RMediation (version 1.1.3)

pprodnormal: Percentile for the Distribution of Product of Two Normal Variables

Description

Generates percentiles (100 based quantiles) for the distribution of product of two normal random variables and the mediated effect

Usage

pprodnormal(q, mu.x, mu.y, se.x=1, se.y=1, rho = 0, lower.tail=TRUE,
type="prodclin", n.mc=1e5)

Arguments

q

quantile or value of the product

mu.x

mean of $x$

mu.y

mean of $y$

se.x

standard error (deviation) of $x$

se.y

standard error (deviation) of $y$

rho

correlation between $x$ and $y$, where -1 < rho < 1. The default value is 0.

lower.tail

logical; if TRUE (default), the probability is $P[X*Y < q]$; otherwise, $P[X*Y > q]$

type

method used to compute $P[X*Y < q]$. It takes on the values "prodclin" (default), "DOP", "MC", or "all".

n.mc

when type="MC", n.mc determines the sample size for the Monte Carlo method. The default sample size is 1E5.

Value

• An object of the type list that contains the following values:
• p
  probability (percentile) corresponding to quantile q
• error
  estimate of the absolute error

concept

• mediation
• mediated effect
• distribution of mediated effect
• distribution of product
• prodclin

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 type should be specified. The default method is type="prodclin", which uses the PRODCLIN program described by MacKinnon et al. (2007). type="DOP" uses the code we wrote in R. Note that both type="prodclin" and type="DOP" use the method described by Meeker and Escobar (1994) to evaluate the CDF of the distribution of product of two normal random variables. type="MC" uses the Monte Carlo approach (Tofighi & MacKinnon, 2011). type="all" prints percentiles using all three options. For methods type="prodclin" and type="DOP", the error is the modulus of absolute error for the numerical integration (for more information see Meeker and Escobar, 1994). For type="MC", the error refers to the Monte Carlo error.

References

MacKinnon, D. P., Fritz, M. S., Williams, J., and Lockwood, C. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods, 39, 384--389. Meeker, W. and Escobar, L. (1994). An algorithm to compute the CDF of the product of two normal random variables. Communications in Statistics: Simulation and Computation, 23, 271--280.

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692--700. doi:10.3758/s13428-011-0076-x

See Also

medci qprodnormal RMediation-package

Examples

pprodnormal(q=0, mu.x=.5, mu.y=.3, se.x=1, se.y=1, rho= 0, type="all")