mat {analogue} | R Documentation |
Modern Analogue Technique (MAT) transfer function models for palaeoecology. The fitted values are the, possibly weighted, averages of the environment for the k-closest modern analogues. MAT is a k-NN method.
mat(x, ...) ## Default S3 method: mat(x, y, method = c("euclidean", "SQeuclidean", "chord", "SQchord", "bray", "chi.square", "SQchi.square", "information", "chi.distance", "manhattan", "kendall", "gower", "alt.gower", "mixed"), ...)
x |
a data frame containing the training set data, usually species data. |
y |
a vector containing the response variable, usually
environmental data to be predicted from x . |
method |
a character string indicating the dissimilarity (distance) coefficient to be used to define modern analogues. See Details, below. |
... |
arguments to or from other methods. |
The Modern Analogue Technique (MAT) is perhaps the simplest of the transfer function models used in palaeoecology. An estimate of the environment, x, for the response for a fossil sample, y, is the, possibly weighted, mean of that variable across the k-closest modern analogues selected from a modern training set of samples. If used, weights are the reciprocal of the dissimilarity between the fossil sample and each modern analogue.
Pairwise sample dissimilarity is defined by dissimilarity or
distance coefficients. A variety of coefficients are supported — see
distance
for details of the supported coefficients.
k is chosen by the user. The simplest choice for k is to evaluate the RMSE of the difference between the predicted and observed values of the environmental variable of interest for the training set samples for a sequence of models with increasing k. The number of analogues chosen is the value of k that has lowest RMSE. However, it should be noted that this value is biased as the data used to build the model are also used to test the predictive power.
An alternative approach is to employ an optimisation data set on which to evaluate the size of k that provides the lowest RMSEP. This may be impractical with smaller sample sizes.
A third option is to bootstrap re-sample the training set many times. At
each bootstrap sample, predictions for samples in the bootstrap test
set can be made for k = 1, ..., n, where n is the
number of samples in the training set. k can be chosen from the
model with the lowest RMSEP. See function bootstrap
for
further details on choosing k.
The output from summary.mat
can be used to choose
k in the first case above. For predictions on an optimsation or
test set see predict.mat
. For bootstrap resampling of
mat
models, see bootstrap.
Returns an object of class mat
with the following components:
standard |
list; the model statistics based on simple averages of k-closest analogues. See below. |
weighted |
list; the model statistics based on weighted of k-closest analogues. See below. |
Dij |
matrix of pairwise sample dissimilarities for the training
set x . |
orig.x |
the original training set data. |
orig.y |
the original environmental data or response, y . |
call |
the matched function call. |
method |
the dissimilarity coefficient used. |
Lists "standard"
and "weighted"
both contain the
following elements:
est
resid
"est"
, but containing the
model residuals.rmse
avg.bias
max.bias
"avg.bias"
, but
containing the maximum bias statistics.r.squared
"avg.bias"
, but
containing the R^2 statistics.Gavin L. Simpson
Gavin, D.G., Oswald, W.W., Wahl, E.R. and Williams, J.W. (2003) A statistical approach to evaluating distance metrics and analog assignments for pollen records. Quaternary Research 60, 356–367.
Overpeck, J.T., Webb III, T. and Prentice I.C. (1985) Quantitative interpretation of fossil pollen spectra: dissimilarity coefficients and the method of modern analogues. Quaternary Research 23, 87–108.
Prell, W.L. (1985) The stability of low-latitude sea-surface temperatures: an evaluation of the CLIMAP reconstruction with emphasis on the positive SST anomalies, Report TR 025. U.S. Department of Energy, Washington, D.C.
Sawada, M., Viau, A.E., Vettoretti, G., Peltier, W.R. and Gajewski, K. (2004) Comparison of North-American pollen-based temperature and global lake-status with CCCma AGCM2 output at 6 ka. Quaternary Science Reviews 23, 87–108.
summary.mat
, bootstrap
for boostrap
resampling of MAT models, predict.mat
for making
predictions from MAT models, fitted.mat
and
resid.mat
for extraction of fitted values and residuals
from MAT models respectively. plot.mat
provides a
plot.lm
-like plotting tool for MAT models.
## continue the RLGH example from ?join example(join) ## fit the MAT model using the squared chord distance measure swap.mat <- mat(swapdiat, swappH, method = "SQchord") swap.mat ## model summary summary(swap.mat) ## fitted values fitted(swap.mat) ## model residuals resid(swap.mat) ## draw summary plots of the model par(mfrow = c(2,2)) plot(swap.mat) par(mfrow = c(1,1)) ## reconstruct for the RLGH core data rlgh.mat <- predict(swap.mat, rlgh, k = 10) rlgh.mat summary(rlgh.mat) rlgh.Wmat <- predict(swap.mat, rlgh, k = 10, weighted = TRUE) rlgh.Wmat summary(rlgh.Wmat) ## plot of pH change in the RLGH depths <- as.numeric(colnames(rlgh.mat$predictions$apparent$predicted)) n.analogues <- rlgh.mat$predictions$apparent$k plot(rlgh.mat$predictions$apparent$predicted[n.analogues, ], depths, ylim = rev(range(depths)), xlab = "pH", ylab = "Depth (cm)", main = "Estimated pH", type = "l")