R/cor_to_ci.R

In easystats/correlation: Methods for Correlation Analysis

#' @rdname cor_to_p
#' @param correction Only used if method is 'spearman' or 'kendall'. Can be
#'   'fieller' (default; Fieller et al., 1957), 'bw' (only for Spearman) or
#'   'none'. Bonett and Wright (2000) claim their correction ('bw') performs
#'   better, though the Bishara and Hittner (2017) paper favours the Fieller
#'   correction. Both are generally very similar.
#' @export
cor_to_ci <- function(cor, n, ci = 0.95, method = "pearson", correction = "fieller", ...) {
  method <- match.arg(tolower(method), c("pearson", "kendall", "spearman"), several.ok = FALSE)

  if (method == "kendall") {
    out <- .cor_to_ci_kendall(cor, n, ci = ci, correction = correction, ...)
  } else if (method == "spearman") {
    out <- .cor_to_ci_spearman(cor, n, ci = ci, correction = correction, ...)
  } else {
    out <- .cor_to_ci_pearson(cor, n, ci = ci, ...)
  }

  out
}


# Kendall -----------------------------------------------------------------
.cor_to_ci_kendall <- function(cor, n, ci = 0.95, correction = "fieller", ...) {
  # by @tsbaguley (https://rpubs.com/seriousstats/616206)

  if (correction == "fieller") {
    tau.se <- (0.437 / (n - 4))^0.5
  } else {
    tau.se <- 1 / (n - 3)^0.5
  }

  moe <- stats::qnorm(1 - (1 - ci) / 2) * tau.se
  zu <- atanh(cor) + moe
  zl <- atanh(cor) - moe

  # Convert back to r
  ci_low <- tanh(zl)
  ci_high <- tanh(zu)

  list(CI_low = ci_low, CI_high = ci_high)
}


# Spearman -----------------------------------------------------------------
.cor_to_ci_spearman <- function(cor, n, ci = 0.95, correction = "fieller", ...) {
  # by @tsbaguley (https://rpubs.com/seriousstats/616206)

  if (correction == "fieller") {
    zrs.se <- (1.06 / (n - 3))^0.5
  } else if (correction == "bw") {
    zrs.se <- ((1 + (cor^2) / 2) / (n - 3))^0.5
  } else {
    zrs.se <- 1 / (n - 3)^0.5
  }

  moe <- stats::qnorm(1 - (1 - ci) / 2) * zrs.se

  zu <- atanh(cor) + moe
  zl <- atanh(cor) - moe

  # Convert back to r
  ci_low <- tanh(zl)
  ci_high <- tanh(zu)

  list(CI_low = ci_low, CI_high = ci_high)
}


# Pearson -----------------------------------------------------------------
.cor_to_ci_pearson <- function(cor, n, ci = 0.95, ...) {
  z <- atanh(cor)
  se <- 1 / sqrt(n - 3) # Sample standard error

  # CI
  alpha <- 1 - (1 - ci) / 2
  ci_low <- z - se * stats::qnorm(alpha)
  ci_high <- z + se * stats::qnorm(alpha)

  # Convert back to r
  ci_low <- tanh(ci_low)
  ci_high <- tanh(ci_high)

  list(CI_low = ci_low, CI_high = ci_high)
}