Generate Data to use in COMMA Functions

Usage

COMMA_data(
  sample_size,
  x_mu,
  x_sigma,
  z_shape,
  c_shape,
  interaction_indicator,
  outcome_distribution,
  true_beta,
  true_gamma,
  true_theta
)

Arguments

sample_size: An integer specifying the sample size of the generated data set.
x_mu: A numeric value specifying the mean of x predictors generated from a Normal distribution.
x_sigma: A positive numeric value specifying the standard deviation of x predictors generated from a Normal distribution.
z_shape: A positive numeric value specifying the shape parameter of z predictors generated from a Gamma distribution.
c_shape: A positive numeric value specifying the shape parameter of c covariates generated from a Gamma distribution.
interaction_indicator: A logical value indicating if an interaction between x and m should be used to generate the outcome variable, y.
outcome_distribution: A character string specifying the distribution of the outcome variable. Options are "Bernoulli", "Normal", or "Poisson".
true_beta: A column matrix of \(\beta\) parameter values (intercept, slope) to generate data under in the true mediator mechanism.
true_gamma: A numeric matrix of \(\gamma\) parameters to generate data in the observed mediator mechanisms. In matrix form, the gamma matrix rows correspond to intercept (row 1) and slope (row 2) terms. The gamma parameter matrix columns correspond to the true mediator categories \(M \in \{1, 2\}\).
true_theta: A column matrix of \(\theta\) parameter values (intercept, slope coefficient for x, slope coefficient for m, slope coefficient for c, and, optionally, slope coefficient for xm if using) to generate data in the outcome mechanism.

Value

COMMA_data returns a list of generated data elements:

obs_mediator: A vector of observed mediator values.
true_mediator: A vector of true mediator values.
outcome: A vector of outcome values.
x: A vector of generated predictor values in the true mediator mechanism, from the Normal distribution.
z: A vector of generated predictor values in the observed mediator mechanism from the Gamma distribution.
c: A vector of generated covariates.
x_design_matrix: The design matrix for the x predictor.
z_design_matrix: The design matrix for the z predictor.
c_design_matrix: The design matrix for the c predictor.

Examples

set.seed(20240709)
sample_size <- 10000

n_cat <- 2 # Number of categories in the binary mediator

# Data generation settings
x_mu <- 0
x_sigma <- 1
z_shape <- 1
c_shape <- 1

# True parameter values (gamma terms set the misclassification rate)
true_beta <- matrix(c(1, -2, .5), ncol = 1)
true_gamma <- matrix(c(1, 1, -.5, -1.5), nrow = 2, byrow = FALSE)
true_theta <- matrix(c(1, 1.5, -2, -.2), ncol = 1)

example_data <- COMMA_data(sample_size, x_mu, x_sigma, z_shape, c_shape,
                           interaction_indicator = FALSE,
                           outcome_distribution = "Bernoulli",
                           true_beta, true_gamma, true_theta)

head(example_data$obs_mediator)
#> [1] 1 2 2 1 2 2
head(example_data$true_mediator) 
#> [1] 1 1 2 1 1 2