Mqs.uncertainty: Function to estimate end-member scores uncertainty

Description

The function uses either existing assemblages of end-member loadings or specified measures of centrality and dispersion as input for Monte Carlo runs to estimate the influence of different end-member loadings on end-member scores. Likewise, the influence of the weight limit quantiles (lw) can be estimated.

Usage

Mqs.uncertainty(X, q, lw, c, rotation = "Varimax", Vqn, Vqn.sd, 
    runs, type.lw, autocorrelation)

Arguments

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

Numeric scalar with the number of end-members to include. Only necessary in combination with Vqn as matrix of user-defined end-member loadings.

Numeric vector with the weight tranformation limits (i.e. quantiles after Klovan & Imbrie, 1971). If the parameter is of length 1, lw is assumed to be a constant, if of length 2, lw defines either mean and standard deviation o

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

rotation

Character scalar, rotation type, default is "Varimax" (cf. Dietze et al., 2012). One out of the rotations provided in GPArotation is possible (cf. rotations).

Vqn

Numeric matrix with existing unscaled end-member loadings. These may represent user-defined loadings (or mean loadings if Vqn.sd is specified). See example section for further information.

Vqn.sd

Numeric matrix with standard deviations of the mean unscaled end-member loadings in Vqn.

runs

Logical scalar with the number of Monte Carlo runs to be performed, default is 100.

type.lw

Character scalar with type of random lw value generation. Either "rnorm" or "runif", default is "runif".

autocorrelation

Numeric scalar optionally specifying the degree of autocorrelation among classes. Autocorrelation is realised as running mean of the specified length. Only odd values are allowed.

Value

A list with numeric vector and matrix objects.
lwRandomised weight limit values.
VqnRandomised unscaled end-member loadings.
MqsModelled end-member scores.
meanModelled end-member score means.
sdModelled end-member score standard deviations.

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. Klovan JE, Imbrie J. 1971. An Algorithm and FORTRAN-IV Program for Large-Scale Q-Mode Factor Analysis and Calculation of Factor Scores. Mathematical Geology 3: 61-77.

Examples

Run this code

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

## set model run parameters
q = 3 # set number of end-members, try 4 to see the difference!
Vqn <- EMMA(X.artificial, q)$Vqn # assign unscaled end-member loadings
Vqn.sd <- Vqn * 0.2 # assign a relative standard deviation of 20 \%
lw.1 <- 0.2 # set lw to 0.2
lw.2 <- c(0.2, 0.08) # set lw to mean = 0.2 and sd = 0.08
runs <-  12 # senseless value to increase comuptation speed

## EXAMPLE 1
## Calculate Mqs uncertainty
M <- Mqs.uncertainty(X = X.artificial, 
                     q = q, 
                     lw = lw.1,
                     runs = runs,
                     Vqn = Vqn,
                     Vqn.sd = Vqn.sd,
                     type.lw = "rnorm",
                     autocorrelation = 3)

## Plot line-point graph with means and standard deviations
plot(NA,
     xlim = c(1, nrow(X.artificial)),
     ylim = c(0.5, q + 1),
     main = "End-member scores with uncertainty")
for(i in 1:q) {
  lines(1:nrow(X.artificial), M$mean[,i] - M$sd[,i] + i, col = i, lty = 2)
  lines(1:nrow(X.artificial), M$mean[,i] + i, col = i, lwd = 2)
  points(1:nrow(X.artificial), M$mean[,i] + i, col = i)
  lines(1:nrow(X.artificial), M$mean[,i] + M$sd[,i] + i, col = i, lty = 2)
}

## EXAMPLE 2
## Calculate Mqs uncertainty
M <- Mqs.uncertainty(X = X.artificial, 
                     q = q, 
                     lw = lw.2,
                     runs = runs,
                     Vqn = Vqn,
                     type.lw = "rnorm")

## Plot point graph with error bars
plot(NA,
     xlim = c(1, nrow(X.artificial)),
     ylim = c(0.5, q + 1),
     main = "End-member scores with uncertainty")
for(i in 1:q) {
  points(1:nrow(X.artificial), M$mean[,i] + i, pch = 3, col = i)
  arrows(1:nrow(X.artificial), M$mean[,i] - M$sd[,i] + i, 
         1:nrow(X.artificial), M$mean[,i] + M$sd[,i] + i, 
         code = 3, angle = 90, length = 0.05, col = i)
}