/DSC-2003/Proceedings/

### See Also

`mosaic`, `strucplot`, `structable`

### Examples

    data(HairEyeColor)
    ## Aggregate over sex:
    (x <- margin.table(HairEyeColor, c(1, 2)))

    ## Ordinary assocplot:
    assoc(x)
    ## and with residual-based shading (of independence)
    assoc(x, main = "Relation between hair and eye color", shade = TRUE)

    ## Aggregate over Eye color:
    (x <- margin.table(HairEyeColor, c(1, 3)))
    chisq.test(x)
    assoc(x, main = "Relation between hair color and sex", shade = TRUE)

    # Visualize multi-way table
    assoc(aperm(HairEyeColor), expected = ~ (Hair + Eye) * Sex,
          labeling_args = list(just_labels = c(Eye = "left"),
                               offset_labels = c(right = -0.5),
                               offset_varnames = c(right = 1.2),
                               rot_labels = c(right = 0),
                               tl_varnames = c(Eye = TRUE))
    )

    assoc(aperm(UCBAdmissions), expected = ~ (Admit + Gender) * Dept, compress = FALSE,
          labeling_args = list(abbreviate = c(Gender = TRUE), rot_labels = 0)
    )

[Package vcd version 0.9-6 Index]