COMMA_PVW_bootstrap_SE function

Estimate Bootstrap Standard Errors using PVW

COMMA_PVW_bootstrap_SE(
  parameter_estimates,
  sigma_estimate,
  n_bootstrap,
  n_parallel,
  outcome_distribution,
  interaction_indicator,
  x_matrix,
  z_matrix,
  c_matrix,
  tolerance = 1e-07,
  max_em_iterations = 1500,
  em_method = "squarem",
  random_seed = NULL
)

Arguments

• parameter_estimates: A column matrix of $\beta$, $\gamma$, and $\theta$ parameter values obtained from a COMMA analysis function. Parameter estimates should be supplied in the following order: 1) $\beta$

  (intercept, slope), 2) $\gamma$ (intercept and slope from the M = 1 mechanism, intercept and slope from the M = 2 mechanism), and 3) $\theta$

  (intercept, slope, coefficient for x, slope coefficient for m, slope coefficient for c, and, optionally, slope coefficient for xm if using).

• sigma_estimate: A numeric value specifying the estimated standard deviation. This value is only required if outcome_distribution

  is "Normal". Default is 1. For non-Normal outcome distributions, the value should be NULL.

• n_bootstrap: A numeric value specifying the number of bootstrap samples to draw.

• n_parallel: A numeric value specifying the number of parallel cores to run the computation on.

• outcome_distribution: A character string specifying the distribution of the outcome variable. Options are "Bernoulli", "Normal", or "Poisson".

• interaction_indicator: A logical value indicating if an interaction between x and m should be used to generate the outcome variable, y.

• x_matrix: A numeric matrix of predictors in the true mediator and outcome mechanisms. x_matrix should not contain an intercept and no values should be NA.

• z_matrix: A numeric matrix of covariates in the observation mechanism. z_matrix should not contain an intercept and no values should be NA.

• c_matrix: A numeric matrix of covariates in the true mediator and outcome mechanisms. c_matrix should not contain an intercept and no values should be NA.

• tolerance: A numeric value specifying when to stop estimation, based on the difference of subsequent log-likelihood estimates. The default is 1e-7.

• max_em_iterations: A numeric value specifying when to stop estimation, based on the difference of subsequent log-likelihood estimates. The default is 1e-7.

• em_method: A character string specifying which EM algorithm will be applied. Options are "em", "squarem", or "pem". The default and recommended option is "squarem".

• random_seed: A numeric value specifying the random seed to set for bootstrap sampling. Default is NULL.

Returns

COMMA_PVW_bootstrap_SE returns a list with two elements: 1) bootstrap_df and 2) bootstrap_SE. bootstrap_df is a data frame containing COMMA_PVW output for each bootstrap sample. bootstrap_SE

is a data frame containing bootstrap standard error estimates for each parameter.

Examples

set.seed(20240709)
sample_size <- 2000

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)
                           
beta_start <- matrix(rep(1, 3), ncol = 1)
gamma_start <- matrix(rep(1, 4), nrow = 2, ncol = 2)
theta_start <- matrix(rep(1, 4), ncol = 1)

Mstar = example_data[["obs_mediator"]]
outcome = example_data[["outcome"]]
x_matrix = example_data[["x"]]
z_matrix = example_data[["z"]]
c_matrix = example_data[["c"]]
                           
PVW_results <- COMMA_PVW(Mstar, outcome, outcome_distribution = "Bernoulli",
                         interaction_indicator = FALSE,
                         x_matrix, z_matrix, c_matrix,
                         beta_start, gamma_start, theta_start)

PVW_results

PVW_SEs <- COMMA_PVW_bootstrap_SE(PVW_results$Estimates, 
                                  sigma_estimate = NULL,
                                  n_bootstrap = 3,
                                  n_parallel = 1,
                                  outcome_distribution = "Bernoulli",
                                  interaction_indicator = FALSE,
                                  x_matrix, z_matrix, c_matrix,
                                  random_seed = 1)
                                  
PVW_SEs$bootstrap_SE