Implementation of a graphical device developed by Rex Galbraith to display several estimates of the same quantity that have different standard errors. Serves as a vehicle to display finite and continuous mixture models.
radialplot(x, ...)# S3 method for default
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
transformation = "log",
sigdig = 2,
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
k = 0,
np = 3,
markers = NULL,
oerr = 3,
units = "",
hide = NA,
omit = NULL,
omit.col = NA,
...
)
# S3 method for other
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
transformation = "log",
sigdig = 2,
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
k = 0,
np = 3,
markers = NULL,
oerr = 3,
units = "",
hide = NA,
omit = NULL,
omit.col = NA,
...
)
# S3 method for fissiontracks
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
transformation = "arcsin",
sigdig = 2,
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for UPb
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
transformation = "log",
type = 4,
cutoff.76 = 1100,
cutoff.disc = discfilter(),
show.numbers = FALSE,
pch = 21,
sigdig = 2,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
common.Pb = 0,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for PbPb
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
common.Pb = 2,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for ArAr
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = FALSE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for KCa
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = FALSE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for ThPb
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = TRUE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for UThHe
radialplot(
x,
from = NA,
to = NA,
xlim = NULL,
z0 = NA,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for ReOs
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = TRUE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for SmNd
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = TRUE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for RbSr
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = TRUE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for LuHf
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
exterr = FALSE,
i2i = TRUE,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
# S3 method for ThU
radialplot(
x,
from = NA,
to = NA,
z0 = NA,
xlim = NULL,
sigdig = 2,
transformation = "log",
show.numbers = FALSE,
pch = 21,
levels = NA,
clabel = "",
bg = c("yellow", "red"),
col = "black",
markers = NULL,
k = 0,
np = 3,
Th0i = 0,
oerr = 3,
hide = NULL,
omit = NULL,
omit.col = NA,
...
)
does not produce any numerical output, but does report the central age and the results of any mixture modelling in the title. An asterisk is added to the plot title if the initial daughter correction is based on an isochron regression, to highlight the circularity of using an isochron to compute a central age, and to indicate that the reported uncertainties do not include the uncertainty of the initial daughter correction. This is because this uncertainty is neither purely random nor purely systematic.
Either an [nx2] matix of (transformed) values z
and their standard errors s
OR
and object of class fissiontracks, UThHe,
ArAr, KCa, ReOs, SmNd, RbSr,
LuHf, ThU, PbPb, ThPb or UPb
additional arguments to the generic points
function
minimum age limit of the radial scale
maximum age limit of the radial scale
central value
one of either log, linear,
sqrt or arcsin (if x has class
fissiontracks and fissiontracks$format \(\neq
1\)).
the number of significant digits of the numerical values reported in the title of the graphical output.
boolean flag (TRUE to show grain
numbers)
plot character (default is a filled circle)
a vector with additional values to be displayed as different background colours of the plot symbols.
label of the colour legend
Fill colour for the plot symbols. This can either be a
single colour or multiple colours to form a colour ramp (to be
used if levels!=NA):
a single colour: rgb(0,1,0,0.5), '#FF000080',
'white', etc.;
multiple colours: c(rbg(1,0,0,0.5),
rgb(0,1,0,0.5)), c('#FF000080','#00FF0080'),
c('blue','red'), c('blue','yellow','red'), etc.;
a colour palette: rainbow(n=100),
topo.colors(n=100,alpha=0.5), etc.; or
a reversed palette: rev(topo.colors(n=100,alpha=0.5)), etc.
for plot symbols, set bg=NA
text colour to be used if show.numbers=TRUE
number of peaks to fit using the finite mixture models of
Galbraith and Laslett (1993). Setting k='auto'
automatically selects an optimal number of components based on
the Bayes Information Criterion (BIC). Setting k='min'
estimates the minimum value using a three parameter model
consisting of a Normal distribution truncated by a discrete
component.
number of parameters for the minimum age model. Must be either 3 or 4.
vector of ages of radial marker lines to add to the plot.
indicates whether the analytical uncertainties of the output are reported in the plot title as:
1: 1\(\sigma\) absolute uncertainties.
2: 2\(\sigma\) absolute uncertainties.
3: absolute (1-\(\alpha\))% confidence intervals, where
\(\alpha\) equales the value that is stored in
settings('alpha').
4: 1\(\sigma\) relative uncertainties (\(\%\)).
5: 2\(\sigma\) relative uncertainties (\(\%\)).
6: relative (1-\(\alpha\))% confidence intervals, where
\(\alpha\) equales the value that is stored in
settings('alpha').
measurement units to be displayed in the legend.
vector with indices of aliquots that should be removed from the radial plot.
vector with indices of aliquots that should be plotted but omitted from the central age calculation or mixture models.
colour that should be used for the omitted aliquots.
maximum limit of the x-axis. If provided as a vector, uses the last value of that vector and ignores the first one.
include the external sources of uncertainty into the error propagation for the central age and mixture models?
scalar indicating whether to plot the
\(^{207}\)Pb/\(^{235}\)U age (type=1), the
\(^{206}\)Pb/\(^{238}\)U age (type=2), the
\(^{207}\)Pb/\(^{206}\)Pb age (type=3), the
\(^{207}\)Pb/\(^{206}\)Pb-\(^{206}\)Pb/\(^{238}\)U age
(type=4), the concordia_age (type=5), or the
\(^{208}\)Pb/\(^{232}\)Th age (type=6). Ignored if
x$format>8.
the age (in Ma) below which the
\(^{206}\)Pb/\(^{238}\)U and above which the
\(^{207}\)Pb/\(^{206}\)Pb age is used. This parameter is
only used if type=4.
discordance cutoff filter. This is an object of
class discfilter.
common lead correction:
0: none
1: use the Pb-composition stored in
settings('iratio','Pb207Pb206') (if x has class
UPb and x$format<4);
settings('iratio','Pb206Pb204') and
settings('iratio','Pb207Pb204') (if x has class
PbPb or x has class UPb and
3<x$format<7); or
settings('iratio','Pb206Pb208') and
settings('iratio','Pb207Pb208') (if x has class
UPb and x$format=7 or 8).
2: remove the common Pb by projecting the data along an
inverse isochron. Note: choosing this option introduces a degree of
circularity in the central age calculation. In this case the radial
plot just serves as a way to visualise the residuals of the data
around the isochron, and one should be careful not to
over-interpret the numerical output.
3: use the Stacey-Kramers two-stage model to infer the
initial Pb-composition
`isochron to intercept': calculates the initial
(aka `inherited', `excess', or `common') \(^{40}\)Ar/\(^{36}\)Ar,
\(^{40}\)Ca/\(^{44}\)Ca, \(^{207}\)Pb/\(^{204}\)Pb,
\(^{87}\)Sr/\(^{86}\)Sr, \(^{143}\)Nd/\(^{144}\)Nd,
\(^{187}\)Os/\(^{188}\)Os, \(^{230}\)Th/\(^{232}\)Th,
\(^{176}\)Hf/\(^{177}\)Hf or \(^{204}\)Pb/\(^{208}\)Pb
ratio from an isochron fit. Setting i2i to FALSE uses
the default values stored in settings('iratio',...).
Note that choosing this option introduces a degree of circularity in the central age calculation. In this case the radial_plot plot just serves as a way to visualise the residuals of the data around the isochron, and one should be careful not to over-interpret the numerical output.
initial \(^{230}\)Th correction.
0: no correction
1: project the data along an isochron fit
2: if x$format is 1 or 2, correct the
data using the measured present day \(^{230}\)Th/\(^{238}\)U,
\(^{232}\)Th/\(^{238}\)U and \(^{234}\)U/\(^{238}\)U
activity ratios in the detritus. If x$format is 3 or
4, correct the data using the measured
\(^{238}\)U/\(^{232}\)Th activity ratio of the whole rock, as
stored in x by the read.data() function.
3: correct the data using an assumed initial
\(^{230}\)Th/\(^{232}\)Th-ratio for the detritus (only relevant
if x$format is 1 or 2).
The radial plot (Galbraith, 1988, 1990) is a graphical device that was specifically designed to display heteroscedastic data, and is constructed as follows. Consider a set of dates \(\{t_1,...,t_i,...,t_n\}\) and uncertainties \(\{s[t_1],...,s[t_i],...,s[t_n]\}\). Define \(z_i = z[t_i]\) to be a transformation of \(t_i\) (e.g., \(z_i = log[t_i]\)), and let \(s[z_i]\) be its propagated analytical uncertainty (i.e., \(s[z_i] = s[t_i]/t_i\) in the case of a logarithmic transformation). Create a scatter plot of \((x_i,y_i)\) values, where \(x_i = 1/s[z_i]\) and \(y_i = (z_i-z_\circ)/s[z_i]\), where \(z_\circ\) is some reference value such as the mean. The slope of a line connecting the origin of this scatter plot with any of the \((x_i,y_i)\)s is proportional to \(z_i\) and, hence, the date \(t_i\).
These dates can be more easily visualised by drawing a radial scale at some convenient distance from the origin and annotating it with labelled ticks at the appropriate angles. While the angular position of each data point represents the date, its horizontal distance from the origin is proportional to the precision. Imprecise measurements plot on the left hand side of the radial plot, whereas precise age determinations are found further towards the right. Thus, radial plots allow the observer to assess both the magnitude and the precision of quantitative data in one glance.
Galbraith, R.F., 1988. Graphical display of estimates having differing standard errors. Technometrics, 30(3), pp.271-281.
Galbraith, R.F., 1990. The radial plot: graphical assessment of spread in ages. International Journal of Radiation Applications and Instrumentation. Part D. Nuclear Tracks and Radiation Measurements, 17(3), pp.207-214.
Galbraith, R.F. and Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks and Radiation Measurements, 21(4), pp.459-470.
peakfit, central
attach(examples)
radialplot(FT1)
dev.new()
radialplot(LudwigMixture,k='min')
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