# pprodnormal: Percentile for the Distribution of Product of Two Normal... In RMediation: Mediation Analysis Confidence Intervals

## Description

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

## Usage

 ```1 2``` ```pprodnormal(q, mu.x, mu.y, se.x=1, se.y=1, rho = 0, lower.tail=TRUE, type="dop", 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 `"dop"` (default), `"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.

## 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="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. `type="MC"` uses the Monte Carlo approach (Tofighi & MacKinnon, 2011). `type="all"` prints percentiles using all three options. For the method `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.

## 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

## Author(s)

Davood Tofighi [email protected] and David P. MacKinnon [email protected]

## 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

`medci` `qprodnormal` `RMediation-package`

## Examples

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

### Example output

```Loading required package: MASS
This is lavaan 0.5-23.1097
lavaan is BETA software! Please report any bugs.
\$`Distribution of Product`
\$`Distribution of Product`\$p
 0.4548488

\$`Distribution of Product`\$error
 5.196031e-05

\$`Monte Carlo`
\$`Monte Carlo`\$p
 0.45917

\$`Monte Carlo`\$error
 4.983326e-06
```

RMediation documentation built on May 2, 2019, 9:41 a.m.