Package 'TFM' reference manual

Title:	Sparse Online Principal Component for TFM
Description:	The Truncated Factor Model is a statistical model designed to handle specific data structures in data analysis. This R package focuses on the Sparse Online Principal Component Estimation method, which is used to calculate data such as the loading matrix and specific variance matrix for truncated data, thereby better explaining the relationship between common factors and original variables. Additionally, the R package also provides other equations for comparison with the Sparse Online Principal Component Estimation method.The philosophy of the package is described in Guangbao Guo. (2023) <doi:10.1007/s00180-022-01270-z>.
Authors:	Beibei Wu [aut], Guangbao Guo [aut, cre]
Maintainer:	Guangbao Guo <[email protected]>
License:	MIT + file LICENSE
Version:	0.1.0
Built:	2024-12-15 06:02:00 UTC
Source:	https://github.com/cran/TFM

Incremental Principal Component Analysis

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_print(x, m, A, D, p)
IPC_print(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(MASS)
library(relliptical)
library(SOPC)

IPC_MSESigmaA = c()
IPC_MSESigmaD = c()
IPC_LSigmaA = c()
IPC_LSigmaD = c()

p = 10
m = 5

# Set n = 2000 for testing
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)

# Sampling from the Truncated Normal distribution
lower = c(rep(-0.5, p - 3), -5, -5, -Inf)
upper = c(rep(0.5, p - 3), 5, 5, Inf)
Sigma = as.matrix(diag(rep(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

# Apply IPC_print for n = 2000
Z = data.frame(IPC_print(data, m = m, A = A, D = D, p = p))[c(3, 4, 5, 6),]
IPC_MSESigmaA = Z[1]
IPC_MSESigmaD = Z[2]
IPC_LSigmaA = Z[3]
IPC_LSigmaD = Z[4]

# Print the results
data_M = data.frame(n = n, MSEA = IPC_MSESigmaA, MSED = IPC_MSESigmaD,
 LSA = IPC_LSigmaA, LSD = IPC_LSigmaD)
print(data_M)

print(data_M)

library(MASS)
library(relliptical)
library(SOPC)

IPC_MSESigmaA = c()
IPC_MSESigmaD = c()
IPC_LSigmaA = c()
IPC_LSigmaD = c()

p = 10
m = 5

# Set n = 2000 for testing
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)

# Sampling from the Truncated Normal distribution
lower = c(rep(-0.5, p - 3), -5, -5, -Inf)
upper = c(rep(0.5, p - 3), 5, 5, Inf)
Sigma = as.matrix(diag(rep(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

# Apply IPC_print for n = 2000
Z = data.frame(IPC_print(data, m = m, A = A, D = D, p = p))[c(3, 4, 5, 6),]
IPC_MSESigmaA = Z[1]
IPC_MSESigmaD = Z[2]
IPC_LSigmaA = Z[3]
IPC_LSigmaD = Z[4]

# Print the results
data_M = data.frame(n = n, MSEA = IPC_MSESigmaA, MSED = IPC_MSESigmaD,
 LSA = IPC_LSigmaA, LSD = IPC_LSigmaD)
print(data_M)

print(data_M)

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

PPC_print(x, m, A, D, p)
PPC_print(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 <- PPC_print(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)
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 <- PPC_print(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)

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_print(x, m, A, D, p)
SAPC_print(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

library(MASS)
library(relliptical)
library(SOPC)

SAPC_MSESigmaA <- c()
SAPC_MSESigmaD <- c()
SAPC_LSigmaA <- c()
SAPC_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 <- SAPC_print(data, m = m, A = A, D = D, p = p)

SAPC_MSESigmaA <- result$MSESigmaA
SAPC_MSESigmaD <- result$MSESigmaD
SAPC_LSigmaA <- result$LSigmaA
SAPC_LSigmaD <- result$LSigmaD

data_K <- data.frame(
  n = n,
  MSEA = SAPC_MSESigmaA,
  MSED = SAPC_MSESigmaD,
  LSA = SAPC_LSigmaA,
  LSD = SAPC_LSigmaD
)

print(data_K)
library(MASS)
library(relliptical)
library(SOPC)

SAPC_MSESigmaA <- c()
SAPC_MSESigmaD <- c()
SAPC_LSigmaA <- c()
SAPC_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 <- SAPC_print(data, m = m, A = A, D = D, p = p)

SAPC_MSESigmaA <- result$MSESigmaA
SAPC_MSESigmaD <- result$MSESigmaD
SAPC_LSigmaA <- result$LSigmaA
SAPC_LSigmaD <- result$LSigmaD

data_K <- data.frame(
  n = n,
  MSEA = SAPC_MSESigmaA,
  MSED = SAPC_MSESigmaD,
  LSA = SAPC_LSigmaA,
  LSD = SAPC_LSigmaD
)

print(data_K)

Sparse Online Principal Component Analysis

Description

This function calculates various metrics for the Sparse Online Principal Component Analysis (SOPC) method. It estimates the factor loadings and uniquenesses while calculating mean squared errors and loss metrics for comparison with true values. Additionally, it computes the proportion of zero factor loadings in the estimated loadings matrix.

Usage

SOPC_Print(data, m, p, gamma, eta, A, D)
SOPC_Print(data, m, p, gamma, eta, A, D)

Arguments

`data`	The data used in the SOPC analysis.
`m`	the number of common factors
`p`	the number of variables
`gamma`	Tuning parameter for the sparseness of the loadings matrix.
`eta`	Tuning parameter for the sparseness of the uniquenesses matrix.
`A`	The true A matrix.
`D`	The true D matrix.

Value

A list of metrics including:

`Aso`	Estimated factor loadings matrix obtained from the SOPC analysis.
`Dso`	Estimated uniquenesses vector obtained from the SOPC analysis.
`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), indicating the sparsity of the loadings.

Examples

library(MASS)
library(relliptical)
library(SOPC)

SOPC_MSEA <- c()
SOPC_MSED <- c()
SOPC_LSA <- c()
SOPC_LSD <- c()
SOPC_TAUA <- c()

p = 10; m = 5
n = 2000  # Set n to 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)

# Sampling from the Truncated Normal distribution
lower = c(rep(-0.5, p - 3), -5, -5, -Inf)
upper = c(rep(0.5, p - 3), 5, 5, Inf)
Sigma = as.matrix(diag(rep(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

Z = data.frame(SOPC_Print(data, m = m, p = p, gamma = 0.1, eta = 0.8, A = A, D = D))
SOPC_MSEA = c(SOPC_MSEA, Z$MSEA)
SOPC_MSED = c(SOPC_MSED, Z$MSED)
SOPC_LSA = c(SOPC_LSA, Z$LSA)
SOPC_LSD = c(SOPC_LSD, Z$LSD)
SOPC_TAUA = c(SOPC_TAUA, Z$tauA)

# Ensure the data frame has the correct column structure, even with one value
data_F = data.frame(n = rep(n, length(SOPC_MSEA)), MSEA = SOPC_MSEA, MSED = SOPC_MSED,
 LSA = SOPC_LSA, LSD = SOPC_LSD, tauA = SOPC_TAUA)
data_F
library(MASS)
library(relliptical)
library(SOPC)

SOPC_MSEA <- c()
SOPC_MSED <- c()
SOPC_LSA <- c()
SOPC_LSD <- c()
SOPC_TAUA <- c()

p = 10; m = 5
n = 2000  # Set n to 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)

# Sampling from the Truncated Normal distribution
lower = c(rep(-0.5, p - 3), -5, -5, -Inf)
upper = c(rep(0.5, p - 3), 5, 5, Inf)
Sigma = as.matrix(diag(rep(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

Z = data.frame(SOPC_Print(data, m = m, p = p, gamma = 0.1, eta = 0.8, A = A, D = D))
SOPC_MSEA = c(SOPC_MSEA, Z$MSEA)
SOPC_MSED = c(SOPC_MSED, Z$MSED)
SOPC_LSA = c(SOPC_LSA, Z$LSA)
SOPC_LSD = c(SOPC_LSD, Z$LSD)
SOPC_TAUA = c(SOPC_TAUA, Z$tauA)

# Ensure the data frame has the correct column structure, even with one value
data_F = data.frame(n = rep(n, length(SOPC_MSEA)), MSEA = SOPC_MSEA, MSED = SOPC_MSED,
 LSA = SOPC_LSA, LSD = SOPC_LSD, tauA = SOPC_TAUA)
data_F

Sparse Principal Component Analysis

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. Additionally, it computes the proportion of zero factor loadings.

Usage

SPC_print(data, A, D, m, p)
SPC_print(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(MASS)
library(relliptical)
library(SOPC)

SPC_MSESigmaA <- c()
SPC_MSESigmaD <- c()
SPC_LSigmaA <- c()
SPC_LSigmaD <- c()
SPC_tau <- 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 <- SPC_print(data, A, D, m, p)

SPC_MSESigmaA <- c(SPC_MSESigmaA, result$MSESigmaA)
SPC_MSESigmaD <- c(SPC_MSESigmaD, result$MSESigmaD)
SPC_LSigmaA <- c(SPC_LSigmaA, result$LSigmaA)
SPC_LSigmaD <- c(SPC_LSigmaD, result$LSigmaD)
SPC_tau <- c(SPC_tau, result$tau)

data_G <- data.frame(n = n,
                     MSEA = SPC_MSESigmaA,
                     MSED = SPC_MSESigmaD,
                     LSA = SPC_LSigmaA,
                     LSD = SPC_LSigmaD,
                     tau = SPC_tau)

print(data_G)
library(MASS)
library(relliptical)
library(SOPC)

SPC_MSESigmaA <- c()
SPC_MSESigmaD <- c()
SPC_LSigmaA <- c()
SPC_LSigmaD <- c()
SPC_tau <- 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 <- SPC_print(data, A, D, m, p)

SPC_MSESigmaA <- c(SPC_MSESigmaA, result$MSESigmaA)
SPC_MSESigmaD <- c(SPC_MSESigmaD, result$MSESigmaD)
SPC_LSigmaA <- c(SPC_LSigmaA, result$LSigmaA)
SPC_LSigmaD <- c(SPC_LSigmaD, result$LSigmaD)
SPC_tau <- c(SPC_tau, result$tau)

data_G <- data.frame(n = n,
                     MSEA = SPC_MSESigmaA,
                     MSED = SPC_MSESigmaD,
                     LSA = SPC_LSigmaA,
                     LSD = SPC_LSigmaD,
                     tau = SPC_tau)

print(data_G)

T-test for Truncated Factor Model

Description

This function performs a simple t-test for each variable in the dataset of a truncated factor model and calculates the False Discovery Rate (FDR) and power.

Usage

ttestTFM(X, p, alpha = 0.05)
ttestTFM(X, p, alpha = 0.05)

Arguments

`X`	A matrix or data frame of simulated or observed data from a truncated factor model.
`p`	The number of variables (columns) in the dataset.
`alpha`	The significance level for the t-test.

Value

A list containing:

`FDR`	The False Discovery Rate calculated from the rejected hypotheses.
`Power`	The power of the test, representing the proportion of true positives among the non-zero hypotheses.
`pValues`	A numeric vector of p-values obtained from the t-tests for each variable.
`RejectedHypotheses`	A logical vector indicating which hypotheses were rejected based on the specified significance level.

Examples

library(MASS)
library(mvtnorm)  # Add this line to load the mvtnorm package
set.seed(100)
p <- 400
n <- 120
K <- 5
B <- matrix(rnorm(p * K), nrow = p, ncol = K)
mu <- c(rep(1, 100), rep(0, p - 100))
FX <- MASS::mvrnorm(n, rep(0, K), diag(K))
U <- mvtnorm::rmvt(n, df = 3, sigma = diag(p))  # Use mvtnorm::rmvt
X <- rep(1, n) %*% t(mu) + FX %*% t(B) + U

# Now we can call the function with the simulated data
results <- ttestTFM(X, p, alpha = 0.05)
print(results)
library(MASS)
library(mvtnorm)  # Add this line to load the mvtnorm package
set.seed(100)
p <- 400
n <- 120
K <- 5
B <- matrix(rnorm(p * K), nrow = p, ncol = K)
mu <- c(rep(1, 100), rep(0, p - 100))
FX <- MASS::mvrnorm(n, rep(0, K), diag(K))
U <- mvtnorm::rmvt(n, df = 3, sigma = diag(p))  # Use mvtnorm::rmvt
X <- rep(1, n) %*% t(mu) + FX %*% t(B) + U

# Now we can call the function with the simulated data
results <- ttestTFM(X, p, alpha = 0.05)
print(results)

The TFM function is to generate Truncated factor model data.

Description

The TFM function generates truncated factor model data supporting various distribution types for related analyses using multiple methods.

Usage

TFM(n, mu, sigma, lower, upper, distribution_type)
TFM(n, mu, sigma, lower, upper, distribution_type)

Arguments

`n`	Total number of observations.
`mu`	The mean of the distribution.
`sigma`	The parameter of the distribution.
`lower`	The lower bound of the interval.
`upper`	The upper bound of the interval.
`distribution_type`	String specifying the distribution type to use.

Value

A list containing:

`X`	A matrix of generated truncated factor model data based on the specified distribution type. Each row corresponds to an observation, and each column corresponds to a variable.

Examples

library(relliptical)
set.seed(123)
mu <- c(0, 1)
n <- 100
sigma <- matrix(c(1, 0.70, 0.70, 3), 2, 2)
lower <- c(-2, -3)
upper <- c(3, 3)
distribution_type <- "truncated_normal"
X <- TFM(n, mu, sigma, lower, upper, distribution_type)
library(relliptical)
set.seed(123)
mu <- c(0, 1)
n <- 100
sigma <- matrix(c(1, 0.70, 0.70, 3), 2, 2)
lower <- c(-2, -3)
upper <- c(3, 3)
distribution_type <- "truncated_normal"
X <- TFM(n, mu, sigma, lower, upper, distribution_type)

Package 'TFM'

Help Index

Incremental Principal Component Analysis

Description

Usage

Arguments

Value

Examples

Projected Principal Component Analysis

Description

Usage

Arguments

Value

Examples

Stochastic Approximation Principal Component Analysis

Description

Usage

Arguments

Value

Examples

Sparse Online Principal Component Analysis

Description

Usage

Arguments

Value

Examples

Sparse Principal Component Analysis

Description

Usage

Arguments

Value

Examples

T-test for Truncated Factor Model

Description

Usage

Arguments

Value

Examples

The TFM function is to generate Truncated factor model data.

Description

Usage

Arguments

Value

Examples