SOPC_LFM: Apply the SOPC method to the Laplace factor model

In LFM: Laplace Factor Model Analysis and Evaluation

Apply the SOPC method to the Laplace factor model

Description

This function calculates various metrics for the SOPC analysis on the Laplace factor model. It estimates the factor loadings and uniquenesses, and computes metrics such as mean squared error, loss metrics, and sparsity.

Usage

SOPC_LFM(data, m, p, A, D)

Arguments

data	A numeric matrix containing the data used in the SOPC analysis.
m	An integer specifying the number of subsets or common factors.
p	An integer specifying the number of variables in the data.
A	A numeric matrix representing the true factor loadings.
D	A numeric matrix representing the true uniquenesses.

Value

A list containing the following metrics:

Aso	Estimated factor loadings matrix.
Dso	Estimated uniquenesses matrix.
MSEA	Mean squared error of the estimated factor loadings (Aso) compared to the true loadings (A).
MSED	Mean squared error of the estimated uniquenesses (Dso) compared to the true uniquenesses (D).
LSA	Loss metric for the estimated factor loadings (Aso), indicating the relative error compared to the true loadings (A).
LSD	Loss metric for the estimated uniquenesses (Dso), indicating the relative error compared to the true uniquenesses (D).
tauA	Proportion of zero factor loadings in the estimated loadings matrix (Aso), representing the sparsity.

Examples

library(MASS)
library(SOPC)
library(matrixcalc)
library(LaplacesDemon)
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 <- SOPC_LFM(data, m, p, A, D)
print(results)

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