#' 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\" ")
}
}
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