The Broken Stick model is one proposed method for estimating the number of statistically significant principal components.
brokenStick(k, n)
bsDimension(lambda, FUZZ = 0.005)The brokenStick function returns, as a real number, the
expected value of the k-th longest piece when breaking a
stick of length one into n total pieces. Most commonly used
via the idiom brokenStick(1:N, N) to get the entire vector of
lengths at one time.
The bsDimension function returns an integer, the number of
significant components under this model. This is computed by finding
the last point at which the observed variance is bugger than the
expected value under the broken stick model by at least FUZZ.
An integer between 1 and n.
An integer; the total number of principal components.
The set of variances from each component from a principal
components analysis. These are assumed to be already sorted in
decreasing order. You can also supply a SamplePCA
object, and the variances will be automatically extracted.
A real number; anything smaller than FUZZ is
assumed to equal zero for all practical purposes.
Kevin R. Coombes <krc@silicovore.com>
The Broken Stick model is one proposed method for estimating the number of statistically significant principal components. The idea is to model \(N\) variances by taking a stick of unit length and breaking it into \(N\) pieces by randomly (and simultaneously) selecting break points from a uniform distribution.
Jackson, D. A. (1993). Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches. Ecology 74, 2204--2214.
Legendre, P. and Legendre, L. (1998) Numerical Ecology. 2nd English ed. Elsevier.
Better methods to address this question are based on the Auer-Gervini
method; see AuerGervini.
brokenStick(1:10, 10)
sum( brokenStick(1:10, 10) )
fakeVar <- c(30, 20, 8, 4, 3, 2, 1)
bsDimension(fakeVar)
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