Generate Kernel Plot

Description

Creates a scatter plot of the input vectors X and Y, and overlays a Nadaraya-Watson kernel regression curve using the specified bandwidth.

Usage

create_kernel_plot(X, Y, bandwidth = bw.nrd(X) * (length(X)^-0.1), nrows = 4)

Arguments

Value

A ggplot object containing the scatter plot(s) with the kernel regression curve(s). If a vector of bandwidths is supplied, the plots are put into a grid using faceting.

References

Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Its Applications, 9(1), 141–142.

Watson, G. S. (1964). Smooth estimates of regression functions. Sankhyā: The Indian Journal of Statistics, Series A, 359-372.

Examples

# Example 1: Basic plot on quadratic function
seed <- 42
set.seed(seed)
X <- runif(500)
Y <- X ^ 2 + rnorm(500, sd = 0.1)
plot <- create_kernel_plot(X, Y, bandwidth = bw.nrd(X) * (length(X) ^ -0.1))

A Simulated Diabetes Dataset

Description

This dataset contains simulated medical measurements for Diabetes and is emulated after data from the Diabetes Prevention Program. Each column represents change in a key metabolic indicators after two years for the placebo group receiving no treatment.

Usage

data("diabetes", package="MonotonicityTest")

Format

A data frame with 1000 rows and 4 variables:

CLDL

Change in low-density lipoprotein (LDL) cholesterol (mg/dL).

GLUCOSE

Change in fasting plasma glucose levels (mg/dL).

TRIG

Change in triglyceride levels (mg/dL).

HBA1C

Change in hemoglobin A1c levels (%).

Examples

data("diabetes", package="MonotonicityTest")
names(diabetes)

Perform Monotonicity Test

Description

Performs a monotonicity test between the vectors X and Y as described in Hall and Heckman (2000). This function uses a bootstrap approach to test for monotonicity in a nonparametric regression setting.

Usage

monotonicity_test(
  X,
  Y,
  bandwidth = bw.nrd(X) * (length(X)^-0.1),
  boot_num = 200,
  m = floor(0.05 * length(X)),
  ncores = 1,
  negative = FALSE,
  seed = NULL
)

Arguments

Details

The test evaluates the following hypotheses:

H_0: The regression function is monotonic

• Non-decreasing if negative = FALSE

• Non-increasing if negative = TRUE

H_A: The regression function is not monotonic

Value

A list with the following components:

p

The p-value of the test. A small p-value (e.g., < 0.05) suggests evidence against the null hypothesis of monotonicity.

dist

The distribution of test statistic under the null from bootstrap samples. The length of dist is equal to boot_num.

stat

The test statistic T_m calculated from the original data.

plot

A ggplot object with a scatter plot where the points of the "critical interval" are highlighted. This critical interval is the interval where T_m is greatest.

interval

Numeric vector containing the indices of the "critical interval". The first index indicates where the interval starts, and the second indicates where it ends in the sorted X vector.

Note

For large datasets (e.g., n \geq 6500) this function may require significant computation time due to having to compute the statistic for every possible interval. Consider reducing boot_num, using a subset of the data, or using parallel processing with ncores to improve performance.

In addition to this, a minimum of 300 observations is recommended for kernel estimates to be reliable.

References

Hall, P., & Heckman, N. E. (2000). Testing for monotonicity of a regression mean by calibrating for linear functions. The Annals of Statistics, 28(1), 20–39.

Examples

# Example 1: Usage on monotonic increasing function
# Generate sample data
seed <- 42
set.seed(seed)

X <- runif(500)
Y <- 4 * X + rnorm(500, sd = 1)
result <- monotonicity_test(X, Y, boot_num = 25, seed = seed)

print(result)

# Example 2: Usage on non-monotonic function
seed <- 42
set.seed(seed)

X <- runif(500)
Y <- (X - 0.5) ^ 2 + rnorm(500, sd = 0.5)
result <- monotonicity_test(X, Y, boot_num = 25, seed = seed)

print(result)