# Generate Data to use in COMMA Functions ```r 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. ## Returns `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 ```r 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$obs_mediator) head(example_data$true_mediator) ```

COMMA_data function