PPC1_TFM: Projected Principal Component Analysis

In TFM: Sparse Online Principal Component for Truncated Factor Model

Projected Principal Component Analysis

Description

This function computes Projected Principal Component Analysis (PPC) for the provided input data, estimating factor loadings and uniquenesses. It calculates mean squared errors and loss metrics for the estimated values compared to true values.

Usage

PPC1_TFM(x, m, A, D, p)

Arguments

x	A matrix of input data.
m	The number of principal components to extract (integer).
A	The true factor loadings matrix (matrix).
D	The true uniquenesses matrix (matrix).
p	The number of variables (integer).

Value

A list containing:

Ap	Estimated factor loadings.
Dp	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(MASS)
library(relliptical)
library(SOPC)

PPC_MSESigmaA <- c()
PPC_MSESigmaD <- c()
PPC_LSigmaA <- c()
PPC_LSigmaD <- c()

p <- 10
m <- 5
n <- 2000

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)

lower <- c(rep(-0.5, p - 3), -5, -5, -Inf)
upper <- c(rep(0.5, p - 3), 5, 5, Inf)
Sigma <- diag(runif(p, 0, 1))
mut <- runif(p, 0, 10)

trnor <- rtelliptical(n, mut, Sigma, lower, upper, dist = "Normal")
epsilon <- matrix(trnor, nrow = n)
D <- Sigma

data <- mu + F %*% t(A) + epsilon

result <- PPC1_TFM(data, m, A, D, p)

data_G <- data.frame(n = n,
                     MSEA = result$MSESigmaA,
                     MSED = result$MSESigmaD,
                     LSA = result$LSigmaA,
                     LSD = result$LSigmaD)

print(data_G)

TFM documentation built on April 16, 2025, 5:10 p.m.