STATIS for Covariance Matrices (generic)

A generic function implementing the STATIS approach for a collection of covariance matrices. Method implementations should return an object of class `covstatis`.

Usage

covstatis(data, ncomp = 2, normalize = TRUE, dcenter = TRUE, ...)

# S3 method for class 'list'
covstatis(data, ncomp = 2, normalize = TRUE, dcenter = TRUE, ...)

Arguments

data

A data object for which a BaDA method is defined (see individual methods for details).

ncomp

Integer; number of components to compute.

normalize

Logical; if `TRUE` (default) each covariance matrix is scaled to have unit Frobenius norm before analysis.

dcenter

Logical; if `TRUE` (default) each covariance matrix is double centred (Gower transformation) prior to analysis.

...

Additional arguments passed to the method.

Value

An object inheriting from class `covstatis`.

Details

The covstatis.list method implements STATIS analysis for a list of covariance matrices.

The method operates as follows:

1. Optionally double-centers each matrix (Gower transformation)

2. Optionally normalizes each matrix to unit Frobenius norm

3. Computes an RV matrix of inner products between matrices

4. Determines optimal weights (alpha) via first eigenvector of the RV matrix. These weights are accessible in the output and can be useful for outlier diagnostics.

5. Creates a compromise matrix as weighted sum of normalized matrices

6. Performs eigendecomposition on the compromise matrix

The partial_scores in the returned object are a list of matrices (one for each subject), with each matrix containing the ROI-level factor scores (ROI x D).

Additional arguments can be passed via ...:

labels

Optional character vector of labels for the rows/columns of the covariance matrices. If NULL, tries to use row names from the first matrix, or generates sequential labels.

norm_method

The normalization method to apply to each matrix. One of "frobenius" (default when normalize=TRUE), "mfa", or "none". Frobenius norm scales each matrix to have a total sum-of-squares of 1. MFA (multiple factor analysis) scales each matrix so its first eigenvalue is 1. "none" applies no normalization.

See also

[covstatis.list] for the reference implementation.

Examples

# Create a list of correlation matrices
Xs <- lapply(1:5, function(i) matrix(rnorm(10*10), 10, 10))
Xs <- lapply(Xs, cor)

# Apply COVSTATIS
res <- covstatis(Xs, ncomp=3)

# Project a new correlation matrix
new_mat <- cor(matrix(rnorm(10*10), 10, 10))
proj <- project_cov(res, new_mat)