prcompNull: Calculate significance of EOFs compared to a null model...

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

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

Description

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

Usage

prcompNull(
  x,
  retx = TRUE,
  center = TRUE,
  scale. = FALSE,
  tol = NULL,
  nperm = 99
)

Arguments

x, retx, center, scale., tol	See prcomp for argument definitions.
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 <- prcompNull(Xp, center=FALSE, scale=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 June 15, 2025, 1:17 a.m.