PC1_LFM: Apply the PC method to the Laplace factor model

In LFM: Laplace Factor Model Analysis and Evaluation

Apply the PC method to the Laplace factor model

Description

This function performs Principal Component Analysis (PCA) on a given data set to reduce dimensionality. It calculates the estimated values for the loadings, specific variances, and the covariance matrix.

Usage

PC1_LFM(data, m, A, D)

Arguments

data	The total data set to be analyzed.
m	The number of principal components to retain in the analysis.
A	The true factor loadings matrix.
D	The true uniquenesses matrix.

Value

A list containing:

A1	Estimated factor loadings.
D1	Estimated uniquenesses.
MSESigmaA	Mean squared error for factor loadings.
MSESigmaD	Mean squared error for uniquenesses.
LSigmaA	Loss metric for factor loadings.
LSigmaD	Loss metric for uniquenesses.

Examples

library(SOPC)
library(LaplacesDemon)
library(MASS)
n=1000
p=10
m=5
mu=t(matrix(rep(runif(p,0,1000),n),p,n))
mu0=as.matrix(runif(m,0))
sigma0=diag(runif(m,1))
F=matrix(mvrnorm(n,mu0,sigma0),nrow=n)
A=matrix(runif(p*m,-1,1),nrow=p)
lanor <- rlaplace(n*p,0,1)
epsilon=matrix(lanor,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- PC1_LFM(data, m, A, D)
print(results)

LFM documentation built on April 16, 2025, 9:07 a.m.