Generate two-dimensional partially observed functional data

Simulates a scalar response together with partially observed functional surfaces. The response is built from the integral of each surface against a fixed coefficient surface, and a rectangular region of each surface can be left unobserved.

Usage

data_generator_po_2d(
  n = 100,
  grid_x = 20,
  grid_y = 20,
  intercept = 0.6,
  noise_sd = 0.25,
  response_type = c("binomial", "gaussian"),
  signal_strength = 2.5,
  beta_index = 1,
  n_missing = 0,
  min_distance_x = NULL,
  min_distance_y = NULL,
  verbose = FALSE
)

Arguments

n

Number of surfaces to generate.

grid_x, grid_y

Number of grid points along each axis.

intercept

Model intercept. For the binomial response it is used as the target proportion of successes.

noise_sd

Standard deviation of the observation noise, relative to the standard deviation of each surface.

response_type

Response distribution, either "binomial" (the default) or "gaussian".

signal_strength

Multiplier controlling the magnitude of the true coefficient surface.

beta_index

Integer selecting the shape of the true coefficient surface, either 1 (the default, a wavy surface) or 2 (a simple inclined plane).

n_missing

Number of unobserved rectangular regions per surface (default 0, i.e. fully observed surfaces).

min_distance_x, min_distance_y

Minimum size of the unobserved regions along each axis.

verbose

If TRUE, print a short summary of the simulation. Defaults to FALSE.

Value

A list with the true surfaces (surfaces), the noisy surfaces (noisy_surfaces), the partially observed surfaces (noisy_surfaces_miss) together with the missing point information (miss_points, missing_points), the response, the true coefficient surface (beta), the grids (points_x, points_y) and additional simulation details.

Examples

set.seed(123)
sim <- data_generator_po_2d(n = 20, grid_x = 10, grid_y = 10,
                            response_type = "gaussian")
str(sim, max.level = 1)
#> List of 16
#>  $ surfaces             :List of 20
#>  $ noisy_surfaces       :List of 20
#>  $ noisy_surfaces_miss  :List of 20
#>  $ miss_points          :List of 20
#>  $ missing_points       :List of 20
#>  $ response             : num [1:20] 0.666 0.467 0.5 0.784 0.723 ...
#>  $ intercept            : num 0.6
#>  $ points_x             : num [1:10] 0 0.111 0.222 0.333 0.444 ...
#>  $ points_y             : num [1:10] 0 0.111 0.222 0.333 0.444 ...
#>  $ beta                 : num [1:10, 1:10] 0.5 1.996 2.74 2.332 0.911 ...
#>  $ stochastic_components: num [1:20, 1:2] -0.441 -1.155 -1.152 1.268 1.111 ...
#>   ..- attr(*, "dimnames")=List of 2
#>  $ functional_effects   : num [1:20] -0.0393 -0.1195 -0.1192 0.1531 0.1353 ...
#>  $ group_assignment     : num [1:20] 2 2 2 1 1 1 1 2 1 1 ...
#>  $ response_type        : chr "gaussian"
#>  $ signal_strength      : num 2.5
#>  $ diagnostics          :List of 2