R/alphaN.R

In alphaN: Set Alpha Based on Sample Size Using Bayes Factors

#' Set the alpha level based on sample size for coefficients in a regression models.
#'
#' @param n Sample size
#' @param BF Bayes factor you would like to match. 1 to avoid Lindley's Paradox, 3 to achieve moderate evidence and 10 to achieve strong evidence.
#' @param method Used for the choice of 'b'. Currently one of:
#' \itemize{
#'   \item "JAB": this choice of b produces Jeffery's approximate BF (Wagenmakers, 2022)
#'   \item "min": uses the minimal training sample for the prior (Gu et al., 2018)
#'   \item "robust": a robust version of "min" that prevents too small b (O'Hagan, 1995)
#'   \item "balanced": this choice of b balances the type I and type II errors (Gu et al, 2016)
#' }
#' @param upper The upper limit for the range of realistic effect sizes. Only relevant when method="balanced". Defaults to 1 such that the range of realistic effect sizes is uniformly distributed between 0 and 1, U(0,1).
#' @return Numeric alpha level required to achieve the desired level of evidence.
#' @export
#'
#' @examples
#'# Plot of alpha level as a function of n
#'seqN <- seq(50, 1000, 1)
#'plot(seqN, alphaN(seqN), type = "l")
#' @section References:
#' Gu et al. (2016). Error probabilities in default Bayesian hypothesis testing. Journal of Mathematical Psychology, 72, 130–143. \cr
#' \cr
#' Gu et al. (2018). Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses. The British Journal of Mathematical and Statistical Psychology, 71(2). \cr
#' \cr
#' O’Hagan, A. (1995). Fractional Bayes Factors for Model Comparison. Journal of the Royal Statistical Society. Series B (Methodological), 57(1), 99–138. \cr
#' \cr
#' Wagenmakers (2002). Approximate Objective Bayes Factors From PValues and Sample Size: The 3pn Rule. psyarxiv. \cr
#' \cr
#' Wulff & Taylor (2023). How and why alpha should depend on sample size: A Bayesian-frequentist compromise for significance testing. PsyArXiv.
#' @importFrom stats pchisq pt integrate
alphaN <- function(n, BF=1, method="JAB", upper = 1) {
  if(method=="JAB") {b <- 1/n}
  if(method=="min") {b <- 2/n}
  if(method=="robust") {b <- max(2/n, 1/sqrt(n))}
  if(method=="balanced") {
    b <- max(2/n, min(0.5,
                      integrate(function(x) exp(-n*x^2/4), lower=0, upper=upper)$value))
  }

  alpha <- 1-pchisq(2*log(BF/sqrt(b)), 1)
  return(alpha)
}