Displays a third variable where the data are represented by open circles whose diameters are proportional to the value of the data at their x-y locations. The rate of change of symbol diameter with value and the absolute size of the symbols are defined by the user. The x-y plot axes may be optionally displayed with logarithmic (base 10) scaling. Optionally a legend may be displayed on the plot.

1 2 3 4 5 | ```
xyplot.z(xx, yy, zz, p = 0.5, sfact = 2.5, zmin = NA, zmax = NA, log = NULL,
xlim = NULL, ylim = NULL, xlab = deparse(substitute(xx)),
ylab = deparse(substitute(yy)), zlab = deparse(substitute(zz)),
main = "", col = 1, iflgnd = FALSE, title = deparse(substitute(zz)),
cex.lgnd = 0.8, ifparams = FALSE, cex.params = 0.8, ...)
``` |

`xx` |
name of the x-axis variable. |

`yy` |
name of the y-axis variable. |

`zz` |
name of the third variable, z, to be plotted. |

`p` |
a parameter that controls the rate of change of symbol diameter with changing value. A default of |

`sfact` |
controls the absolute size of the plotted symbols, by default |

`zmin` |
a value below which all symbols will be plotted at the same minumum size. By default |

`zmax` |
a value above which all symbols will be plotted at the same maximum size. By default |

`log` |
if it is required to display the data with logarithmic axis scaling, set |

`xlim` |
user defined limits for the x-axis, see Details below. |

`ylim` |
user defined limits for the y-axis, see Details below. |

`xlab` |
by default the character string for |

`ylab` |
by default the character string for |

`zlab` |
by default, |

`main` |
an alternative plot title, see Details below. |

`col` |
the colour of the symbols, the default is black, |

`iflgnd` |
the default is no legend. If a legend is required set |

`title` |
a short title for the legend, e.g., |

`cex.lgnd` |
controls the scaling of the legend box and text, but not the symbols so that they match those on the plot, the default is |

`ifparams` |
if |

`cex.params` |
controls the size of the text for the parameters display, defaults to |

`...` |
further arguments to be passed to methods. For example, if it is required to make the plot title smaller, add |

The symbol diameter is computed as a function of the value `z`

to be plotted:

`diameter = dmin + (dmax - dmin) * {(z - zmin)/(zmax - zmin)}^p`

where `dmin`

and `dmax`

are defined as 0.1 and 1 units, so the symbol diameters range over an order of magnitude (and symbol areas over two); `zmin`

and `zmax`

are the observed range of the data, or the range over which the user wants the diameters to be computed; and `p`

is a power defined by the user. The value of `(z - zmin)/(zmax - zmin)`

is the value of `z`

normalized, 0 - 1, to the range over which the symbol diameters are to be computed. After being raised to the power `p`

, which will result in a number in the range 0 to 1, this value is multiplied by the permissable range of diameters and added to the minimum diameter. This results in a diameter between 0.1 and 1 units that is proportional to the value of `z`

.

A `p`

value of `1`

results in a linear rate of change. Values of `p`

less than unity lead to a rapid intial rate of change with increasing value of `z`

which is often suitable for displaying positively skewed data sets, see the example below. In contrast, values of `p`

greater than unity result in an initial slow rate of change with increasing value of `z`

which is often suitable for displaying negatively skewed data sets. To obtain a logarithmic scaling set `p = 0.3679`

, i.e. `1/e`

, and a value of `p = 0.5`

is equivalent to a square root transformation, the default, that is appropriate for a linear-area relationship. These values of `p`

are equivalent to plotting `log(x)`

or `log10(x)`

and `sqrt(x)`

, respectively. Experimentation is often necessary to obtain a satisfactory visual effect. See `syms.pfunc`

for a graphic demonstrating the effect of varying the `p`

parameter.

If `zmin`

or `zmax`

are defined this has the effect of setting a minimum or maximum value of `z`

, respectively, beyond which changes in the value of `z`

do not result in changes in symbol diameter. This can be useful in limiting the effect of one, or a few, extreme outlier(s) while still plotting them, they simply plot at the minimum or maximum symbol size and are not involved in the calculation of the range of `z`

over which the symbol diameters vary. **Note:** If the variable `z`

includes a transform, e.g., `log10(z)`

, the values of `zmin`

and/or `zmax`

must be in those transform units.

If `zlab`

and `main`

are undefined a default a plot title is generated by appending the input variable name text string to `"Proportional Symbol Plot for "`

. If no plot title is required set `zlab = " "`

, and if some user defined plot title is required it should be defined in `main`

, e.g. `main = "Plot Title Text"`

.

If the default selection for `xlim`

is inappropriate it can be set, e.g., `xlim = c(0, 200)`

or `c(2, 200)`

, the latter being appropriate for a logarithmically scaled plot, i.e. `log = "x"`

. If the defined limits lie within the observed data range a truncated plot will be displayed. The same procedure applies to setting `ylim`

.

Any less than detection limit values represented by negative values, or zeros or other numeric codes representing blanks in the data, must be removed prior to executing this function, see `ltdl.fix.df`

.

The legend consists of five proportional symbols and their corresponding `z`

values: `zmin`

; the three quartiles; and `zmax`

. If `zmin`

and `zmax`

have been user defined it is over their range that the symbol sizes are computed and displayed. When defining `zmin`

and/or `zmax`

it is useful to set `ifparams = TRUE`

as a reminder, whilst developing the required display.

Any data vectors containing `NA`

s are removed prior to displaying the plot.

Robert G. Garrett

`syms`

, `syms.pfunc`

, `ltdl.fix.df`

, `remove.na`

, `display.lty`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
## Make test data available
data(sind)
attach(sind)
## Display a default symbol plot, p = 0.5 and sfact = 2.5
xyplot.z(Fe, Mn, Zn)
## Plot with logarithmically scaled symbols and more appropriately
## labelled axes
xyplot.z(Fe, Mn, log10(Zn), p = 1, log = "y",
xlab = "Fe (pct) in stream sediment",
ylab = "Mn (mg/kg) in stream sediment")
## Plot with differently scaled symbols in red and more appropriate
## scaling and labelling with a user specified title
xyplot.z(Fe, Mn, Zn, p = 0.3, sfact = 2.0, log = "y",
xlab = "Fe (pct) in stream sediment",
ylab = "Mn (mg/kg) in stream sediment",
main = "Howarth & Sinding-Larsen Test Data\nZn (mg/kg)", symcolr = 2)
## Plot as above but where outliers above a value of 1000 displayed
## with the same symbol
xyplot.z(Fe, Mn, Zn, p = 0.3, sfact = 2.0, zmax = 1000, log = "y",
xlab = "Fe (pct) in stream sediment",
ylab = "Mn (mg/kg) in stream sediment",
main = "Howarth & Sinding-Larsen Test Data\nZn (mg/kg)", symcolr = 2)
## Detach test data
detach(sind)
``` |

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