ludwig {IsoplotR} | R Documentation |
Linear regression of U-Pb data with correlated errors, taking into account decay constant uncertainties.
Description
Implements the maximum likelihood algorithm for Total-Pb/U isochron regression of Ludwig (1998) and extends the underlying methodology to accommodate U-Th-Pb data and initial U-series disequilibrium.
Usage
ludwig(
x,
model = 1,
anchor = 0,
exterr = FALSE,
type = "joint",
plot = FALSE,
...
)
ludwig(
x,
model = 1,
anchor = 0,
exterr = FALSE,
type = "joint",
plot = FALSE,
...
)
Arguments
x |
an object of class |
model |
one of three regression models:
|
anchor |
control parameters to fix the intercept age or common Pb composition of the isochron fit. This can be a scalar or a vector. If If If If |
exterr |
propagate external sources of uncertainty (i.e. decay constants)? |
type |
only relevant if
|
plot |
logical. Only relevant for datasets with measured
disequilibrium. If |
... |
optional arguments |
Details
The 3-dimensional regression algorithm of Ludwig and Titterington
(1994) was modified by Ludwig (1998) to fit so-called 'Total Pb-U
isochrons'. These are constrained to a radiogenic endmember
composition that falls on the concordia
line. In its
most sophisticated form, this algorithm does not only allow for
correlated errors between variables, but also between
aliquots. IsoplotR
currently uses this algorithm to
propagate decay constant uncertainties in the total Pb-U isochron
ages.
Value
- par
a vector with the lower concordia intercept, the common Pb ratios, the dispersion parameter (if
model=3
), and the initial{}^{234}
U/{}^{238}
U and{}^{230}
Th/{}^{238}
U activity ratio (in the presence of initial disequilibrium).- cov
the covariance matrix of
par
- df
the degrees of freedom of the model fit (
n-2
ifx$format<4
or2n-3
ifx$format>3
, wheren
is the number of aliquots).- mswd
the mean square of weighted deviates (a.k.a. reduced Chi-square statistic) for the fit.
- p.value
p-value of a Chi-square test for the linear fit
References
Ludwig, K.R., 1998. On the treatment of concordant uranium-lead ages. Geochimica et Cosmochimica Acta, 62(4), pp.665-676.
Ludwig, K.R. and Titterington, D.M., 1994. Calculation of
^{230}
Th/U isochrons, ages, and errors. Geochimica et
Cosmochimica Acta, 58(22), pp.5031-5042.
See Also
concordia
, titterington
,
isochron
Examples
f <- system.file("UPb4.csv",package="IsoplotR")
d <- read.data(f,method="U-Pb",format=4)
fit <- ludwig(d)