simple_pc_testing {HMC}

Simple plug-in test for two-sample mean comparison.

Description

Simple plug-in test for two-sample mean comparison.

Usage

simple_pc_testing(
  sample_1,
  sample_2 = NULL,
  pca_method = "sparse_pca",
  mean_method = "naive",
  num_latent_factor = 1,
  n_folds = 5,
  verbose = TRUE
)

Arguments

sample_1

Group 1 sample. Each row is a subject and each column corresponds to a feature.

sample_2

Group 2 sample. Each row is a subject and each column corresponds to a feature.

pca_method

Methods used to estimate principle component The default is "sparse_pca", using sparse PCA from package PMA. Other choices are "dense_pca"—the regular PCA; and "hard"— hard-thresholding PCA, which also induces sparsity.

mean_method

Methods used to estimate the mean vector. Default is sample mean "naive". There is also a hard-thresholding sparse estiamtor "hard".

num_latent_factor

Number of principle to be estimated/tested. Default is 1.

n_folds

Number of splits when performing cross-fitting. The default is 5, if computational time allows, you can try to set it to 10.

verbose

Print information to the console. Default is TRUE.

Value

A list of test statistics.

test_statistics

Test statistics. Each entry corresponds to the test result of one principle component.

standard_error

Estimated standard error of test_statistics_before_studentization.

test_statistics_before_studentization

Similar to test_statistics but does not have variance = 1.

split_data

Intermediate quantities needed for further assessment and interpretation of the test results.

Examples

sample_size_1 <- sample_size_2 <- 300
true_mean_1 <- matrix(c(rep(1, 10), rep(0, 90)), ncol = 1)
true_mean_2 <- matrix(c(rep(1.5, 10), rep(0, 90)), ncol = 1)
pc1 <- c(rep(1, 10), rep(0, 90))
pc1 <- pc1/norm(pc1, type = '2')

simulation_covariance <- 10 * pc1 %*% t(pc1)
simulation_covariance <- simulation_covariance + diag(1, 100)

sample_1 <- data.frame(MASS::mvrnorm(sample_size_1,
                                     mu = true_mean_1,
                                     Sigma = simulation_covariance))
sample_2 <- data.frame(MASS::mvrnorm(sample_size_2,
                                     mu = true_mean_2,
                                     Sigma = simulation_covariance))
result <- simple_pc_testing(sample_1, sample_2)
result$test_statistics
##these are test statistics. Each one of them corresponds to one PC.
summarize_pc_name(result, latent_fator_index = 1) #shows which features contribute to PC1
extract_pc(result) # extract the estimated leading PCs.