CoFM (version 1.1.4)

PPC_new: Center-then-PCA: Projection on the Orthogonal Complement of the Mean Vector

Description

This function performs a specific type of Projected PCA where the data is projected onto the orthogonal complement of the mean vector. It effectively applies the centering projection \(P = I - (1/n)J\) (where \(J\) is the all-ones matrix), optionally rescales the columns, and then performs PCA on the covariance matrix. This allows estimation of factor loadings and residual variances after removing the mean structure.

Usage

PPC_new(data, m)

Value

A list containing:

Apro

Estimated factor loading matrix (p x m).

Dpro

Estimated residual variances (p x p diagonal matrix).

Sigmahatpro

Covariance matrix of the projected data.

Arguments

data

A matrix or data frame of input data (n x p).

m

Integer. The number of principal components (factors) to keep.

Examples

# Examples should be fast and reproducible for CRAN checks
set.seed(1)
dat <- matrix(stats::rnorm(200), ncol = 4)
ans <- PPC_new(data = dat, m = 2)
str(ans)
head(ans$Apro)