Screeplots for Ordination Results and Broken Stick Distributions
Description
Screeplot methods for plotting variances of ordination axes/components
and overlaying broken stick distributions. Also, provides alternative
screeplot methods for princomp
and prcomp
.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48  ## S3 method for class 'cca'
screeplot(x, bstick = FALSE, type = c("barplot", "lines"),
npcs = min(10, if (is.null(x$CCA)  x$CCA$rank == 0) x$CA$rank else x$CCA$rank),
ptype = "o", bst.col = "red", bst.lty = "solid",
xlab = "Component", ylab = "Inertia",
main = deparse(substitute(x)), legend = bstick,
...)
## S3 method for class 'decorana'
screeplot(x, bstick = FALSE, type = c("barplot", "lines"),
npcs = 4,
ptype = "o", bst.col = "red", bst.lty = "solid",
xlab = "Component", ylab = "Inertia",
main = deparse(substitute(x)),
...)
## S3 method for class 'prcomp'
screeplot(x, bstick = FALSE, type = c("barplot", "lines"),
npcs = min(10, length(x$sdev)),
ptype = "o", bst.col = "red", bst.lty = "solid",
xlab = "Component", ylab = "Inertia",
main = deparse(substitute(x)), legend = bstick,
...)
## S3 method for class 'princomp'
screeplot(x, bstick = FALSE, type = c("barplot", "lines"),
npcs = min(10, length(x$sdev)),
ptype = "o", bst.col = "red", bst.lty = "solid",
xlab = "Component", ylab = "Inertia",
main = deparse(substitute(x)), legend = bstick,
...)
bstick(n, ...)
## Default S3 method:
bstick(n, tot.var = 1, ...)
## S3 method for class 'cca'
bstick(n, ...)
## S3 method for class 'prcomp'
bstick(n, ...)
## S3 method for class 'princomp'
bstick(n, ...)
## S3 method for class 'decorana'
bstick(n, ...)

Arguments
x 
an object from which the component variances can be determined. 
bstick 
logical; should the broken stick distribution be drawn? 
npcs 
the number of components to be plotted. 
type 
the type of plot. 
ptype 
if 
bst.col, bst.lty 
the colour and line type used to draw the broken stick distribution. 
xlab, ylab, main 
graphics parameters. 
legend 
logical; draw a legend? 
n 
an object from which the variances can be extracted or the
number of variances (components) in the case of

tot.var 
the total variance to be split. 
... 
arguments passed to other methods. 
Details
The functions provide screeplots for most ordination methods in
vegan and enhanced versions with broken stick for
prcomp
and princomp
.
Function bstick
gives the brokenstick values which are ordered
random proportions, defined as p[i] = tot/n sum(from x=i to n) 1/x (Legendre & Legendre 2012), where
tot is the total and n is the number of brokenstick
components (cf. radfit
). Broken stick has
been recommended as a stopping rule in principal component analysis
(Jackson 1993): principal components should be retained as long as
observed eigenvalues are higher than corresponding random broken stick
components.
The bstick
function is generic. The default needs the number of
components and the total, and specific methods extract this
information from ordination results. There also is a bstick
method for cca
. However, the broken stick model is not
strictly valid for correspondence analysis (CA), because eigenvalues
of CA are defined to be <=1, whereas brokenstick
components have no such restrictions. The brokenstick components are not
available for decorana
where the sum of eigenvalues
(total inertia) is unknown, and the eigenvalues of single axes are not
additive in detrended analysis.
Value
Function screeplot
draws a plot on the currently active device,
and returns invisibly the xy.coords
of the points or
bars for the eigenvalues.
Function bstick
returns a numeric vector of broken stick
components.
Author(s)
Gavin L. Simpson
References
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. (2012) Numerical Ecology. 3rd English ed. Elsevier.
See Also
cca
, decorana
, princomp
and
prcomp
for the ordination functions, and
screeplot
for the stock version.
Examples
1 2 3 4 
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