# ci: CI for a nonlinear function of coefficients estimates In RMediation: Mediation Analysis Confidence Intervals

## 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

 ```1 2 3``` ```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., `~b1*b2*b3*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 [email protected] and David P. MacKinnon [email protected]

## 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

`medci` `RMediation-package`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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) ) ```

### Example output

```Loading required package: MASS
This is lavaan 0.6-3
lavaan is BETA software! Please report any bugs.
\$MC
\$MC[[1]]
2.5 %     97.5 %
0.02327788 0.50148971

\$MC\$Estimate
[1] 0.189122

\$MC\$SE
[1] 0.1253406

\$MC\$MCError
[1] 1.253406e-07

\$MC\$p
[1] 0.011528

attr(,"quant")
~b1 * b2 * b3 * b4

\$Asymptotic
\$Asymptotic\$`97.5% CI`
[1] -0.04040623  0.41840623

\$Asymptotic\$Estimate
[1] 0.189

\$Asymptotic\$SE
[,1]
[1,] 0.1170461

attr(,"quant")
~b1 * b2 * b3 * b4

[[1]]
[[1]][[1]]
2.5 %      97.5 %
0.001570451 0.093490055

[[1]]\$Estimate
[1] 0.03601567

[[1]]\$SE
[1] 0.02396109

[[1]]\$MCError
[1] 2.396109e-08

[[1]]\$p
[1] 0.03636

attr(,"quant")
~b1 * b2 * b3

[[2]]
[[2]]\$CI
2.5 %       97.5 %
-0.002164623  0.074296014

[[2]]\$Estimate
[1] 1.902105e-05

[[2]]\$SE
[1] 0.01840343

[[2]]\$p
[1] 0.06073

[[2]][[5]]
b1  b2  b3
0.3 0.4 0.0

[[1]]
[[1]][[1]]
2.5 %      97.5 %
0.001484511 0.093643023

[[1]]\$Estimate
[1] 0.0360057

[[1]]\$SE
[1] 0.02398737

[[1]]\$MCError
[1] 2.398737e-08

[[1]]\$p
[1] 0.036824

attr(,"quant")
~b1 * b2 * b3

[[2]]
[[2]]\$CI
2.5 %     97.5 %
0.02054618 0.05156672

[[2]]\$Estimate
[1] 1.200391e-05

[[2]]\$SE
[1] 0.007146034

[[2]]\$p
[1] 0.002568

[[2]][[5]]
b1  b2  b3
0.0 0.4 0.1
```

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