RMediation: ci – R documentation

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ci

CI for a nonlinear function of coefficients estimates

Description

This function returns a (1-α)% confidence interval (CI) for a well–defined nonlinear function of the coefficients in single–level and multilevel structural equation models. The ci function uses the Monte Carlo (type="MC") and the asymptotic normal theory (type="asymp") with the multivariate delta standard error (Asymptotic–Delta) method (Sobel, 1982) to compute a CI. In addition, for each of the methods, when a user specifies plot=TRUE and plotCI=TRUE, a plot of the sampling distribution of the quantity of interest in the quant argument and an overlaid plot of the CI will be produced. When type="all" and plot=TRUE, two overlaid plots of the sampling distributions corresponding to each method will be produced; when plotCI=TRUE, then the overlaid plots of the CIs for both methods will be displayed as well.

Usage

ci(mu, Sigma, quant, alpha = 0.05, type = "MC", plot = FALSE,
  plotCI = FALSE, n.mc = 1e+06, H0 = FALSE, mu0 = NULL, Sigma0 = NULL,
  ...)

Arguments

`mu`	(1) a vector of means (e.g., coefficient estimates) for the normal random variables. A user can assign a name to each mean value, e.g., `mu=c(b1=.1,b2=3)`; otherwise, the coefficient names are assigned automatically as follows: `b1,b2,...`. Or, a lavaan object.
`Sigma`	either a covariance matrix or a vector that stacks all the columns of the lower triangle variance–covariance matrix one underneath the other.
`quant`	quantity of interest, which is a nonlinear/linear function of the model parameters. Argument `quant` is a formula that must start with the symbol "tilde" (`~`): e.g., `~b1b2b3*b4`. The names of coefficients must conform to the names provided in the argument `mu` or to the default names, i.e., `b1,b2,...`.
`alpha`	significance level for the CI. The default value is .05.
`type`	method used to compute a CI. It takes on the values `"MC"` (default) for Monte Carlo, `"asymp"` for Asymptotic–Delta, or `"all"` that produces CIs using both methods.
`plot`	when `TRUE`, plot the approximate sampling distribution of the quantity of interest using the specified method(s) in the argument `type`. The default value is `FALSE`. When `type="all"`, superimposed density plots generated by both methods are displayed.
`plotCI`	when `TRUE`, overlays a CI plot with error bars on the density plot of the sampling distribution of `quant`. When `type="all"`, the superimposed CI plots generated by both methods are added to the density plots. Note that to obtain a CI plot, one must also specify `plot="TRUE"`. The default value is `FALSE`.
`n.mc`	Monte Carlo sample size. The default sample size is 1e+6.
`H0`	False. If `TRUE`, it will estimate the sampling distribution of H_{0}:f(\bm b)=0. See the arguments `mu0` and `Sigma0`.
`mu0`	a vector of means (e.g., coefficient estimates) for the normal random variables that satisft the null hypothesis H_{0}:f(\bm b)=0. If it is not provided, smallest z value of `mu` is zet to zero.
`Sigma0`	either a covariance matrix or a vector that stacks all the columns of the lower triangle variance–covariance matrix one underneath the other. If it is not provided, then `Sigma` is used instead.
`...`	additional arguments.

Value

When type is "MC" or "asymp", ci 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.

When type="all", ci returns a list of two objects, each of which a list that contains the results produced by each method as described above.

Note

The web applications for this function is available at http://amp.gatech.edu/MonteCarlo.

Author(s)

Davood Tofighi dtofighi@unm.edu and David P. MacKinnon davidpm@asu.edu

References

Tofighi, D., and MacKinnon, D. P. (2016). Monte Carlo confidence intervals for complex functions of indirect effects. Structural Equation Modeling: A Multidisciplinary Journal, 23, 194-205. http://doi.org/10.1080/10705511.2015.1057284

Examples

ci(mu=c(b1=1,b2=.7,b3=.6, b4= .45), Sigma=c(.05,0,0,0,.05,0,0,.03,0,.03), 
quant=~b1*b2*b3*b4, type="all", plot=TRUE, plotCI=TRUE)

#An Example of Conservative Null Sampling Distribution
ci(c(b1=.3,b2=.4,b3=.3), c(.01,0,0,.01,0,.02), 
quant=~b1*b2*b3, type="mc", plot=TRUE, plotCI=TRUE, 
H0=TRUE, mu0=c(b1=.3,b2=.4,b3=0)  )

#An Example of Less Conservative Null Sampling Distribution
ci(c(b1=.3,b2=.4,b3=.3), c(.01,0,0,.01,0,.02),
quant=~b1*b2*b3, type="mc", plot=TRUE, plotCI=TRUE, 
H0=TRUE, mu0=c(b1=0,b2=.4,b3=0.1)  )

RMediation

Mediation Analysis Confidence Intervals

v1.1.4

GPL-2

Authors

Davood Tofighi <dtofighi@unm.com> and David P. MacKinnon <davidpm@asu.edu>

Initial release

2016-3-12

ci