Two-Sample Covariance Test by Cai, Liu and Xia (2013)

Description

Given two sets of data matrices X and Y, where X is an n_1 \times p matrix and Y is an n_2 \times p matrix, this function conducts a hypothesis test for the equality of two covariance matrices. The null hypothesis is

H_0 : \Sigma_1 = \Sigma_2,

where \Sigma_1 and \Sigma_2 are the covariance matrices of X and Y, respectively. The test is based on the method proposed by Cai, Liu and Xia (2013). When the p-value is smaller than the significance level (usually 0.05), the null hypothesis is rejected.

Usage

CLX(X, Y, alpha = 0.05)

Arguments

Value

A list with the following components:

Examples

p <- 500
n1 <- 100
n2 <- 150
X <- matrix(rnorm(n1 * p), ncol = p)
Y <- matrix(rnorm(n2 * p), ncol = p)
CLX(X, Y, alpha = 0.05)

Chinese Herbal Tea Consumer Survey Data

Description

A questionnaire survey on consumers' perceptions and intentions regarding Chinese herbal tea (CHT). The dataset is used in the real-data analysis for covariance-based hypothesis testing and related factor-structure exploration.

Usage

Chinese_Herbal_Tea

Format

A data frame with 723 rows and 15 variables:

a1_price_reasonable

Perceived price reasonableness of Chinese herbal tea products (Likert 5-point; 1 = strongly disagree, 5 = strongly agree).

a2_brand_awareness

Perceived brand awareness/familiarity influencing evaluation or purchase intention (Likert 5-point).

a3_packaging_appeal

Perceived attractiveness of packaging/appearance (Likert 5-point).

a4_taste_flavor

Perceived taste and flavor satisfaction (Likert 5-point).

b1_nutrition_value

Perceived nutritional value (Likert 5-point). Note: a rare value -2 appears and is recommended to be recoded to NA.

b2_safety_assurance

Perceived safety assurance (e.g., ingredient safety, quality control) (Likert 5-point).

b3_health_benefit

Perceived health benefits (Likert 5-point).

c1_celebrity_endorsement

Influence of celebrity endorsement on purchase/consumption intention (Likert 5-point).

c2_ip_collaboration

Influence of IP/brand collaborations (co-branding) on purchase/consumption intention (Likert 5-point).

c3_tcm_institution_collab

Influence of collaboration with traditional Chinese medicine (TCM) institutions/organizations on purchase/consumption intention (Likert 5-point).

c4_discount_promotion

Influence of discounts and promotions on purchase/consumption intention (Likert 5-point).

q26_gov_support_increases_willingness

Agreement that government support/policies would increase willingness to purchase/consume Chinese herbal tea (Likert 5-point).

q27_future_purchase_intent

Future purchase/consumption intention (Likert 5-point).

q28_future_recommend_intent

Future intention to recommend Chinese herbal tea to others (Likert 5-point).

q29_satisfaction

Overall satisfaction with Chinese herbal tea products/experience (Likert 5-point).

Details

Most variables are measured on a 5-point Likert scale (coded as integers 1–5), where larger values indicate stronger agreement/more positive evaluation. One variable contains a rare special code (-2) that should be treated as missing/invalid in downstream analysis.

Source

Consumer survey dataset on Chinese herbal tea perceptions, marketing influences, and behavioral intentions.

Apply the FanPC method to the Truncated 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_TFM(data, m, A, D, p)

Arguments

Value

A list containing:

Examples

library(SOPC)
library(MASS)
set.seed(123)
p <- 10  
m <- 3   
n <- 50  
A <- matrix(rnorm(p * m), nrow = p, ncol = m)
D <- diag(runif(p, 0.2, 0.8))
F_mat <- matrix(rnorm(n * m), nrow = n, ncol = m)
E_mat <- MASS::mvrnorm(n, mu = rep(0, p), Sigma = D)
simulated_data <- F_mat %*% t(A) + E_mat
results <- FanPC_TFM(data = simulated_data, m = m, A = A, D = D, p = p)
print(results)

Daily Google Stock Data

Description

Daily OHLCV data for Google (ticker: GOOG) from 2018-01-01 to 2020-12-31, split-adjusted.

Usage

GOOG

Format

A data frame with 756 rows and 10 variables:

open, high, low, close

Raw OHLC prices (USD)

adjOpen, adjHigh, adjLow, adjClose

Split-adjusted OHLC prices (USD)

volume

Raw trading volume (shares)

adjVolume

Split-adjusted trading volume (shares)

Source

https://finance.yahoo.com/

Two-Sample Covariance Test by Li and Chen (2012)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is:

Usage

LC(X, Y, delta_sigma = NULL, alpha = 0.05)

Arguments

Details

H_0 : \Sigma_1 = \Sigma_2

\Sigma_1 and \Sigma_2 are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Li and Chen (2012). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Value

Examples

p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
LC(X,Y)

Truncated Factor Model Data Generator

Description

The TFM function generates truncated factor model data using methods implemented in the tmvtnorm package. It currently supports truncated multivariate normal and truncated multivariate Student-t distributions.

Usage

TFM(n, mu, sigma, lower, upper, distribution_type, df = 4)

Arguments

Value

A matrix containing the generated truncated factor model data.

Examples

set.seed(123)
n <- 100
mu <- c(0, 1)
sigma <- matrix(c(1, 0.7, 0.7, 3), 2, 2)
lower <- c(-2, -3)
upper <- c(3, 3)
X_norm <- TFM(n, mu, sigma, lower, upper,
              distribution_type = "truncated_normal")
X_t <- TFM(n, mu, sigma, lower, upper,
           distribution_type = "truncated_student", df = 5)

Admission Prediction Data

Description

A dataset containing parameters relevant to graduate admission prediction.

Usage

admission_predict

Format

A data frame representing student profiles.

One-Sample Covariance Test by Cai and Ma (2013)

Description

Given a data matrix, this function performs a one-sample test for the covariance matrix. The null hypothesis is

H_0 : \Sigma_n = \Sigma_0,

where \Sigma_n is the covariance matrix of the data and \Sigma_0 is a hypothesized covariance matrix. The test procedure is based on the method proposed by Cai and Ma (2013).

Usage

cm13(X, Sigma0, alpha)

Arguments

Value

A named list with the following components:

statistic

The test statistic.

threshold

The rejection threshold for the test.

reject

Logical; TRUE if the null hypothesis is rejected, and FALSE otherwise.

Examples

p <- 5
n <- 10
X <- matrix(rnorm(n * p), ncol = p)
alpha <- 0.05
Sigma0 <- diag(ncol(X))
cm13(X, Sigma0, alpha)

Concrete Compressive Strength

Description

Data about the compressive strength of concrete based on its ingredients and age.

Usage

concrete

Format

A data frame with component details and strength values.

New Energy Vehicle Purchase Intention Survey Data

Description

A questionnaire survey on consumers' purchase intention toward new energy vehicles (NEVs) and its influencing factors. The dataset includes (i) household vehicle purchase history, (ii) attitudes toward policy/product/economic/firm factors measured on a 5-point Likert scale, and (iii) demographic information.

Usage

new_energy_vehicle

Format

A data frame with 520 rows and multiple variables:

household_ice_owned

Whether the household has purchased an internal-combustion (fuel) vehicle (single choice).

household_nev_owned

Whether the household has purchased a new energy vehicle (single choice).

policy_subsidy_intention

Effect of subsidy policies (e.g., toll exemptions, lower purchase price, low-interest loans) on NEV purchase intention (Likert 5-point).

policy_license_intention

Effect of license-plate policies (e.g., free registration, road-restriction privileges) on NEV purchase intention (Likert 5-point).

environmental_intention

Effect of environmental concerns on NEV purchase intention (Likert 5-point).

infrastructure_intention

Effect of charging infrastructure convenience on NEV purchase intention (Likert 5-point).

driving_experience_factor

Effect of driving experience (product factor) on NEV purchase intention (Likert 5-point).

battery_performance_factor

Effect of battery performance (range, lifespan, capacity, charging efficiency) on NEV purchase intention (Likert 5-point).

safety_factor

Effect of safety and technology maturity/reliability on NEV purchase intention (Likert 5-point).

depreciation_cost_factor

Effect of depreciation/durability concerns (economic factor) on NEV purchase intention (Likert 5-point).

purchase_cost_factor

Effect of purchase price (economic factor) on NEV purchase intention (Likert 5-point).

charging_cost_factor

Effect of charging cost (economic factor) on NEV purchase intention (Likert 5-point).

maintenance_cost_factor

Effect of maintenance/repair cost (economic factor) on NEV purchase intention (Likert 5-point).

service_factor

Effect of firm service (pre-sales and after-sales) on NEV purchase intention (Likert 5-point).

brand_factor

Effect of brand (firm factor) on NEV purchase intention (Likert 5-point).

technology_advantage_factor

Effect of perceived technological advantages (firm factor) on NEV purchase intention (Likert 5-point).

purchase_intent

Stated intention to purchase an NEV (Likert 5-point).

recommend_intent

Willingness to recommend NEVs to others (Likert 5-point).

repurchase_intent

Willingness to prioritize buying an NEV next time (Likert 5-point).

gender

Gender (single choice).

age

Age group (single choice).

education

Education level (single choice).

occupation

Occupation (single choice).

hukou

Household registration type (rural/urban; single choice).

household_income

Average monthly household income (categorical; single choice).

Details

The Likert scale options are: A = Strongly disagree, B = Disagree, C = Neutral, D = Agree, E = Strongly agree.

Source

Consumer survey dataset on NEV purchase intention and influencing factors.

Data Frame 'protein'

Description

This is the Protein Data Set from the UCI Machine Learning Repository. It contains information about protein concentration in different samples.

Usage

protein

Format

A data frame with 45730 rows and 10 columns.

• SampleID: A unique identifier for each sample.

• Protein1: Concentration of Protein 1.

• Protein2: Concentration of Protein 2.

• Protein3: Concentration of Protein 3.

• Protein4: Concentration of Protein 4.

• Protein5: Concentration of Protein 5.

• Protein6: Concentration of Protein 6.

• Protein7: Concentration of Protein 7.

• Protein8: Concentration of Protein 8.

• Protein9: Concentration of Protein 9.

• Protein10: Concentration of Protein 10.

Real Estate Valuation

Description

Historical market data of real estate valuation.

Usage

real_estate_valuation

Format

A data frame with property attributes and price.

Travel Review Dataset

Description

This dataset contains travel reviews from TripAdvisor.com, covering destinations in 10 categories across East Asia. Each traveler's rating is mapped to a scale from Terrible (0) to Excellent (4), and the average rating for each category per user is provided.

Usage

data(review)

Format

A data frame with multiple rows and 10 columns.

1

Unique identifier for each user (Categorical)

2

Average user feedback on art galleries

3

Average user feedback on dance clubs

4

Average user feedback on juice bars

5

Average user feedback on restaurants

6

Average user feedback on museums

7

Average user feedback on resorts

8

Average user feedback on parks and picnic spots

9

Average user feedback on beaches

10

Average user feedback on theaters

Details

The dataset is populated by crawling TripAdvisor.com and includes reviews on destinations in 10 categories across East Asia. Each traveler's rating is mapped as follows:

• Excellent (4)

• Very Good (3)

• Average (2)

• Poor (1)

• Terrible (0)

The average rating for each category per user is used.

Note

This dataset is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Source

UCI Machine Learning Repository

Examples

# Load the dataset
data(review)

# Print the first few rows
head(review)

# Access specific columns (note the backticks for numeric names)
review$`1`  # User IDs
mean(review$`5`)  # Average rating for restaurants

Riboflavin Production Data

Description

This dataset contains measurements of riboflavin (vitamin B2) production by Bacillus subtilis, a Gram-positive bacterium commonly used in industrial fermentation processes. The dataset includes n = 71 observations with p = 4088 predictors, representing the logarithm of the expression levels of 4088 genes. The response variable is the log-transformed riboflavin production rate.

Usage

data(riboflavin)

Format

y

Log-transformed riboflavin production rate (original name: q_RIBFLV). This is a continuous variable indicating the efficiency of riboflavin production by the bacterial strain.

x

A matrix of dimension 71 \times 4088 containing the logarithm of the expression levels of 4088 genes. Each column corresponds to a gene, and each row corresponds to an observation (experimental condition or time point).

Note

The dataset is provided by DSM Nutritional Products Ltd., a leading company in the field of nutritional ingredients. The data have been preprocessed and normalized to account for technical variations in the microarray measurements.

Examples

# Load the riboflavin dataset
data(riboflavin)

# Display the dimensions of the dataset
print(dim(riboflavin$x))
print(length(riboflavin$y))

Riboflavin Production Data (Top 100 Genes)

Description

This dataset is a subset of the riboflavin production data by Bacillus subtilis, containing n = 71 observations. It includes the response variable (log-transformed riboflavin production rate) and the 100 genes with the largest empirical variances from the original dataset.

Usage

data(riboflavinv100)

Format

y

Log-transformed riboflavin production rate (original name: q_RIBFLV). This is a continuous variable indicating the efficiency of riboflavin production by the bacterial strain.

x

A matrix of dimension 71 \times 100 containing the logarithm of the expression levels of the 100 genes with the largest empirical variances.

Note

The dataset is provided by DSM Nutritional Products Ltd., a leading company in the field of nutritional ingredients. The data have been preprocessed and normalized.

Examples

# Load the riboflavinv100 dataset
data(riboflavinv100)

# Display the dimensions of the dataset
print(dim(riboflavinv100$x))
print(length(riboflavinv100$y))

One Sample Covariance Test by Srivastava, Yanagihara, and Kubokawa (2014)

Description

Given data, it performs 1-sample test for Covariance where the null hypothesis is

H_0 : \Sigma_n = \Sigma_0

where \Sigma_n is the covariance of data model and \Sigma_0 is a hypothesized covariance based on a procedure proposed by Srivastava, Yanagihara, and Kubokawa (2014).

Usage

syk(data, Sigma0, alpha)

Arguments

Value

a named list containing

statistic

a test statistic value.

threshold

rejection criterion to be compared against test statistic.

reject

a logical; TRUE to reject null hypothesis, FALSE otherwise.

Examples

p = 5;n=10
data = matrix(rnorm(n*p), ncol=p)
alpha=0.05
Sigma0=diag(ncol(data))
syk(data, Sigma0, alpha)

Taxi Trip Pricing

Description

Data recording taxi trip details and pricing.

Usage

taxi_trip_pricing

Format

A data frame with trip duration, distance, and fare.

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)

Arguments

Value

A list containing:

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)

White Wine Quality

Description

Physicochemical tests of white Portuguese "Vinho Verde" wine.

Usage

winequality.white

Format

A data frame with chemical properties and quality score.

Yacht Hydrodynamics

Description

Data concerning the hydrodynamics of sailing yachts.

Usage

yacht_hydrodynamics

Format

A data frame with hull geometry and resistance.