Generate 2D functional data for simulation studies

Creates synthetic 2D functional data with optional noise components and different coefficient patterns. Uses Simpson's rule for accurate integration.

Usage

generate_2d_po_functional_data(
  n = 20,
  grid_x = 20,
  grid_y = 20,
  noise_sd = 0.015,
  rsq = 0.95,
  beta_type = c("saddle", "exp"),
  response_type = c("gaussian", "binomial"),
  a1 = NULL,
  a2 = NULL,
  sub_response = 50,
  n_missing = 1,
  min_distance_x = NULL,
  min_distance_y = NULL
)

Arguments

n

Number of samples to generate.

grid_x

Number of points in x-axis grid. Default is 20.

grid_y

Number of points in y-axis grid. Default is 20.

noise_sd

Standard deviation of measurement noise. Default is 0.015.

rsq

Desired R-squared value for the response. Default is 0.95.

beta_type

Type of coefficient surface ("saddle" or "exp"). Default is "saddle".

response_type

Type of the response variable ("gaussian" or "binomial"). Default is "gaussian".

a1

Optional fixed value for first stochastic component. If provided, a2 must also be provided.

a2

Optional fixed value for second stochastic component. If provided, a1 must also be provided.

sub_response

Number of intervals for Simpson integration. Default is 50.

n_missing

Number of holes in every curve.

min_distance_x

Length of the holes in the x axis.

min_distance_y

Length of the holes in the y axis.

Value

A list containing:

• surfaces: List of n true (noiseless) surfaces

• noisy_surfaces: List of n observed (noisy) surfaces

• response: Vector of n response values

• grid_x: x-axis grid points

• grid_y: y-axis grid points

• beta: True coefficient surface

• stochastic_components: Matrix of a1 and a2 values used for each surface