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)Returns the standardized data frame, and adds an attribute
"decostand" giving the name of applied standardization
"method" and attribute "parameters" with appropriate
transformation parameters.
Community data, a matrix-like object. For
decobackstand standardized data.
Standardization method. See Details for available options.
Margin, if default is not acceptable. 1 = rows,
and 2 = columns of x.
Matrix from which the range is found in
method = "range". This allows using same ranges across
subsets of data. The dimensions of MARGIN must match with
x.
The logarithm base used in method = "log".
Ignore missing values in row or column
standardizations. The NA values remain as NA, but they
are ignored in standardization of other values.
Make near-zero values exact zeros to avoid negative values and exaggerated estimates of species richness.
Other arguments to the function (ignored).
Jari Oksanen, Etienne Laliberté
(method = "log"), Leo Lahti (alr,
"clr" and "rclr").
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 non-zero items, so that the average of non-zero 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
Chi-square 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:
$$alr = [log\frac{x_1}{x_D}, ..., log\frac{x_{D-1}}{x_D}]$$
where the denominator sample \(x_D\) can be chosen
arbitrarily. This transformation is often used with pH and other
chemistry measurements. 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", na.rm = TRUE, pseudocount = 1). Adding
pseudocount will inevitably introduce some bias; see
the rclr method for an alternative.
rclr: robust clr ("rclr") is similar to regular clr
(see above) but it allows data with zeroes. This method can avoid
the use of pseudocounts, unlike the standard clr. The robust clr
(rclr) the logarithmizes the data and divides it by the geometric
mean of the observed features within each sample. 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
sample-wide values \(x\) that are positive (> 0). The optspace
algorithm performs matrix completion for the missing values
that result from log transformation of the zero entries in the
original input data. See optspace for more details.
The following parameters can be passed to optspace
through decostand: "ropt" NA to guess the rank, or a positive
integer as a pre-defined rank (default: 3); "niter" maximum
number of iterations allowed (default: 5); "tol" stopping
criterion for reconstruction in Frobenius norm (default: 1e-5);
"verbose" a logical value; TRUE to show progress, FALSE otherwise
(default: FALSE); "impute" to switch on/off the matrix completion
(default: impute=TRUE).
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 round-off errors and back-transformation is not
exact, and it is wise not to overwrite the original data. With
zap=TRUE original zeros should be exact.
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., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barcel'o-Vidal, C. (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology 35, 279--300.
Gloor, G.B., Macklaim, J.M., Pawlowsky-Glahn, V. & Egozcue, J.J. (2017) Microbiome Datasets Are Compositional: And This Is Not Optional. Frontiers in Microbiology 8, 2224.
Keshavan, R. H., Montanari, A., Oh, S. (2010). Matrix Completion From a Few Entries. IEEE Transactions on Information Theory 56, 2980--2998.
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 heath-like 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)
# Robust CLR (rclr) transformation for rows, no pseudocount necessary
varespec.rclr <- decostand(varespec, "rclr", impute = TRUE)
# ALR transformation for rows, with pseudocount and reference sample
varespec.alr <- decostand(varespec, "alr", pseudocount = 1, reference = 1)
## Chi-square: 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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