# Extrapolate coverage and width using sub-sampled bootstrap confidence intervals. Given a set of bootstrap confidence intervals calculated across sub-samples with different numbers of replications, extrapolates confidence interval coverage and width of bootstrap confidence intervals to a specified (larger) number of bootstraps. The function also calculates the associated Monte Carlo standard errors. The confidence interval percentage is based on how you calculated the lower and upper bounds. ```r extrapolate_rejection( data, pvalue_subsamples, B_target = Inf, alpha = 0.05, nested = FALSE, format = "wide" ) ``` ## Arguments - `data`: data frame or tibble containing the simulation results. - `pvalue_subsamples`: list or name of column from `data` containing list of confidence intervals calculated based on sub-samples with different numbers of replications. - `B_target`: number of bootstrap replications to which the criteria should be extrapolated, with a default of `B = Inf`. - `alpha`: scalar or vector indicating the nominal alpha level(s). Default value is set to the conventional .05. - `nested`: logical value controlling the format of the output. If `FALSE` (the default), then the results will be returned as a data frame with rows for each distinct number of bootstraps. If `TRUE`, then the results will be returned as a data frame with a single row, with each performance criterion containing a nested data frame. - `format`: character string controlling the format of the output when `CI_subsamples` has results for more than one type of confidence interval. If `"wide"` (the default), then each performance criterion will have a separate column for each CI type. If `"long"`, then each performance criterion will be a single variable, with separate rows for each CI type. ## Returns A tibble containing the number of simulation iterations, performance criteria estimate(s) and the associated MCSE. ## Examples ```r # function to generate data from two distinct populations dgp <- function(N_A, N_B, shape_A, scale_A, shape_B, scale_B) { data.frame( group = rep(c("A","B"), c(N_A, N_B)), y = c( rgamma(N_A, shape = shape_A, scale = scale_A), rgamma(N_B, shape = shape_B, scale = scale_B) ) ) } # function to do a bootstrap t-test estimator <- function( dat, B_vals = c(49,59,89,99), # number of booties to evaluate pval_reps = 4L ) { stat <- t.test(y ~ group, data = dat)$statistic # create bootstrap replications under the null of no difference boot_dat <- dat booties <- replicate(max(B_vals), { boot_dat$group <- sample(dat$group) t.test(y ~ group, data = boot_dat)$statistic }) # calculate multiple bootstrap p-values using sub-sampling of replicates res <- data.frame(stat = stat) res$pvalue_subsamples <- bootstrap_pvals( boot_stat = booties, stat = stat, B_vals = B_vals, reps = pval_reps, enlist = TRUE ) res } # create simulation driver simulate_boot_pvals <- bundle_sim( f_generate = dgp, f_analyze = estimator ) # replicate the bootstrap process x <- simulate_boot_pvals( reps = 50L, N_A = 20, N_B = 25, shape_A = 7, scale_A = 2, shape_B = 4, scale_B = 3, B_vals = c(49, 99, 149, 199), pval_reps = 2L ) extrapolate_rejection( data = x, pvalue_subsamples = pvalue_subsamples, B_target = 1999, alpha = c(.01, .05, .10) ) extrapolate_rejection( data = x, pvalue_subsamples = pvalue_subsamples, B_target = Inf, alpha = c(.01, .05, .10), nested = TRUE ) ``` ## References \insertRef boos2000MonteCarloEvaluationsimhelpers

extrapolate_rejection function