mat(x, ...)## S3 method for class 'default':
mat(x, y,
method = c("euclidean", "SQeuclidean", "chord", "SQchord",
"bray", "chi.square", "SQchi.square",
"information", "chi.distance", "manhattan",
"kendall", "gower", "alt.gower", "mixed"),
kmax, ...)
## S3 method for class 'formula':
mat(formula, data, subset, na.action,
method = c("euclidean", "SQeuclidean", "chord", "SQchord",
"bray", "chi.square", "SQchi.square",
"information", "chi.distance", "manhattan",
"kendall", "gower", "alt.gower", "mixed"),
model = FALSE, ...)
## S3 method for class 'mat':
fitted(object, k, weighted = FALSE, \dots)
## S3 method for class 'mat':
residuals(object, k, weighted = FALSE, \dots)
x.as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables NAs. The default is set by the
na.action setting of options, and is
TRUE the model frame of the fit is
returned.kmax is equal to $n - 1$,
where $n$ is the number of sites. For large data sets this is
just wasteful as we wouldn't expect to be averaging overmat.distance to
provide additional optios required for some dissimilarities.mat returns an object of class mat with the following
components:x.y.model = TRUE then additional components "terms" and
"model" are returned containing the terms object
and model frame used.
fitted.mat returns a list with the following components:
FALSE, the fitted values are the average of the environment
for the k-closest analogues. A typical model has the form response ~ terms where
response is the (numeric) response data frame and terms
is a series of terms which specifies a linear predictor for
response. A typical form for terms is .,
which is shorthand for "all variables" in data. If . is
used, data must also be provided. If specific species
(variables) are required then terms should take the form
spp1 + spp2 + spp3.
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.mat 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.mat.
The fitted values are for the training set and are taken as the,
possibly weighted, mean of the environmental variable in question
across the k-closest analogues. The fitted value for each
sample does not include a contribution from itself --- it is
the closest analogue, having zero dissimilarity. This spurious
distance is ignored and analogues are ordered in terms of the non-zero
distances to other samples in the training set, with the
k-closest contributing to the fitted value.
Typical usages for residuals.mat are:
resid(object, k, weighted = FALSE, \dots)
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.mat 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.## Imbrie and Kipp Sea Surface Temperature
data(ImbrieKipp)
data(SumSST)
data(V12.122)
## merge training set and core samples
dat <- join(ImbrieKipp, V12.122, verbose = TRUE)
## extract the merged data sets and convert to proportions
ImbrieKipp <- dat[[1]] / 100
ImbrieKippCore <- dat[[2]] / 100
## fit the MAT model using the squared chord distance measure
ik.mat <- mat(ImbrieKipp, SumSST, method = "chord")
ik.mat
## model summary
summary(ik.mat)
## fitted values
fitted(ik.mat)
## model residuals
resid(ik.mat)
## draw summary plots of the model
par(mfrow = c(2,2))
plot(ik.mat)
par(mfrow = c(1,1))
## reconstruct for the V12.122 core data
coreV12.mat <- predict(ik.mat, V12.122, k = 3)
coreV12.mat
summary(coreV12.mat)
## draw the reconstruction
reconPlot(coreV12.mat, use.labels = TRUE, display.error = "bars",
xlab = "Depth", ylab = "SumSST")
## fit the MAT model using the squared chord distance measure
## and restrict the number of analogues we fit models for to 1:20
ik.mat2 <- mat(ImbrieKipp, SumSST, method = "chord", kmax = 20)
ik.mat2Run the code above in your browser using DataLab