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#' Add Other p-values
#'
#' Add pvalues for the Liu and Xie and Bonferroni based
#' tests using the estimated parameter estimates and
#' corresponding standard errors.
#'
#' @param test_result The test result from mv_pn_test
#'
#' @return The same test result object with additional p-values for
#' the Liu and Xie (2021) test (liu_xie_pvalue) and the Bonferroni based
#' test (bonf_pvalue)
#' @export
#'
#' @examples
#' ## NOTE: More monte-carlo samples should be taken are taken here. This is
#' ## only done to lower computation time.
#' set.seed(10)
#' test <- mv_pn_test(data.frame(y = rnorm(100), x = rnorm(100)),
#' ic.pearson, test.control(n_peld_mc_samples = 20,
#' ts_ld_bs_samp = 20))
#' test_with_extra <- add_oth_pvals(test)
#' test_with_extra[c("pvalue", "liu_xie_pvalue", "bonf_pvalue")]
add_oth_pvals <- function(test_result) {
new_results <- test_result
zscores <- abs(test_result$param_ests / test_result$param_ses)
# Liu and Xie p-value
cauchy_pvalue <- 1 - stats::pcauchy(mean(tan((
2 * stats::pnorm(zscores) - 3/2) * pi
)))
new_results$liu_xie_pvalue <- cauchy_pvalue
# Bonferroni based p-value
bonf <- min(2 * stats::pnorm(-zscores)) * length(zscores)
new_results$bonf_pvalue <- bonf
return(new_results)
}
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