# medci: Confidence Interval for the Mediated Effect In RMediation: Mediation Analysis Confidence Intervals

## Description

Produces confidence intervals for the mediated effect and the product of two normal random variables.

## Usage

 ```1 2``` ```medci(mu.x, mu.y, se.x, se.y, rho = 0, alpha = 0.05, type = "dop", plot=FALSE, plotCI=FALSE, n.mc = 1e+05, ...) ```

## Arguments

 `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. `alpha` significance level for the confidence interval. The default value is .05. `type` method used to compute confidence interval. It takes on the values `"dop"` (default), `"MC"`, `"asymp"` or `"all"`. `plot` when `TRUE`, plots the distribution of `n.mc` data points from the distribution of product of two normal random variables using the density estimates provided by the function `density`. The default value is `FALSE`. `plotCI` when `TRUE`, overlays a confidence interval with error bars on the plot for the mediated effect. Note that to obtain the CI plot, one must also specify `plot="TRUE"`. The default value is `FALSE`. `n.mc` when `type="MC"`, `n.mc` determines the sample size for the Monte Carlo method. The default sample size is 1E5. `...` additional arguments to be passed on to the function.

## Details

This function returns a (1-α)% confidence interval for the mediated effect (product of two normal random variables). To obtain a confidence interval using a specific method, the argument `type` should be specified. The default is `type="dop"`, which uses the code we wrote in R to implement the distribution of product of the coefficients method described by Meeker and Escobar (1994) to evaluate the CDF of the distribution of product. `type="MC"` uses the Monte Carlo approach to compute the confidence interval (Tofighi & MacKinnon, 2011). `type="asymp"` produces the asymptotic normal confidence interval. Note that except for the Monte Carlo method, the standard error for the indirect effect is based on the analytical results by Craig (1936):

√(se.y^2 μ.x^2+se.x^2 μ.y^2+2 μ.x μ.y ρ se.x se.y+ se.x^2 se.y^2+se.x^2 se.y^2 ρ^2)

In addition, the estimate of indirect effect is μ.xμ.y +σ.xy ; `type="all"` prints confidence intervals using all four options.

## Value

A vector of lower confidence limit and upper confidence limit. When `type` is `"prodclin"` (default), `"DOP"`, `"MC"` or `"asymp"`, `medci` returns a list that contains:

 `(1-α)% CI` a vector of lower and upper confidence limits, `Estimate` a point estimate of the quantity of interest, `SE` standard error of the quantity of interest, `MC Error` When `type="MC"`, error of the Monte Carlo estimate.

Note that when `type="all"`, `medci` returns a list of four objects, each of which a list that contains the results produced by each method as described above.

## Note

The PRODCLIN programs may be downloaded from http://www.public.asu.edu/~davidpm/ripl/Prodclin/. A web application of the RMediation program is available from http://amp.gatech.edu/RMediation.

## Author(s)

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

## References

Craig, C. C. (1936). On the frequency function of xy. The Annals of Mathematical Statistics, 7, 1–15.

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

`qprodnormal` `pprodnormal` `ci` `RMediation-package`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```##produces CI using PRODCLIN and density plot of distribution of xy (res <- medci(mu.x=.2, mu.y=.4, se.x=1, se.y=1, rho=0, alpha=.05, type="prodclin", plot=TRUE, plotCI=TRUE) ) ## To get a vector of CI estimates res[] ## To get the point estimate of the indirect effect res[["Estimate"]] # Estimate ## To get the SE of the indirect effect res[["SE"]] # SE ```