decostand  R Documentation 
The function provides some popular (and effective) standardization methods for community ecologists.
decostand(x, method, MARGIN, range.global, logbase = 2, na.rm=FALSE, ...)
wisconsin(x)
decobackstand(x, zap = TRUE)
x 
Community data, a matrixlike object. For

method 
Standardization method. See Details for available options. 
MARGIN 
Margin, if default is not acceptable. 
range.global 
Matrix from which the range is found in

logbase 
The logarithm base used in 
na.rm 
Ignore missing values in row or column
standardizations. The 
zap 
Make nearzero values exact zeros to avoid negative values and exaggerated estimates of species richness. 
... 
Other arguments to the function (ignored). 
The function offers following standardization methods for community data:
total
: divide by margin total (default MARGIN = 1
).
max
: divide by margin maximum (default MARGIN = 2
).
frequency
: divide by margin total and multiply by the
number of nonzero items, so that the average of nonzero entries is
one (Oksanen 1983; default MARGIN = 2
).
normalize
: make margin sum of squares equal to one (default
MARGIN = 1
).
range
: standardize values into range 0 ... 1 (default
MARGIN = 2
). If all values are constant, they will be
transformed to 0.
rank, rrank
: rank
replaces abundance values by
their increasing ranks leaving zeros unchanged, and rrank
is
similar but uses relative ranks with maximum 1 (default
MARGIN = 1
). Average ranks are used for tied values.
standardize
: scale x
to zero mean and unit variance
(default MARGIN = 2
).
pa
: scale x
to presence/absence scale (0/1).
chi.square
: divide by row sums and square root of
column sums, and adjust for square root of matrix total
(Legendre & Gallagher 2001). When used with the Euclidean
distance, the distances should be similar to the
Chisquare distance used in correspondence analysis. However, the
results from cmdscale
would still differ, since
CA is a weighted ordination method (default MARGIN = 1
).
hellinger
: square root of method = "total"
(Legendre & Gallagher 2001).
log
: logarithmic transformation as suggested by
Anderson et al. (2006): \log_b (x) + 1
for
x > 0
, where b
is the base of the logarithm; zeros are
left as zeros. Higher bases give less weight to quantities and more
to presences, and logbase = Inf
gives the presence/absence
scaling. Please note this is not \log(x+1)
.
Anderson et al. (2006) suggested this for their (strongly) modified
Gower distance (implemented as method = "altGower"
in
vegdist
), but the standardization can be used
independently of distance indices.
alr
: Additive log ratio ("alr") transformation
(Aitchison 1986) reduces data skewness and compositionality
bias. The transformation assumes positive values, pseudocounts can
be added with the argument pseudocount
. One of the
rows/columns is a reference that can be given by reference
(name of index). The first row/column is used by default
(reference = 1
). Note that this transformation drops one
row or column from the transformed output data. The alr
transformation is defined formally as follows:
alr = [log\frac{x_1}{x_D}, ..., log\frac{x_{D1}}{x_D}]
where the denominator sample x_D
can be chosen
arbitrarily. This transformation is often used with pH and other
chemistry measurenments. It is also commonly used as multinomial
logistic regression. Default MARGIN = 1
uses row as the
reference
.
clr
: centered log ratio ("clr") transformation proposed by
Aitchison (1986) and it is used to reduce data skewness and compositionality bias.
This transformation has frequent applications in microbial ecology
(see e.g. Gloor et al., 2017). The clr transformation is defined as:
clr = log\frac{x}{g(x)} = log x  log g(x)
where x
is a single value, and g(x) is the geometric mean of
x
.
The method can operate only with positive data;
a common way to deal with zeroes is to add pseudocount
(e.g. the smallest positive value in the data), either by
adding it manually to the input data, or by using the argument
pseudocount
as in
decostand(x, method = "clr", pseudocount = 1)
. Adding
pseudocount will inevitably introduce some bias; see
the rclr
method for one available solution.
rclr
: robust clr ("rclr") is similar to regular clr
(see above) but allows data that contains zeroes. This method
does not use pseudocounts, unlike the standard clr.
The robust clr (rclr) divides the values by geometric mean
of the observed features; zero values are kept as zeroes, and not
taken into account. In high dimensional data,
the geometric mean of rclr approximates the true
geometric mean; see e.g. Martino et al. (2019)
The rclr
transformation is defined formally as follows:
rclr = log\frac{x}{g(x > 0)}
where x
is a single value, and g(x > 0)
is the geometric
mean of samplewide values x
that are positive (> 0).
Standardization, as contrasted to transformation, means that the entries are transformed relative to other entries.
All methods have a default margin. MARGIN=1
means rows (sites
in a normal data set) and MARGIN=2
means columns (species in a
normal data set).
Command wisconsin
is a shortcut to common Wisconsin double
standardization where species (MARGIN=2
) are first standardized
by maxima (max
) and then sites (MARGIN=1
) by
site totals (tot
).
Most standardization methods will give nonsense results with
negative data entries that normally should not occur in the community
data. If there are empty sites or species (or constant with
method = "range"
), many standardization will change these into
NaN
.
Function decobackstand
can be used to transform standardized
data back to original. This is not possible for all standardization
and may not be implemented to all cases where it would be
possible. There are roundoff errors and backtransformation is not
exact, and it is wise not to overwrite the original data. With
zap=TRUE
original zeros should be exact.
Returns the standardized data frame, and adds an attribute
"decostand"
giving the name of applied standardization
"method"
and attribute "parameters"
with appropriate
transformation parameters.
Common transformations can be made with standard R functions.
Jari Oksanen, Etienne Laliberté
(method = "log"
), Leo Lahti (alr
,
"clr"
and "rclr"
).
Aitchison, J. The Statistical Analysis of Compositional Data (1986). London, UK: Chapman & Hall.
Anderson, M.J., Ellingsen, K.E. & McArdle, B.H. (2006) Multivariate dispersion as a measure of beta diversity. Ecology Letters 9, 683–693.
Egozcue, J.J., PawlowskyGlahn, V., MateuFigueras, G., Barcel'oVidal, C. (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology 35, 279–300.
Gloor, G.B., Macklaim, J.M., PawlowskyGlahn, V. & Egozcue, J.J. (2017) Microbiome Datasets Are Compositional: And This Is Not Optional. Frontiers in Microbiology 8, 2224.
Legendre, P. & Gallagher, E.D. (2001) Ecologically meaningful transformations for ordination of species data. Oecologia 129, 271–280.
Martino, C., Morton, J.T., Marotz, C.A., Thompson, L.R., Tripathi, A., Knight, R. & Zengler, K. (2019) A novel sparse compositional technique reveals microbial perturbations. mSystems 4, 1.
Oksanen, J. (1983) Ordination of boreal heathlike vegetation with principal component analysis, correspondence analysis and multidimensional scaling. Vegetatio 52, 181–189.
data(varespec)
sptrans < decostand(varespec, "max")
apply(sptrans, 2, max)
sptrans < wisconsin(varespec)
# CLR transformation for rows, with pseudocount
varespec.clr < decostand(varespec, "clr", pseudocount=1)
# ALR transformation for rows, with pseudocount and reference sample
varespec.alr < decostand(varespec, "alr", pseudocount=1, reference=1)
## Chisquare: PCA similar but not identical to CA.
## Use wcmdscale for weighted analysis and identical results.
sptrans < decostand(varespec, "chi.square")
plot(procrustes(rda(sptrans), cca(varespec)))
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