R/qprodnormal.R

In quantPsych/RMediation: Mediation Analysis Confidence Intervals

#' Quantile for the Distribution of Product of Two Normal Variables
#'
#' Generates quantiles for the distribution of product of two normal random
#' variables
#'
#' @param p probability
#' @param mu.x  mean of \eqn{x}
#' @param mu.y mean of \eqn{y}
#' @param se.x standard error (deviation) of \eqn{x}
#' @param se.y  standard error (deviation) of \eqn{y}
#' @param rho correlation between \eqn{x} and \eqn{y}, where -1 <\code{rho} < 1.
#'   The default value is 0.
#' @param lower.tail logical; if \code{TRUE} (default), the probability is
#'   \eqn{P[X*Y < q]}; otherwise, \eqn{P[X*Y > q]}
#' @param type method used to compute confidence interval. It takes on the
#'   values \code{"dop"} (default), \code{"MC"}, \code{"asymp"} or \code{"all"}
#' @param n.mc when \code{type="MC"}, \code{n.mc} determines the sample size for
#'   the Monte Carlo method. The default sample size is 1E5.
#' @details   This function returns a quantile and the associated error
#'   (accuracy) corresponding the requested percentile (probability) \code{p} of
#'   the distribution of product of mediated effect (product of two normal
#'   random variables). To obtain a quantile using a specific method, the
#'   argument \code{type} should be specified. The default method is
#'   \code{type="dop"}, which uses the method described by Meeker and Escobar
#'   (1994) to evaluate the CDF of the distribution of product of two normal
#'   variables. \code{type="MC"} uses the Monte Carlo approach (Tofighi &
#'   MacKinnon, 2011). \code{type="all"} prints quantiles using all three
#'   options. For the method \code{type="dop"}, the error is the modulus of
#'   absolute error for the numerical integration (for more information see
#'   Meeker and Escobar, 1994). For \code{type="MC"}, the error refers to the
#'   Monte Carlo error.
#' @return   An object of the type \code{\link{list}} that contains the
#'   following values: \item{q}{quantile corresponding to probability \code{p}}
#'   \item{error}{estimate of the absolute error}
#' @author Davood Tofighi \email{dtofighi@@gmail.com}
#' @references  Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R
#'   package for mediation analysis confidence intervals. \emph{Behavior
#'   Research Methods}, \bold{43}, 692--700. doi:10.3758/s13428-011-0076-x
#' @seealso \code{\link{medci}} \code{\link{RMediation-package}}
#' @examples
#' ## lower tail
#' qprodnormal(
#'   p = .1, mu.x = .5, mu.y = .3, se.x = 1, se.y = 1, rho = 0,
#'   lower.tail = TRUE, type = "all"
#' )
#' ## upper tail
#' qprodnormal(
#'   p = .1, mu.x = .5, mu.y = .3, se.x = 1, se.y = 1, rho = 0,
#'   lower.tail = FALSE, type = "all"
#' )
#' @export


qprodnormal <-
  function(p, mu.x, mu.y, se.x, se.y, rho = 0, lower.tail = TRUE, type = "dop", n.mc = 1e5) {
    if (p <= -1 || p >= 1) {
      stop("p must be between -1 and 1!")
    }
    if (!is.numeric(mu.x)) {
      stop("Argument mu.x must be numeric!")
    }
    if (!is.numeric(mu.y)) {
      stop("Argument mu.y must be numeric!")
    }
    if (!is.numeric(se.x)) {
      stop("Argument se.x must be numeric!")
    }
    if (!is.numeric(se.y)) {
      stop("Argument se.y must be numeric!")
    }
    if (!is.numeric(rho)) {
      stop("Argument rho  must be numeric!")
    }
    if (rho <= -1 || rho >= 1) {
      stop("rho must be between -1 and 1!")
    }
    if (!is.numeric(n.mc) || is.null(n.mc)) {
      n.mc <- 1e5
    } # sets n.mc to default

    if (type == "all" || type == "All" || type == "ALL") {
      ## cat("Meeker method:\n")
      q2 <- qprodnormalMeeker(p, mu.x, mu.y, se.x, se.y, rho, lower.tail)
      ## cat("Monte Carlo method:\n")
      q3 <- qprodnormalMC(p, mu.x, mu.y, se.x, se.y, rho, lower.tail, n.mc)
      res <- list(q2, q3)
      names(res) <- c("Distribution of Product", "Monte Carlo")
      return(res)
    } else if (type == "DOP" || type == "dop") {
      ## cat("Meeker method:\n")
      q2 <- qprodnormalMeeker(p, mu.x, mu.y, se.x, se.y, rho, lower.tail)
      return(q2)
    } else if (type == "MC" || type == "mc" || type == "Mc") {
      ## cat("Monte Carlo method:\n")
      q3 <- qprodnormalMC(p, mu.x, mu.y, se.x, se.y, rho, lower.tail, n.mc)
      return(q3)
    } else {
      stop("Wrong type! please specify type=\"all\", \"DOP\", or \"MC\" ")
    }
  }