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#' Percentile for the Distribution of Product of Two Normal Variables
#'
#' Generates percentiles (100 based quantiles) for the distribution of product
#' of two normal random variables and the mediated effect
#'
#' @param q quantile or value of the product
#' @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 the percentile (probability) and the
#' associated error for the distribution of product of mediated effect (two
#' normal random variables). To obtain a percentile using a specific method,
#' the argument \code{type} should be specified. The default method is
#' \code{type="dop"}, which is based on the method described by Meeker and
#' Escobar (1994) to evaluate the CDF of the distribution of product of two
#' normal random variables. \code{type="MC"} uses the Monte Carlo approach
#' (Tofighi & MacKinnon, 2011). \code{type="all"} prints percentiles 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{p}{probability (percentile) corresponding to
#' quantile \code{q}} \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
#' pprodnormal(q=0, mu.x=.5, mu.y=.3, se.x=1, se.y=1, rho= 0, type="all")
#' @export
pprodnormal<- function(q, mu.x, mu.y, se.x=1, se.y=1, rho=0, lower.tail=TRUE, type="dop", n.mc=1e5){
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")
{
p2 <- pprodnormalMeeker(q, mu.x, mu.y, se.x, se.y, rho, lower.tail)
##cat("Monte Carlo method:\n")
p3 <- pprodnormalMC(q, mu.x, mu.y, se.x, se.y, rho, lower.tail, n.mc)
res <- list(p2,p3)
names(res) <- c( "Distribution of Product", "Monte Carlo")
return(res)
}
else if (type=="DOP" || type=="dop")
{
##cat("Meeker method:\n")
p2 <- pprodnormalMeeker(q, mu.x, mu.y, se.x, se.y, rho, lower.tail)
return(p2)
}
else if (type=="MC" || type=="mc" || type=="Mc")
{
##cat("Monte Carlo method:\n")
p3 <- pprodnormalMC(q, mu.x, mu.y, se.x, se.y, rho, lower.tail, n.mc)
return(p3)
}
else stop("Wrong type! please specify type=\"all\", \"DOP\", or \"MC\" ")
}
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