analogue (version 0.10-0)

RMSEP: Root mean square error of prediction

Description

Calculates or extracts the RMSEP from transfer function models.

Usage

RMSEP(object, ...)
## S3 method for class 'mat':
RMSEP(object, k, weighted = FALSE,
          \dots)
## S3 method for class 'bootstrap.mat':
RMSEP(object, type = c("birks1990", "standard"),
          ...)
## S3 method for class 'bootstrap.wa':
RMSEP(object, type = c("birks1990", "standard"),
          ...)

Arguments

object

An R object.

k

numeric; the number of analogues to use in calculating the RMSEP. May be missing. If missing, k is extracted from the model using getK.

weighted

logical; Return the RMSEP for the weighted or unweighted model? The default is for an unweighted model.

type

The type of RMSEP to return/calculate. See Details, below.

...

Arguments passed to other methods.

Value

• A numeric vector of length 1 that is the RMSEP of object.

Details

There are two forms of RMSEP in common usage. Within palaeoecology, the RMSEP of Birks et al. (1990) is most familiar: $$\mathrm{RMSEP} = \sqrt{s_1^2 + s_2^2}$$ where where $s_1$ is the standard deviation of the out-of-bag (OOB) residuals and $s_2$ is the mean bias or the mean of the OOB residuals.

In the wider statistical literature, the following form of RMSEP is more commonly used: $$\mathrm{RMSEP} = \sqrt{\frac{\sum_{i=1}^n (y_i - \hat{y}_i)^2}{n}}$$ where $y_i$ are the observed values and $\hat{y}_i$ the transfer function predictions/fitted values.

The first form of RMSEP is returned by default or if type = "birks1990" is supplied. The latter form is returned if type = "standard" is supplied.

The RMSEP for objects of class "mat" is a leave-one-out cross-validated RMSEP, and is calculated as for type = "standard".

References

Birks, H.J.B., Line, J.M., Juggins, S., Stevenson, A.C. and ter Braak, C.J.F. (1990). Diatoms and pH reconstruction. Philosophical Transactions of the Royal Society of London; Series B, 327; 263--278.

See Also

mat, bootstrap, wa, bootstrap.wa.

Examples

## Imbrie and Kipp example
## load the example data
data(ImbrieKipp)
data(SumSST)
data(V12.122)

## merge training and test set on columns
dat <- join(ImbrieKipp, V12.122, verbose = TRUE)

## extract the merged data sets and convert to proportions
ImbrieKipp <- dat[[1]] / 100
V12.122 <- dat[[2]] / 100

## fit the MAT model using the squared chord distance measure
(ik.mat <- mat(ImbrieKipp, SumSST, method = "chord"))

## Leave-one-out RMSEP for the MAT model
RMSEP(ik.mat)

## bootstrap training set
(ik.boot <- bootstrap(ik.mat, n.boot = 100))

## extract the Birks et al (1990) RMSEP
RMSEP(ik.boot)

## Calculate the alternative formulation
RMSEP(ik.boot, type = "standard")