| Type: | Package |
| Title: | Informative Procrustean Matrix Correlation |
| Version: | 1.0.8 |
| Author: | Eric Coissac, Christelle Gonindard-Melodelima |
| Maintainer: | Eric Coissac <eric.coissac@metabarcoding.org> |
| Description: | Estimates corrected Procrustean correlation between matrices for removing overfitting effect. Coissac Eric and Gonindard-Melodelima Christelle (2019) <doi:10.1101/842070>. |
| License: | CeCILL-2 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.1 |
| Depends: | R (≥ 3.1.0) |
| Imports: | MASS, permute, Matrix, stats, foreach, Rdpack |
| Suggests: | knitr, rmarkdown, roxygen2, vegan, testthat, ade4, doParallel |
| RdMacros: | Rdpack |
| Collate: | 'internals.R' 'procmod_frame.R' 'multivariate.R' 'procmod.R' 'covls.R' 'corls_test.R' 'procuste.R' 'simulate.R' |
| NeedsCompilation: | no |
| Packaged: | 2021-05-11 13:33:05 UTC; coissac |
| Repository: | CRAN |
| Date/Publication: | 2021-05-12 06:52:11 UTC |
Compute the trace of a square matrix.
Description
The trace of a square matrix is defined as the sum of its diagonal elements.
Usage
.Trace(X)
Arguments
X |
a square matrix |
Value
the trace of X
Note
Internal function do not use.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
m <- matrix(1:16, nrow = 4)
ProcMod:::.Trace(m)
Generate permutation matrix according to a schema.
Description
The permutation schema is defined using the 'how' function. The implementation of this function is inspired from the VEGAN package and reproduced here to avoid an extra dependency on an hidden vegan function.
Usage
.getPermuteMatrix(permutations, n, strata = NULL)
Arguments
permutations |
a list of control values for the permutations as returned
by the function |
n |
numeric; the number of observations in the sample set.
May also be any object that nobs knows about;
see |
strata |
A factor, or an object that can be coerced to a factor via as.factor, specifying the strata for permutation. |
Note
Internal function do not use.
Internal function coercing the data to a matrix.
Description
Transforme the x value into a numeric matrix of
the correct size or into a dist object.
Usage
.procmod_coerce_value(x, nrows = 0, contrasts = NULL)
Arguments
x |
The data to coerce |
nrows |
an interger value specifying the number of row of the returned matrix |
contrasts |
see the |
Value
a new numeric matrix with correct size.
Note
Internal function do not use.
Author(s)
Eric Coissac <eric.coissac@metabarcoding.org>
Christelle Gonindard-Melodelima <christelle.gonindard@metabarcoding.org>
Internal function repeating a matrix.
Description
repeats several times the rows of a matrix to create a new matrix with more rows. The final row count must be a multiple of the initial row count
Usage
.rep_matrix(x, nrow)
Arguments
x |
The matrix to replicate |
nrow |
an interger value specifying the number of row of the returned matrix |
Value
a new matrix with the same number of columns but with 'nrow' rows.
Note
Internal function do not use.
Author(s)
Eric Coissac <eric.coissac@metabarcoding.org>
Christelle Gonindard-Melodelima <christelle.gonindard@metabarcoding.org>
Converts a dist object to a data.frame object.
Description
The created data.frame has a attribute is.dist set to
the logical value TRUE.
Usage
## S3 method for class 'dist'
as.data.frame(x, row.names = NULL, optional = FALSE, ...)
Arguments
x |
the |
row.names |
NULL or a |
optional |
logical. If |
... |
additional arguments to be passed to or from methods. |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
data(bacteria)
bacteria_rel_freq <- sweep(bacteria,
1,
rowSums(bacteria),
"/")
bacteria_hellinger <- sqrt(bacteria_rel_freq)
bacteria_dist <- dist(bacteria_hellinger)
bdf <- as.data.frame(bacteria_dist)
Coerce to a ProcMod Frame.
Description
Conversion methods are proposed for list,
matrix and array.
Usage
as_procmod_frame(data, ...)
## S3 method for class 'list'
as_procmod_frame(data, ...)
## S3 method for class 'procmod_frame'
as_procmod_frame(data, ...)
## S3 method for class 'array'
as_procmod_frame(data, ...)
## S3 method for class 'matrix'
as_procmod_frame(data, ...)
Arguments
data |
a R object to coerce. |
... |
supplementary parameters used in some implementation of that method |
Value
a procmod_frame object
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
# Builds a list containing two random matrices
m1 <- simulate_matrix(10,20)
m2 <- simulate_matrix(10,30)
l <- list(m1 = m1, m2 = m2)
# Converts the list to a procmod_frame
pmf1 <- as_procmod_frame(l)
# Builds a procmod_frame from a matrix
m3 <- matrix(1:12,nrow=3)
pmf2 <- as_procmod_frame(matrix(1:12,nrow=3))
# Returns 4, the column count of the input matrix
length(pmf2)
# Builds a 3D array
a <- array(1:24,dim = c(3,4,2))
# The conversion to a procmod_frame makes
# an procmod element from each third dimension
as_procmod_frame(a)
Double centering of a matrix.
Description
colSums and rowSums of the returned matrix are all equal to zero.
Usage
bicenter(m)
Arguments
m |
a |
Details
Inspired from the algorithm described in stackoverflow https://stackoverflow.com/questions/43639063/double-centering-in-r
Value
a numeric matrix centred by rows
and columns
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
data(bacteria)
bact_bc <- bicenter(bacteria)
sum(rowSums(bact_bc))
sum(colSums(bact_bc))
Monte-Carlo Test on the sum of the singular values of a procustean rotation.
Description
performs a Monte-Carlo Test on the sum of the singular values of a
procustean rotation (see procuste.rtest).
Usage
corls_test(
...,
permutations = permute::how(nperm = 999),
p_adjust_method = "holm"
)
Arguments
... |
the set of matrices or a |
permutations |
a list of control values for the permutations as returned
by the function |
p_adjust_method |
the multiple test correction method used
to adjust p values. |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
References
Jackson DA (1995). “PROTEST: A PROcrustean Randomization TEST of community environment concordance.” Écoscience, 2(3), 297–303.
See Also
Examples
A <- simulate_matrix(10,3)
B <- simulate_matrix(10,5)
C <- simulate_correlation(B,10,r2=0.6)
# Computes the correlation matrix
data <- procmod_frame(A = A, B = B, C = C)
corls_test(data, permutations = 100)
Dimensions of a ProcMod Frame.
Description
Dimension 1 is the number of rows (individus) shared by the aggregated matrices. Dimension 2 is the number of aggregated matrices
Usage
## S3 method for class 'procmod_frame'
dim(x)
Arguments
x |
a |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
# Builds a procmod_frame with two random matrices
m1 <- simulate_matrix(10,20)
m2 <- simulate_matrix(10,30)
pmf <- procmod_frame(m1 = m1, m2 = m2)
dim(pmf)
DNA metabarcoding Australia South-North Gradient
Description
This data set of five data.frame
is a simplified version of a full data set
describing biodiversity changes along a South-North
gradient on the Australian East Coast, from Sidney to
North Cap using a DNA metabarcoding approach.
The gradient is constituted of 21 locations.
Usage
data(eukaryotes)
data(bacteria)
data(climat)
data(soil)
data(geography)
Format
five data.frame of 21 rows
An object of class data.frame with 21 rows and 2150 columns.
An object of class data.frame with 21 rows and 6 columns.
An object of class data.frame with 21 rows and 12 columns.
An object of class data.frame with 21 rows and 2 columns.
Details
- bacteria
is a 21 x 2150
data.framedescribing bacterial community at each one of the 21 locations. Each number is the relative frequency of a molecular operational taxonomy unit (MOTU) at a site after data cleaning and averaging of 135 pontual measures.- bacteria
is a 21 x 1393
data.framedescribing eukariote community at each one of the 21 locations. Each number is the relative frequency of a molecular operational taxonomy unit (MOTU) at a site after data cleaning and averaging of 135 pontual measures.- climat
is a 21 x 6
data.framedescribing climatic conditions at each site using worldclim descriptors (https://www.worldclim.org).- Aspect
- TempSeasonality
- MaxMonTemp
Max Temperature of Warmest Month
- MeanMonTempRange
- AnnMeanTemp
- Isothemality
Mean Diurnal Range / Temperature Annual Range, with
- Mean Diurnal Range
Mean of monthly (max temp - min temp)
- Temperature Annual Range
Max Temperature of Warmest Month - Min Temperature of Coldest Month
- soil
s a 21 x 6
data.framedescribing soil chemistery at each site. Each variable is reduced and centered- KLg
Logarithm of the potassium concentration
- pH
Soil Ph
- AlLg
Logarithm of the aluminium concentration
- FeLg
Logarithm of the iron concentration
- PLg
Logarithm of the phosphorus concentration
- SLg
Logarithm of the sulphur concentration
- CaLg
Logarithm of the calcium concentration
- MgLg
Logarithm of the magnesium concentration
- MnLg
Logarithm of the manganese concentration
- CNratio
carbon / nitrogen concentration ratio
- CLg
Logarithm of the carbon concentration
- NLg
Logarithm of the nitrogen concentration
- geography
Author(s)
Christelle Gonindard-Melodelima
Eric Coissac
Test if the distance matrix is euclidean.
Description
Actually a simplified version of the ADE4 implementation
(is.euclid).
Usage
is_euclid(distances, tol = 1e-07)
Arguments
distances |
an object of class 'dist' |
tol |
a tolerance threshold : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue. |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
library(vegan)
data(bacteria)
bacteria_rel_freq <- sweep(bacteria,
1,
rowSums(bacteria),
"/")
bacteria_bray <- vegdist(bacteria_rel_freq,method = "bray")
is_euclid(bacteria_bray)
bacteria_chao <- vegdist(floor(bacteria*10000),method = "chao")
is_euclid(bacteria_chao)
Check if an object is a ProcMod Frame.
Description
Check if an object is a ProcMod Frame.
Usage
is_procmod_frame(x)
Arguments
x |
a R |
Value
a logical value equals to
TRUE if x is a procmod_frame,
FALSE otherwise.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
# Builds a procmod_frame with two random matrices
m1 <- simulate_matrix(10,20)
m2 <- simulate_matrix(10,30)
pmf <- procmod_frame(m1 = m1, m2 = m2)
# Returns TRUE
is_procmod_frame(pmf)
# Returns FALSE
is_procmod_frame(3)
The Names of the elements of a Correlation Matrix
Description
Returns the names of the elements associated to a procmod_corls
object.
Usage
## S3 method for class 'procmod_corls'
names(x)
Arguments
x |
a |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
See Also
Examples
# Build Three matrices of 3 rows.
A <- simulate_matrix(10,3)
B <- simulate_matrix(10,5)
C <- simulate_correlation(B,10,r2=0.6)
# Computes the correlation matrix
data <- procmod_frame(A = A, B = B, C = C)
cls <- corls(data, nrand = 100)
names(cls)
The Names of the elements of a Variance / Covariance Matrix.
Description
Returns the names of the elements associated to a procmod_varls
object.
Usage
## S3 method for class 'procmod_varls'
names(x)
Arguments
x |
a |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
See Also
Examples
# Build Three matrices of 3 rows.
A <- simulate_matrix(10,3)
B <- simulate_matrix(10,5)
C <- simulate_correlation(B,10,r2=0.6)
# Computes the variance covariance matrix
data <- procmod_frame(A = A, B = B, C = C)
v <- varls(data, nrand = 100)
names(v)
Project a distance matrix in a euclidean space (NMDS).
Description
Project a set of points defined by a distance matrix in
an eucleadean space using the Kruskal's Non-metric
Multidimensional Scaling. This function is mainly a simplified
interface on the isoMDS function using as
much as possible dimensions to limit the stress. The aims of this
NDMS being only to project point in an orthogonal space therefore
without any correlation between axis. Because a non-metric method
is used no condition is required on the used distance.
Usage
nmds(distances, maxit = 100, trace = FALSE, tol = 0.001, p = 2)
Arguments
distances |
a |
maxit |
The maximum number of iterations. |
trace |
Logical for tracing optimization. Default |
tol |
convergence tolerance. |
p |
Power for Minkowski distance in the configuration space. |
Value
a numeric matrix with at most n-1 dimensions, with
n the number pf observations. This matrix defines the
coordinates of each point in the orthogonal space.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
data(bacteria)
bacteria_rel_freq <- sweep(bacteria,
1,
rowSums(bacteria),
"/")
bacteria_hellinger <- sqrt(bacteria_rel_freq)
bacteria_dist <- dist(bacteria_hellinger)
project <- nmds(bacteria_dist)
Project a dataset in a euclidean space.
Description
Project a set of points defined by a distance matrix
or a set of variables in an eucleadean space.
If the distance matrix is a metric, this is done using
the pcoa function,
for other distance the nmds is used.
When points are described by a set of variable the
nmds is used.
Usage
ortho(data, ...)
## S3 method for class 'dist'
ortho(data, tol = 1e-07, ...)
## S3 method for class 'matrix'
ortho(data, scale = FALSE, ...)
## S3 method for class 'data.frame'
ortho(data, scale = FALSE, ...)
## S3 method for class 'procmod_frame'
ortho(data, ...)
Arguments
data |
a numeric matrix describing the points |
... |
other parameters specific to some implementation |
tol |
a tolerance threshold : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue. |
scale |
a |
Value
a numeric matrix with at most n-1 dimensions, with
n the number pf observations. This matrix defines the
coordinates of each point in the orthogonal space.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
library(vegan)
data(bacteria)
data(eukaryotes)
data(soil)
dataset <- procmod_frame(euk = vegdist(decostand(eukaryotes,
method = "hellinger"),
method = "euclidean"),
bac = vegdist(decostand(bacteria,
method = "hellinger"),
method = "euclidean"),
soil = scale(soil,
center = TRUE,
scale = TRUE))
dp <- ortho(dataset)
bacteria_rel_freq <- sweep(bacteria,
1,
rowSums(bacteria),
"/")
bacteria_hellinger <- sqrt(bacteria_rel_freq)
bacteria_dist <- dist(bacteria_hellinger)
project <- ortho(bacteria_dist)
Project a set of points in a euclidean space (PCA).
Description
Project a set of points defined by a set of numeric variables in
an eucleadean space using the pricipal componant analysis.
This function is mainly a simplified
interface on the prcomp function using as
much as possible dimensions to keep all the variation. The aims of this
PCA being only to project point in an orthogonal space therefore
without any correlation between axis. Data are centered by not scaled by
default.
Usage
pca(data, scale = FALSE)
Arguments
data |
a numeric matrix describing the points |
scale |
a |
Value
a numeric matrix with at most n-1 dimensions, with
n the number pf observations. This matrix defines the
coordinates of each point in the orthogonal space.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
data(bacteria)
bacteria_rel_freq <- sweep(bacteria,
1,
rowSums(bacteria),
"/")
bacteria_hellinger <- sqrt(bacteria_rel_freq)
project <- pca(bacteria_hellinger)
Project a distance matrix in a euclidean space (PCOA).
Description
Project a set of points defined by a distance matrix in
an eucleadean space using the Principal Coordinates Analysis
method. This function is mainly a simplified
interface on the cmdscale function using as
much as possible dimensions for the projection. The aims of this
PCoA being only to project point in an orthogonal space therefore
without any correlation between axis. Because a metric method
is used the used distance must be euclidean
(cf is_euclid).
Usage
pcoa(distances)
Arguments
distances |
a |
Value
a numeric matrix with at most n-1 dimensions, with
n the number pf observations. This matrix defines the
coordinates of each point in the orthogonal space.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
data(bacteria)
bacteria_rel_freq <- sweep(bacteria,
1,
rowSums(bacteria),
"/")
bacteria_hellinger <- sqrt(bacteria_rel_freq)
bacteria_dist <- dist(bacteria_hellinger)
project <- pcoa(bacteria_dist)
Print a procrustean Correlation Matrix.
Description
Print a procrustean Correlation Matrix.
Usage
## S3 method for class 'procmod_corls'
print(x, ...)
Arguments
x |
a |
... |
other parameters passed to other functions |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
See Also
Examples
# Build Three matrices of 3 rows.
A <- simulate_matrix(10,3)
B <- simulate_matrix(10,5)
C <- simulate_correlation(B,10,r2=0.6)
# Computes the correlation matrix
data <- procmod_frame(A = A, B = B, C = C)
cls <- corls(data, nrand = 100)
print(cls)
Print procrustean Variance / Covariance Matrix.
Description
Print procrustean Variance / Covariance Matrix.
Usage
## S3 method for class 'procmod_varls'
print(x, ...)
Arguments
x |
a |
... |
other parameters passed to other functions |
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
See Also
Examples
# Build Three matrices of 3 rows.
A <- simulate_matrix(10,3)
B <- simulate_matrix(10,5)
C <- simulate_correlation(B,10,r2=0.6)
# Computes the variance covariance matrix
data <- procmod_frame(A = A, B = B, C = C)
v <- varls(data, nrand = 100)
print(v)
Informative Procrustean Matrix Correlation
Description
Estimates corrected Procrustean correlation between matrices for removing overfitting effect.
Details
The functions in the ProcMod package aims to estimate and to test correlation between matrices, correcting for the spurious correlations because of the over-fitting effect.
The ProcMod package is developed on the metabarcoding.org gitlab (https://git.metabarcoding.org/lecasofts/ProcMod). The gitlab of metabarcoding.org provides up-to-date information and forums for bug reports.
Author(s)
Christelle Gonindard-Melodelima
Eric Coissac
The procmod_frame data structure.
Description
A procmod_frame can be considered as the analog of a
data.frame for vector data. In a procmod_frame
each element, equivalent to a column in a data.frame
is a numeric matrix or a distance matrix object (dist).
Every element must describe the same number of individuals.
Therefore every numeric matrix must have the same number of row
(nrow) and every distance matrix must have the same size
(attr(d,"Size")). A procmod_frame can simultaneously
contain both types of data, numeric and distance matrix.
Usage
procmod_frame(
...,
row_names = NULL,
check_rows = TRUE,
reorder_rows = TRUE,
contrasts_arg = NULL
)
Arguments
... |
a set of objects to aggregate into a
|
row_names |
a character vector containing names associated to each row. |
check_rows |
a logical value. When set to |
reorder_rows |
a logical value. When set to |
contrasts_arg |
A list, whose entries are values (numeric matrices or character strings naming functions) to be used as replacement values for the contrasts replacement function and whose names are the names of columns of data containing factors. |
Value
a procmod_frame instance.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
library(vegan)
data(bacteria)
data(eukaryotes)
data(soil)
dataset <- procmod_frame(euk = vegdist(decostand(eukaryotes,
method = "hellinger"),
method = "euclidean"),
bac = vegdist(decostand(bacteria,
method = "hellinger"),
method = "euclidean"),
soil = scale(soil,
center = TRUE,
scale = TRUE))
length(dataset)
nrow(dataset)
ncol(dataset)
dataset$euk
Rotate the src matrix to fit into the space of the dest matrix.
Description
The optimal rotation is computed according to the procruste methode. Rotation is based on singular value decomposition (SVD). No scaling and no centrering are done, before computing the SVD.
Usage
protate(src, dest)
Arguments
src |
a numeric matrix to be rotated |
dest |
a numeric matrix used as reference space |
Value
a numeric matrix
Author(s)
Christelle Gonindard-Melodelima
Eric Coissac
Examples
# Generates two random matrices of size 10 x 15
m1 <- simulate_matrix(10, 15)
m2 <- simulate_matrix(10, 20)
# Rotates matrix m1 on m2
mr <- protate(m1, m2)
Simulate n points of dimension p correlated to a reference matrix.
Description
Simulates a set of point correlated to another set according to the
procrustean correlation definition.
Points are simulated by drawing values of each dimension from a normal
distribution of mean 0 and standard deviation equals to 1.
The mean of each dimension is forced to 0 (data are centred).
By default variable are also scaled to enforce a strandard deviation
strictly equal to 1. Covariances between dimensions are not controled.
Therefore they are expected to be equal to 0 and reflect only the
random distribution of the covariance between two random vectors.
The intensity of the correlation is determined by the r2
parameter.
Usage
simulate_correlation(reference, p, r2, equal_var = TRUE)
Arguments
reference |
a numeric matrix to which the simulated data will be correlated |
p |
an |
r2 |
the fraction of variation shared between the |
equal_var |
a |
Value
a numeric matrix of nrow(reference) rows and p columns
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
sim1 <- simulate_matrix(25,10)
class(sim1)
dim(sim1)
sim2 <- simulate_correlation(sim1,20,0.8)
corls(sim1, sim2)^2
Simulate n points of dimension p.
Description
Points are simulated by drawing values of each dimension from a normal distribution of mean 0 and standard deviation equals to 1. The mean of each dimension is forced to 0 (data are centred). By default variable are also scaled to enforce a strandard deviation strictly equal to 1. Covariances between dimensions are not controled. Therefore they are expected to be equal to 0 and reflect only the random distribution of the covariance between two random vectors.
Usage
simulate_matrix(n, p, equal_var = TRUE)
Arguments
n |
an |
p |
an |
equal_var |
a |
Value
a numeric matrix of n rows and p columns
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
sim1 <- simulate_matrix(25,10)
class(sim1)
dim(sim1)
Subsetting Procmod Frames
Description
This is the implementation of the subset generic function for
procmod_frame.
Usage
## S3 method for class 'procmod_frame'
subset(x, subset, select, drop = FALSE, ...)
Arguments
x |
object to be subsetted. |
subset |
logical expression indicating elements or rows to keep: missing values are taken as false. |
select |
expression, indicating columns to select from a data frame. |
drop |
passed on to [ indexing operator. |
... |
further arguments to be passed to or from other methods. |
Details
The subset argument works on rows. Note that subset will be evaluated in the
procmod_frame, so columns can be referred to (by name) as variables
in the expression (see the examples).
The select argument if provided indicates with matrices
have to be conserved. It works by first replacing column names in the selection
expression with the corresponding column numbers in the procmod_frame and then using
the resulting integer vector to index the columns. This allows the use of the
standard indexing conventions so that for example ranges of columns can
be specified easily, or single columns can be dropped (see the examples). Remember
that each column of a procmod_frame is actually a matrix.
The drop argument is passed on to the procmod_frame indexing method.
The default value is FALSE.
Value
A procmod_frame containing just the selected rows and columns.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
Examples
library(vegan)
data(bacteria)
data(eukaryotes)
data(soil)
dataset <- procmod_frame(euk = vegdist(decostand(eukaryotes,
method = "hellinger"),
method = "euclidean"),
bac = vegdist(decostand(bacteria,
method = "hellinger"),
method = "euclidean"),
soil = scale(soil,
center = TRUE,
scale = TRUE))
dim(dataset)
higher_ph = subset(dataset,soil[,"pH"] > 0)
dim(higher_ph)
without_bacteria = subset(dataset,soil[,"pH"] > 0, -bac)
dim(without_bacteria)
Procrustean Correlation, and Variance / Covariance Matrices.
Description
varls, corls compute the procrustean
variance / covariance, or correlation matrices
between a set of real matrices and dist objects.
Usage
varls(..., nrand = 100, p_adjust_method = "holm")
corls(..., nrand = 100, p_adjust_method = "holm")
Arguments
... |
the set of matrices or a |
nrand |
number of randomisation used to estimate the mean
covariance observed between two random matrix.
If rand is |
p_adjust_method |
the multiple test correction method used
to adjust p values. |
Details
Procrustean covariance between two matrices X and Y, is defined as the sum of the singular values of the X'Y matrix (Gower 1971; Lingoes and Schönemann 1974). Both the X and Y matrices must have the same number of rows.
The variances and covariances and correlations are corrected to avoid over fitting (Coissac and Gonindard-Melodelima 2019).
The inputs must be numeric matrices or dist object.
The set of input matrices can be aggregated un a
procmod_frame.
Before computing the coefficients, matrices are projected into an
orthogonal space using the ortho function.
The denominator n - 1 is used which gives an unbiased estimator of the (co)variance for i.i.d. observations.
Value
a procmod_varls object which corresponds to a numeric
matrix annotated by several attributes.
The following attribute is always added:
- nrand an integer value indicating the number of
randomisations used to estimate the mean of the random
covariance.
When nrand is greater than 0 a couple of attributes
is added:
- rcovls a numeric matrix containing the estimation
of the mean of the random covariance.
- p.value a numeric matrix containing the estimations
of the p.values of tests checking that the observed
covariance is larger than the mean of the random covariance.
p.values are corrected for multiple tests according to the
method specified by the p_adjust_method parameter.
Author(s)
Eric Coissac
Christelle Gonindard-Melodelima
References
Gower JC (1971). “Statistical methods of comparing different multivariate analyses of the same data.” Mathematics in the archaeological and historical sciences, 138–149.
Lingoes JC, Schönemann PH (1974). “Alternative measures of fit for the Schönemann-carroll matrix fitting algorithm.” Psychometrika, 39(4), 423–427.
Coissac E, Gonindard-Melodelima C (2019). “Assessing the shared variation among high-dimensional data matrices: a modified version of the Procrustean correlation coefficient.” in prep.
See Also
Examples
# Build Three matrices of 3 rows.
A <- simulate_matrix(10,3)
B <- simulate_matrix(10,5)
C <- simulate_correlation(B,10,r2=0.6)
# Computes the variance covariance matrix
varls(A = A, B = B, C = C)
data = procmod_frame(A = A, B = B, C = C)
varls(data)
# Computes the correlation matrix
corls(data, nrand = 100)