TFM (version 0.3.0)

ttest.TFM: 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

ttest.TFM(X, p, alpha = 0.05)

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.

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.

Examples

# Load necessary libraries
library(MASS)
library(mvtnorm)

set.seed(100)
# Set parameters for the simulation
p <- 400  # Number of features
n <- 120  # Number of samples
K <- 5    # Number of latent factors
true_non_zero <- 100  # Assume 100 features have non-zero means

# Simulate factor loadings matrix B (p x K)
B <- matrix(rnorm(p * K), nrow = p, ncol = K)

# Simulate factor scores (n x K)
FX <- MASS::mvrnorm(n, rep(0, K), diag(K))

# Simulate noise U (n x p), assuming Student's t-distribution with 3 degrees of freedom
U <- mvtnorm::rmvt(n, df = 3, sigma = diag(p))

# Create the data matrix X based on the truncated factor model
# Non-zero means for the first 100 features
mu <- c(rep(1, true_non_zero), rep(0, p - true_non_zero))
X <- rep(1, n) %*% t(mu) + FX %*% t(B) + U  # The observed data

# Apply the t-test function on the data
results <- ttest.TFM(X, p, alpha = 0.05)

# Print the results
print(results)