eofNull: Calculate significance of EOFs compared to a null model (eof...

In marchtaylor/sinkr: Collection of functions with emphasis in multivariate data analysis

Calculate significance of EOFs compared to a null model (eof version)

Description

The eofNull function uses a randomization approach to calculate a null model for use in Empirical Orthogonal Function analysis (EOF) with the eof function. EOF mode significance is assessed against the distribution of EOF singular values ("Lambda") calculated by the null models

Usage

eofNull(
  F1,
  centered = TRUE,
  scaled = FALSE,
  nu = NULL,
  method = NULL,
  recursive = FALSE,
  nperm = 99
)

Arguments

F1	A data field. The data should be arraunged as samples in the column dimension (typically each column is a time series for a spatial location).
centered	Logical (TRUE/FALSE) to define if F1 should be centered prior to the analysis. Defaults to 'TRUE'
scaled	Logical (TRUE/FALSE) to define if F1 should be scaled prior to the analysis. Defaults to 'TRUE'
nu	Numeric value. Defines the number of EOFs to return. Defaults to return the full set of EOFs.
method	Method for matrix decomposition ('svd', 'eigen', 'irlba'). Defaults to 'svd' when method = NULL. Use of 'irlba' can dramatically speed up computation time when recursive = TRUE but may produce errors in computing trailing EOFs. Therefore, this option is only advisable when the field F1 is large and when only a partial decomposition is desired (i.e. nu << dim(F1)[2]). All methods should give identical results when recursive=TRUE. svd and eigen give similar results for non-gappy fields, but will differ slightly with gappy fields due to decomposition of a nonpositive definite covariance matrix. Specifically, eigen will produce negative eigenvalues for trailing EOFs, while singular values derived from svd will be strictly positive.
recursive	Logical. When TRUE, the function follows the method of "Recursively Subtracted Empirical Orthogonal Functions" (RSEOF). See eof for details
nperm	Numeric. The number of null model permutations to calculate.

Examples

# Generate data
m=50
n=100
frac.gaps <- 0.5 # the fraction of data with NaNs
N.S.ratio <- 0.1 # the Noise to Signal ratio for adding noise to data
x <- (seq(m)*2*pi)/m
t <- (seq(n)*2*pi)/n

# True field
Xt <- 
  outer(sin(x), sin(t)) + 
  outer(sin(2.1*x), sin(2.1*t)) + 
  outer(sin(3.1*x), sin(3.1*t)) +
  outer(tanh(x), cos(t)) + 
  outer(tanh(2*x), cos(2.1*t)) + 
  outer(tanh(4*x), cos(0.1*t)) + 
  outer(tanh(2.4*x), cos(1.1*t)) + 
  tanh(outer(x, t, FUN="+")) + 
  tanh(outer(x, 2*t, FUN="+"))

Xt <- t(Xt)

# Noise field
set.seed(1)
RAND <- matrix(runif(length(Xt), min=-1, max=1), nrow=nrow(Xt), ncol=ncol(Xt))
R <- RAND * N.S.ratio * Xt

# True field + Noise field
Xp <- Xt + R

res <- eofNull(Xp, method="svd", centered=FALSE, scaled=FALSE, nperm=499)
ylim <- range(res$Lambda.orig, res$Lambda)
boxplot(res$Lambda, log="y", col=8, border=2, outpch="", ylim=ylim)
points(res$Lambda.orig)
abline(v=res$n.sig+0.5, lty=2, col=4)
mtext(paste("Significant PCs =", res$n.sig), side=3, line=0.5, col=4)

marchtaylor/sinkr documentation built on July 4, 2022, 5:48 p.m.