| Type: | Package |
| Title: | A Package for Analyzing Skew Factor Models |
| Version: | 0.2.1 |
| Description: | Generates Skew Factor Models data and applies Sparse Online Principal Component (SOPC), Incremental Principal Component (IPC), Projected Principal Component (PPC), Perturbation Principal Component (PPC), Stochastic Approximation Principal Component (SAPC), Sparse Principal Component (SPC) and other PC methods to estimate model parameters. It includes capabilities for calculating mean squared error, relative error, and sparsity of the loading matrix.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, SOPC, matrixcalc, sn, stats,psych |
| NeedsCompilation: | no |
| Language: | en-US |
| Author: | Guangbao Guo [aut, cre], Yu Jin [aut] |
| Maintainer: | Guangbao Guo <ggb11111111@163.com> |
| Suggests: | testthat (≥ 3.0.0), ggplot2 |
| Packaged: | 2025-04-15 09:02:05 UTC; AIERXUAN |
| Depends: | R (≥ 3.5.0) |
| Repository: | CRAN |
| Date/Publication: | 2025-04-15 09:40:02 UTC |
Apply the FanPC method to the Skew 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.SFM(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(SOPC)
library(matrixcalc)
library(MASS)
library(sn)
library(psych)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- FanPC.SFM(data, m, A, D, p)
print(results)
Apply the GulPC method to the Skew factor model
Description
This function performs General Unilateral Loading Principal Component (GulPC) analysis on a given data set. It calculates the estimated values for the first layer and second layer loadings, specific variances, and the mean squared errors.
Usage
GulPC.SFM(data, m, A, D)
Arguments
data |
A matrix of input data. |
m |
The number of principal components. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
Value
A list containing:
AU1 |
The first layer loading matrix. |
AU2 |
The second layer loading matrix. |
DU3 |
The estimated specific variance matrix. |
MSESigmaD |
Mean squared error for uniquenesses. |
LSigmaD |
Loss metric for uniquenesses. |
Examples
library(SOPC)
library(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- GulPC.SFM(data, m, A, D)
print(results)
Apply the IPC method to the Skew factor model
Description
This function performs Incremental Principal Component Analysis (IPC) on the provided data. It updates the estimated factor loadings and uniquenesses as new data points are processed, calculating mean squared errors and loss metrics for comparison with true values.
Usage
IPC.SFM(x, m, A, D, p)
Arguments
x |
The data used in the IPC analysis. |
m |
The number of common factors. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
p |
The number of variables. |
Value
A list of metrics including:
Ai |
Estimated factor loadings updated during the IPC analysis, a matrix of estimated factor loadings. |
Di |
Estimated uniquenesses updated during the IPC analysis, a vector of estimated uniquenesses corresponding to each variable. |
MSESigmaA |
Mean squared error of the estimated factor loadings (Ai) compared to the true loadings (A). |
MSESigmaD |
Mean squared error of the estimated uniquenesses (Di) compared to the true uniquenesses (D). |
LSigmaA |
Loss metric for the estimated factor loadings (Ai), indicating the relative error compared to the true loadings (A). |
LSigmaD |
Loss metric for the estimated uniquenesses (Di), indicating the relative error compared to the true uniquenesses (D). |
Examples
library(SOPC)
library(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
result <- IPC.SFM(data, m = m, A = A, D = D, p = p)
print(result)
Apply the OPC method to the Skew factor model
Description
This function computes Online Principal Component Analysis (OPC) for the provided input data, estimating factor loadings and uniquenesses. It calculates mean squared errors and sparsity for the estimated values compared to true values.
Usage
OPC.SFM(data, m = 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:
Ao |
Estimated factor loadings. |
Do |
Estimated uniquenesses. |
MSEA |
Mean squared error for factor loadings. |
MSED |
Mean squared error for uniquenesses. |
tau |
The sparsity. |
Examples
library(SOPC)
library(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- OPC.SFM(data, m, A, D, p)
print(results)
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.SFM(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(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- PC1.SFM(data, m, A, D)
print(results)
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
PC2.SFM(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:
A2 |
Estimated factor loadings. |
D2 |
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(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- PC2.SFM(data, m, A, D)
print(results)
Apply the PPC method to the Skew 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.SFM(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(SOPC)
library(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- PPC1.SFM(data, m, A, D, p)
print(results)
Apply the PPC method to the Skew factor model
Description
This function performs Projected Principal Component Analysis (PPC) on a given data set to reduce dimensionality. It calculates the estimated values for the loadings, specific variances, and the covariance matrix.
Usage
PPC2.SFM(data, m, A, D)
Arguments
data |
The total data set to be analyzed. |
m |
The number of principal components. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
Value
A list containing:
Ap2 |
Estimated factor loadings. |
Dp2 |
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(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- PPC2.SFM(data, m, A, D)
print(results)
Stochastic Approximation Principal Component Analysis
Description
This function calculates several metrics for the SAPC method, including the estimated factor loadings and uniquenesses, and various error metrics comparing the estimated matrices with the true matrices.
Usage
SAPC.SFM(x, m, A, D, p)
Arguments
x |
The data used in the SAPC analysis. |
m |
The number of common factors. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
p |
The number of variables. |
Value
A list of metrics including:
Asa |
Estimated factor loadings matrix obtained from the SAPC analysis. |
Dsa |
Estimated uniquenesses vector obtained from the SAPC analysis. |
MSESigmaA |
Mean squared error of the estimated factor loadings (Asa) compared to the true loadings (A). |
MSESigmaD |
Mean squared error of the estimated uniquenesses (Dsa) compared to the true uniquenesses (D). |
LSigmaA |
Loss metric for the estimated factor loadings (Asa), indicating the relative error compared to the true loadings (A). |
LSigmaD |
Loss metric for the estimated uniquenesses (Dsa), indicating the relative error compared to the true uniquenesses (D). |
Examples
p = 10
m = 5
n = 2000
mu = t(matrix(rep(runif(p, 0, 100), n), p, n))
mu0 = as.matrix(runif(m, 0))
sigma0 = diag(runif(m, 1))
F = matrix(MASS::mvrnorm(n, mu0, sigma0), nrow = n)
A = matrix(runif(p * m, -1, 1), nrow = p)
xi = 5
omega = 2
alpha = 5
r <- sn::rsn(n * p, omega = omega, alpha = alpha)
D0 = omega * diag(p)
D = diag(D0)
epsilon = matrix(r, nrow = n)
data = mu + F %*% t(A) + epsilon
result <- SAPC.SFM(data, m = m, A = A, D = D, p = p)
print(result)
The SFM function is to generate Skew Factor Models data.
Description
The function supports various distribution types for generating the data, including: Skew-Normal Distribution, Skew-Cauchy Distribution, Skew-t Distribution.
Usage
SFM(n, p, m, xi, omega, alpha, distribution_type)
Arguments
n |
Sample size. |
p |
Sample dimensionality. |
m |
Number of factors. |
xi |
A numerical parameter used exclusively in the "Skew-t" distribution, representing the distribution's xi parameter. |
omega |
A numerical parameter representing the omega parameter of the distribution, which affects the degree of skewness in the distribution. |
alpha |
A numerical parameter representing the alpha parameter of the distribution, which influences the shape of the distribution. |
distribution_type |
The type of distribution. |
Value
A list containing:
data |
A matrix of generated data. |
A |
A matrix representing the factor loadings. |
D |
A diagonal matrix representing the unique variances. |
Examples
library(MASS)
library(SOPC)
library(sn)
library(matrixcalc)
library(psych)
n <- 100
p <- 10
m <- 5
xi <- 5
omega <- 2
alpha <- 5
distribution_type <- "Skew-Normal Distribution"
X <- SFM(n, p, m, xi, omega, alpha, distribution_type)
SOPC Estimation Function
Description
This function processes Skew Factor Model (SFM) data using the Sparse Online Principal Component (SOPC) method.
Usage
SOPC.SFM(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(SOPC)
library(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- SOPC.SFM(data, m, p, A, D)
print(results)
Apply the SPC method to the Skew factor model
Description
This function performs Sparse Principal Component Analysis (SPC) on the input data. It estimates factor loadings and uniquenesses while calculating mean squared errors and loss metrics for comparison with true values.
Usage
SPC.SFM(data, A, D, m, p)
Arguments
data |
The data used in the SPC analysis. |
A |
The true factor loadings matrix. |
D |
The true uniquenesses matrix. |
m |
The number of common factors. |
p |
The number of variables. |
Value
A list containing:
As |
Estimated factor loadings, a matrix of estimated factor loadings from the SPC analysis. |
Ds |
Estimated uniquenesses, a vector of estimated uniquenesses corresponding to each variable. |
MSESigmaA |
Mean squared error of the estimated factor loadings (As) compared to the true loadings (A). |
MSESigmaD |
Mean squared error of the estimated uniquenesses (Ds) compared to the true uniquenesses (D). |
LSigmaA |
Loss metric for the estimated factor loadings (As), indicating the relative error compared to the true loadings (A). |
LSigmaD |
Loss metric for the estimated uniquenesses (Ds), indicating the relative error compared to the true uniquenesses (D). |
tau |
Proportion of zero factor loadings in the estimated loadings matrix (As). |
Examples
library(SOPC)
library(matrixcalc)
library(MASS)
library(psych)
library(sn)
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)
r <- rsn(n*p,0,1)
epsilon=matrix(r,nrow=n)
D=diag(t(epsilon)%*%epsilon)
data=mu+F%*%t(A)+epsilon
results <- SPC.SFM(data, A, D, m, p)
print(results)
calculate_errors Function
Description
This function calculates the Mean Squared Error (MSE) and relative error for factor loadings and uniqueness estimates obtained from factor analysis.
Usage
calculate_errors(data, A, D)
Arguments
data |
Matrix of SFM data. |
A |
Matrix of true factor loadings. |
D |
Matrix of true uniquenesses. |
Value
A named vector containing:
MSEA |
Mean Squared Error for factor loadings. |
MSED |
Mean Squared Error for uniqueness estimates. |
LSA |
Relative error for factor loadings. |
LSD |
Relative error for uniqueness estimates. |
Examples
set.seed(123) # For reproducibility
# Define dimensions
n <- 10 # Number of samples
p <- 5 # Number of factors
# Generate matrices with compatible dimensions
A <- matrix(runif(p * p, -1, 1), nrow = p) # Factor loadings matrix (p x p)
D <- diag(runif(p, 1, 2)) # Uniquenesses matrix (p x p)
data <- matrix(runif(n * p), nrow = n) # Data matrix (n x p)
# Calculate errors
errors <- calculate_errors(data, A, D)
print(errors)
Data Frame 'concrete_slump'
Description
This is the Concrete Slump Test data set containing various features of concrete mixtures and their slump test results.
Usage
data("concrete_slump")Format
A data frame with 103 rows and 11 columns.
Cement: Amount of cement in kg/m³.Slag: Amount of blast furnace slag in kg/m³.Flyash: Amount of fly ash in kg/m³.Water: Amount of water in kg/m³.SP: Amount of superplasticizer in kg/m³.Coarseagg: Amount of coarse aggregate in kg/m³.Fineagg: Amount of fine aggregate in kg/m³.SLUMP: Slump of the concrete mixture in mm.FLOW: Flow of the concrete mixture in mm.CompressiveStrength: Compressive strength of the concrete in MPa.
Examples
data(concrete_slump)
Data Frame 'protein'
Description
This is the Protein Data Set containing various features related to protein structure and properties.
Usage
data("protein")Format
A data frame with 45730 rows and 10 columns.
Feature1: Description of Feature1.Feature2: Description of Feature2.Feature3: Description of Feature3.Feature4: Description of Feature4.Feature5: Description of Feature5.Feature6: Description of Feature6.Feature7: Description of Feature7.Feature8: Description of Feature8.Feature9: Description of Feature9.Feature10: Description of Feature10.
Examples
data(protein)
Data Frame 'yacht_hydrodynamics'
Description
This is the Yacht Hydrodynamics data set containing various features of yacht design and their performance metrics.
Usage
data("yacht_hydrodynamics")Format
A data frame with 364 rows and 7 columns.
LongitudinalPosition: Longitudinal position of the center of buoyancy.PrismaticCoefficient: Prismatic coefficient.LengthDisplacementRatio: Length-displacement ratio.BeamDraughtRatio: Beam-draught ratio.LengthBeamRatio: Length-beam ratio.FroudeNumber: Froude number.ResiduaryResistance: Residuary resistance per unit weight of displacement.
Examples
data(yacht_hydrodynamics)