Estimation of the relationship between Calibrated age and depth

Estimates the relationship of Calibrated age and depth for palaeorecords. The function uses a smooth spline from the mgcv library by Simon Wood. It produces predicted confidence interval for the relationship approximating a mixed effect model, as there are two levels of uncertainty, i.e. within dated object and between dated objects.

Usage

agelme(
  depup,
  depdo,
  bpup,
  bpdo,
  use,
  weights = c(1, rep(0, length(depup) - 1)),
  vspan = 1,
  k = length(depup) - 1,
  m = 2,
  diagnostic = FALSE
)

Arguments

depup

The upper depths of the dated slides

depdo

The lower depths of the dated slides

bpup

The younger calibrated ages of the dated slides

bpdo

The older calibrated ages of the dated slides

use

Logical vector of dates to include in the model. Default is to use all.

weights

Weights to be used for the estimation, default is fixed top-layer followed by inverse variance of within dated object

vspan

The span to be used for the diagnostic plots, default span = 1

k

Number of base function to start the shrinkage in the gam estimation procedure

m

The order of penalty for the term, i.e. the degree of continuity at the knots (default, m = 2 gives cubic smooth spline)

diagnostic

Logical, should diagnostic plots be made.

Value

A list of class 'agelme' with the following items:

tdf

Degrees of freedom used by the cubic smooth spline, a vector with first value for constant variance and second vector for variance equal to mu.

weights

A vector of the weights used by the cubic smooth spline

Constant

A matrix with the numerical results for the dated points using a constant variance

Muvar

A matrix with the numerical results for the dated points using variance equal to mu

RES

A vector of the Residual sum of squares

Models

A list with the models from the cubic smooth spline, constant and mu variance, respectively

Data

A data.frame including the data used for the estimation

Details

Note that the fixation of the top layer is done by a weight = 1, whereas the other weights follows inverse variance within object.

The diagnostic plots is used to check the quality of the estimation and to see if there is a need for an assumption of between object variance proportional to mean. The latter however is rarely encountered for palaeodata.

References

Heegaard, E., Birks, HJB. & Telford, RJ. 2005. Relationships between calibrated ages and depth in stratigraphical sequences: an estimation procedure by mixed-effect regression. The Holocene 15: 612-618 doi:10.1191/0959683605hl836rr

Author

Einar Heegaard

Examples

data(STOR)

fit.mod <- with(STOR, agelme(depthup, depthdo, cageup, cagedo))

# Predicting using the constant variance model,
# for each cm between 70 and 400 cm.
fit.pre <- predict(fit.mod, 1, 70:400)
plot(fit.pre)