Estimate Bootstrap Standard Errors using OLS

Usage

COMMA_OLS_bootstrap_SE(
  parameter_estimates,
  sigma_estimate = 1,
  n_bootstrap,
  n_parallel,
  x_matrix,
  z_matrix,
  c_matrix,
  tolerance = 1e-07,
  max_em_iterations = 1500,
  em_method = "squarem"
)

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. Default is 1.
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.
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".

Value

COMMA_OLS_bootstrap_SE returns a list with two elements: 1) bootstrap_df and 2) bootstrap_SE. bootstrap_df is a data frame containing COMMA_OLS 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 = "Normal",
                           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"]]
                           
OLS_results <- COMMA_OLS(Mstar, outcome,
                         x_matrix, z_matrix, c_matrix,
                         beta_start, gamma_start, theta_start)
                         
OLS_results
#>    Parameter  Estimates Convergence Method
#> 1      beta1  0.8272721        TRUE    OLS
#> 2      beta2 -1.6154039        TRUE    OLS
#> 3      beta3  0.3586729        TRUE    OLS
#> 4    gamma11  1.2279060        TRUE    OLS
#> 5    gamma21  1.3535571        TRUE    OLS
#> 6    gamma12 -0.4846708        TRUE    OLS
#> 7    gamma22 -1.4126826        TRUE    OLS
#> 8     theta0  0.8900722        TRUE    OLS
#> 9    theta_m -1.9041094        TRUE    OLS
#> 10   theta_x  1.5529579        TRUE    OLS
#> 11  theta_c1  2.0215448        TRUE    OLS

OLS_SEs <- COMMA_OLS_bootstrap_SE(OLS_results$Estimates, sigma_estimate = 1,
                                  n_bootstrap = 3,
                                  n_parallel = 1,
                                  x_matrix, z_matrix, c_matrix)
                                  
OLS_SEs$bootstrap_SE
#> # A tibble: 11 × 3
#>    Parameter   Mean     SE
#>    <chr>      <dbl>  <dbl>
#>  1 beta1      0.836 0.0726
#>  2 beta2     -1.54  0.0381
#>  3 beta3      0.310 0.108 
#>  4 gamma11    1.25  0.189 
#>  5 gamma12   -0.293 0.577 
#>  6 gamma21    1.52  0.424 
#>  7 gamma22   -2.05  0.571 
#>  8 theta0     2.01  0.118 
#>  9 theta_c1   2.03  0.0255
#> 10 theta_m    1.36  0.154 
#> 11 theta_x   -1.97  0.0790