TFM (version 0.3.0)

PPC1_TFM: 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)

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.

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).

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)