EMMAgeo (version 0.9.0)

test.L: Function to evaluate the initial cumulative explained variance.

Description

This function performs eigenspace decomposition using the weight-transformed matrix W and returns the cumulative explained variance of the resulting eigenvalues prior to factor rotation. Depending on the number of provided weight transformation limits (lw) a single vector or a matrix is returned.

Usage

test.L(X, lw, c, r.min = 0.95, plot = FALSE, legend, ..., pm = FALSE)

Arguments

X

Numeric matrix with m samples (rows) and n variables (columns).

lw

Numeric vector specifying the weight tranformation limits, i.e. quantiles; default is 0.

c

Numeric scalar specifying the constant sum scaling parameter, e.g. 1, 100, 1000; default is 100.

r.min

Numeric scalar, minimum value of explained variance to be reached by the end-members included, default is 0.95.

plot

Logical scalar, optional graphical output of the results, default is FALSE.,

legend

Character scalar, specify legend position (cf. legend). If omitted, no legend will be plotted, default is no legend.

...

Additional arguments passed to the plot function. Use colour instead of col to create different colours.

pm

Logical scalar to enable pm.

Value

• A list with objects
• L
  Vector or matrix of cumulative explained variance.
• q.min
  Vector with number of factors that passed r.min.

Details

The results may be used to define a minimum number of end-members for subsequent modelling steps, e.g. by using the Kaiser criterion, which demands a minimum number of eigenvalues to reach a squared R of 0.95.

References

Dietze E, Hartmann K, Diekmann B, IJmker J, Lehmkuhl F, Opitz S, Stauch G, Wuennemann B, Borchers A. 2012. An end-member algorithm for deciphering modern detrital processes from lake sediments of Lake Donggi Cona, NE Tibetan Plateau, China. Sedimentary Geology 243-244: 169-180.

Examples

## load example data set
data(X.artificial, envir = environment())

## create sequence of weight transformation limits
lw <- seq(0, 0.2, 0.02)

## perform the test and show q.min
L <- test.L(X = X.artificial, lw = lw, c = 100, plot = TRUE)
L$q.min

## a visualisation with more plot parameters
L <- test.L(X = X.artificial, lw = lw, c = 100, plot = TRUE, 
            ylim = c(0.5, 1), xlim = c(1, 7), 
            legend = "bottomright", cex = 0.7)

## another visualisation, a close-up
plot(1:7, L$L[1,1:7], type = "l", 
     xlab = "q", ylab = "Explained variance")
for(i in 2:7) {lines(1:7, L$L[i,1:7], col = i)}