Confidence Interval for the Mediated Effect
Produces confidence intervals for the mediated effect and the product of two normal random variables.
medci(mu.x, mu.y, se.x, se.y, rho = 0, alpha = 0.05, type = "dop", plot=FALSE, plotCI=FALSE, n.mc = 1e+05, ...)
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 <
|
alpha |
significance level for the confidence interval. The default value is .05. |
type |
method used to compute confidence interval. It takes on
the values |
plot |
when |
plotCI |
when |
n.mc |
when |
... |
additional arguments to be passed on to the function. |
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.
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 |
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.
Davood Tofighi dtofighi@unm.edu and David P. MacKinnon davidpm@asu.edu
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
##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[[1]]
## To get the point estimate of the indirect effect
res[["Estimate"]] # Estimate
## To get the SE of the indirect effect
res[["SE"]] # SEPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.