Data simulation

Simulates a predictor matrix, an effect vector and a response vector. The simulated datasets can be used for modelling a response based on grouped and correlated primary and auxiliary predictors.

Usage

simulate_data(
  n0 = 50L,
  n1 = 20L,
  p = 30L,
  q = 10L,
  family = "gaussian",
  rho_between = 0,
  rho_within = 0.5,
  prob_primary = 0.5,
  prob_group = 0.5,
  prob_predictor = 0.8,
  signal_strength = 1,
  seed = 1L
)

Arguments

n0

number of training observations: positive integer scalar (minimum 1, maximum \(10\,000\))

n1

number of testing observations: non-negative integer scalar (minimum 0, maximum \(100\,000\))

p

number of predictors: positive integer scalar (minimum 1 leads to a single predictor, maximum \(1\,000\))

q

number of predictor groups: positive integer scalar (minimum 1 assigns all predictors to the same group. maximum p assigns each predictor to its own group)

family

character string "gaussian", "binomial", "poisson", or "cox"

rho_between

correlation coefficient for predictors in different groups: positive numeric scalar in the unit interval (minimum 0 leads to uncorrelated predictors between groups, maximum rho_within leads to same correlation between and within groups)

rho_within

correlation coefficient for predictors within the same group: positive numeric scalar in the unit interval (minimum 0 leads to uncorrelated predictors within each group, maximum 1 leads to identical predictors within each group)

prob_primary

probability for each predictor to be primary (rather than auxiliary): numeric scalar in the unit interval (minimum 0 leads to auxiliary predictors only, maximum 1 leads to primary predictors only)

prob_group

probability for each predictor group to be active: numeric scalar in the unit interval (minimum 0 makes all groups inactive, maximum 1 makes all groups active)

prob_predictor

probability for each predictor in an active group to be active: numeric scalar in the unit interval (minimum 0 makes all predictors inactive, maximum 1 makes all predictors in active groups active)

signal_strength

non-negative numeric scalar for multiplying the effect sizes (default: signal_strength=1.0, minimum 0 sets all effect sizes to 0, maximum 2 to avoid undefined values)

seed

random seed for reproducibility: integer scalar (unrestricted)

Value

Returns a named list with the following slots:

• x_train: predictor matrix of the training observations (\(n_0\) rows, \(p\) columns)

• y_train: response vector of the training observations (length \(n_0\))

• group: integer vector indicating the group of the predictors (length \(p\))

• primary: logical vector indicating primary (TRUE) and auxiliary (FALSE) predictors (length \(p\))

• beta: numeric vector of the effects of the predictors on the response (length \(p\))

• x_test: \(n_1 \times p\) predictor matrix for the test observations

• y_test: response vector for the test observations of length \(n_1\)

Details

Use the objects x_train, y_train, group, and primary for model training. Estimated coefficients can be compared with beta.

Use the object x_test for model testing. Predicted values can be compared with y_test.

Training and testing observations are named train_ or test_, respectively, followed by a number indexing the observations (e.g., train_1 or test_1).

Primary and auxiliary predictors are named pri_ or aux_, respectively, followed by a number indexing the predictor groups, a point, and a number indexing the predictors within this group (e.g., pri_1.1 or aux_1.1).

See also

This function calls the internal functions .simulate_predictors(), .simulate_effects(), and .simulate_response() for simulating the predictor matrix, the effect vector, or the response vector, respectively.

Examples

data <- simulate_data(n0 = 50L, n1 = 20L, p = 30L, q = 10L,
                     family = "gaussian", rho_between = 0.0,
                     rho_within = 0.5, prob_primary = 0.5,
                     signal_strength = 1.0, prob_group = 0.5,
                     prob_predictor = 0.8, seed = 1L)
utils::str(data, vec.len = 2L)
#> List of 7
#>  $ x_train: num [1:50, 1:30] 0.266 -1.91 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:50] "train_1" "train_2" ...
#>   .. ..$ : chr [1:30] "aux_1.1" "aux_1.2" ...
#>  $ y_train: Named num [1:50] -0.761 -1.743 ...
#>   ..- attr(*, "names")= chr [1:50] "train_1" "train_2" ...
#>  $ group  : Named int [1:30] 1 1 1 2 2 ...
#>   ..- attr(*, "names")= chr [1:30] "aux_1.1" "aux_1.2" ...
#>  $ primary: Named logi [1:30] FALSE FALSE TRUE ...
#>   ..- attr(*, "names")= chr [1:30] "aux_1.1" "aux_1.2" ...
#>  $ beta   : Named num [1:30] 0 0 0 0 0 ...
#>   ..- attr(*, "names")= chr [1:30] "aux_1.1" "aux_1.2" ...
#>  $ x_test : num [1:20, 1:30] NA NA NA NA NA ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:20] "test_1" "test_2" ...
#>   .. ..$ : chr [1:30] "aux_1.1" "aux_1.2" ...
#>  $ y_test : Named num [1:20] -4.52 -2.65 ...
#>   ..- attr(*, "names")= chr [1:20] "test_1" "test_2" ...