| Version: | 0.5.0 |
| Title: | Elliptical Factor Models |
| Description: | The elliptical factor model, as an extension of the traditional factor model, effectively overcomes the limitations of the traditional model when dealing with heavy-tailed characteristic data. This package implements sparse principal component methods (SPC) and bi-sparse online principal component estimation (SPOC) for parameter estimation. Includes functionality for calculating mean squared error, relative error, and loading matrix sparsity.The philosophy of the package is described in Guo G. (2023) <doi:10.1007/s00180-022-01270-z>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | MASS, stats, SOPC, matrixcalc |
| Suggests: | testthat (≥ 3.0.0), ggplot2, pracma, psych, sn |
| Depends: | R (≥ 3.5.0) |
| NeedsCompilation: | no |
| Language: | en-US |
| Maintainer: | Guangbao Guo <ggb11111111@163.com> |
| Packaged: | 2025-10-17 03:33:53 UTC; 86187 |
| Author: | Guangbao Guo [aut, cre], Yuanyuan Zhou [aut] |
| Repository: | CRAN |
| Date/Publication: | 2025-10-21 18:00:02 UTC |
The EFM function is to generate Elliptical Factor Models data.
Description
The function supports various distribution types for generating the data, including: Elliptical-Normal Distribution, Elliptical-t Distribution.
Usage
EFM(n, p, m, nu, distribution_type)
Arguments
n |
Sample size. |
p |
Sample dimensionality. |
m |
Number of factors. |
nu |
A numerical parameter used exclusively in the "Elliptical-t" distribution, representing the degrees of freedom. |
distribution_type |
The type of distribution ("Elliptical-Normal Distribution" or "Elliptical-t Distribution"). |
Value
A list containing:
data |
A matrix of generated data (n x p). |
A |
A matrix representing the factor loadings (p x m). |
D |
A diagonal matrix representing the unique variances (p x p). |
Examples
library(MASS)
library(pracma)
n <- 2000
p <- 10
m <- 5
nu <- 5
distribution_type <- "Elliptical-Normal Distribution"
X <- EFM(n, p, m, nu, distribution_type)
Apply the FanPC method to the Elliptical Factor Model
Description
This function performs Factor Analysis via Principal Component (FanPC) on a given data set. It calculates the estimated factor loading matrix (AF), specific variance matrix (DF), and the mean squared errors.
Usage
FanPC.EFM(data, m, A, D, p)
Arguments
data |
A matrix of input data. |
m |
The number of principal components. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
p |
The number of variables. |
Value
A list containing:
AF |
Estimated factor loadings. |
DF |
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(matrixcalc)
library(MASS)
n <- 100
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 <- matrix(mvrnorm(n, mu0, sigma0), nrow = n)
A <- matrix(runif(p * m, -1, 1), nrow = p)
r <- rnorm(n * p, 0, 1)
epsilon <- matrix(r, nrow = n)
D <- diag(as.vector(apply(epsilon, 2, function(x) sum(x^2))))
data <- mu + F_matrix %*% t(A) + epsilon
results <- FanPC.EFM(data, m, A, D, p)
print(results)
Apply the PC method to the Elliptical 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.EFM(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(matrixcalc)
library(MASS)
n <- 100
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 <- matrix(mvrnorm(n, mu0, sigma0), nrow = n)
A <- matrix(runif(p * m, -1, 1), nrow = p)
r <- rnorm(n * p, 0, 1)
epsilon <- matrix(r, nrow = n)
D <- diag(as.vector(apply(epsilon, 2, function(x) sum(x^2))))
data <- mu + F_matrix %*% t(A) + epsilon
results <- PC1.EFM(data, m, A, D)
print(results)
Apply the PPC method to the Elliptical Factor Model
Description
This function computes Perturbation 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.EFM(data, m, A, D, p)
Arguments
data |
A matrix of input data. |
m |
The number of principal components. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
p |
The number of variables. |
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(matrixcalc)
library(MASS)
n <- 100
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 <- matrix(mvrnorm(n, mu0, sigma0), nrow = n)
A <- matrix(runif(p * m, -1, 1), nrow = p)
r <- rnorm(n * p, 0, 1)
epsilon <- matrix(r, nrow = n)
D <- diag(as.vector(apply(epsilon, 2, function(x) sum(x^2))))
data <- mu + F_matrix %*% t(A) + epsilon
results <- PPC1.EFM(data, m, A, D, p)
print(results)
SOPC Estimation Function for Elliptical Factor Model
Description
This function processes Elliptical Factor Model (EFM) data using the Sparse Online Principal Component (SOPC) method.
Usage
SOPC.EFM(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(matrixcalc)
library(MASS)
n <- 100
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 <- matrix(mvrnorm(n, mu0, sigma0), nrow = n)
A <- matrix(runif(p * m, -1, 1), nrow = p)
r <- rnorm(n * p, 0, 1)
epsilon <- matrix(r, nrow = n)
D <- diag(as.vector(apply(epsilon, 2, function(x) sum(x^2))))
data <- mu + F_matrix %*% t(A) + epsilon
results <- SOPC.EFM(data, m, p, A, D)
print(results)
Calculate errors for elliptical distributions
Description
This function calculates errors for elliptical distributions, including Elliptical-Normal Distribution and Elliptical-t Distribution.
Usage
elliptical_errors(data, distribution = "normal", df = NULL)
Arguments
data |
Matrix of data following an elliptical distribution. |
distribution |
Type of elliptical distribution ("normal" or "t"). |
df |
Degrees of freedom for Elliptical-t Distribution (required if distribution is "t"). |
Details
Calculate errors for elliptical distributions
Value
A list containing error metrics for the specified elliptical distribution.
Examples
set.seed(123)
n <- 100; p <- 5
data_normal <- MASS::mvrnorm(n, rep(0, p), diag(p))
errors_normal <- elliptical_errors(data_normal, distribution = "normal")
data_t <- matrix(stats::rt(n * p, df = 5), nrow = n, ncol = p)
errors_t <- elliptical_errors(data_t, distribution = "t", df = 5)
print(errors_normal)
print(errors_t)