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, ...)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:
a vector of lower and upper confidence limits,
a point estimate of the quantity of interest,
standard error of the quantity of interest,
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.
mean of \(x\)
mean of \(y\)
standard error (deviation) of \(x\)
standard error (deviation) of \(y\)
correlation between \(x\) and \(y\), where -1 <
rho < 1. The default value is 0.
significance level for the confidence interval. The default value is .05.
method used to compute confidence interval. It takes on
the values "dop" (default),
"MC", "asymp" or "all".
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.
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.
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.
Davood Tofighi dtofighi@unm.edu and David P. MacKinnon davidpm@asu.edu
This function returns a (\(1-\alpha\))% 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):
$$\sqrt(se.y^2 \mu.x^2+se.x^2 \mu.y^2+2 \mu.x \mu.y \rho se.x se.y+ se.x^2 se.y^2+se.x^2 se.y^2 \rho^2) $$
In addition, the estimate of indirect effect is \(\mu.x\mu.y +\sigma.xy \); type="all" prints confidence intervals using all four options.
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
##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"]] # SE
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