| varls {ProcMod} | R Documentation |
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)