# indirectEffect: Estimate the asymptotic covariance matrix of standardized or... In metaSEM: Meta-Analysis using Structural Equation Modeling

## Description

It estimates the standardized or unstandardized indirect and direct effects and their asymptotic sampling covariance matrix.

## Usage

 `1` ```indirectEffect(x, n, standardized = TRUE, direct.effect = TRUE, run = TRUE) ```

## Arguments

 `x` A 3x3 correlation/covariance matrix or a list of correlation/covariance matrices. Variables are arranged as the dependent variable (y), mediator (m) and independent variable (x) `n` Sample size or a vector of sample sizes `standardized` Logical. Whether the indirect effect is standardized. `direct.effect` Logical. Whether the direct effect is estimated. If it is `FALSE`, the direct effect is fixed at zero. `run` Logical. If `FALSE`, only return the mx model without running the analysis.

## Details

Cheung (2009) estimated the standardized indirect effect and its standard error with non-linear constraints. Since `OpenMx` does not generate standard errors when there are non-linear constraints, Kwan and Chan's (2011) approach is used in this function. Delta method is used to calculate the asymptotic covariance matrix.

## Value

A vector (or a matrix if the input is a list of matrices) of (standardized) indirect effect, standardized direct effect, and their asymptotic sampling covariance matrices

## Author(s)

Mike W.-L. Cheung <[email protected]>

## References

Cheung, M. W.-L. (2009). Comparison of methods for constructing confidence intervals of standardized indirect effects. Behavior Research Methods, 41, 425-438.

Kwan, J., & Chan, W. (2011). Comparing standardized coefficients in structural equation modeling: a model reparameterization approach. Behavior Research Methods, 43, 730-745.

## Examples

 ```1 2 3 4 5 6 7``` ```## A correlation matrix as input x <- matrix(c(1, 0.4, 0.2, 0.4, 1, 0.3, 0.2, 0.3, 1), ncol=3) dimnames(x) <- list( c("y", "m", "x"), c("y", "m", "x") ) indirectEffect(x, n=300) ## A list of correlation matrices indirectEffect( list(x, x), n=c(300,500), standardized=FALSE ) ```

### Example output

```Loading required package: OpenMx
To take full advantage of multiple cores, use:
"SLSQP" is set as the default optimizer in OpenMx.
mxOption(NULL, "Gradient algorithm") is set at "central".
mxOption(NULL, "Optimality tolerance") is set at "6.3e-14".
mxOption(NULL, "Gradient iterations") is set at "2".
sh: 1: cannot create /dev/null: Permission denied
sh: 1: wc: Permission denied
ind_eff       dir_eff       ind_var   ind_dir_cov       dir_var
0.1132090112  0.0887913809  0.0006683899 -0.0002723687  0.0031515457
ind_eff    dir_eff      ind_var   ind_dir_cov     dir_var
[1,] 0.1120879 0.08791209 0.0006980476 -0.0002746040 0.003051160
[2,] 0.1120879 0.08791209 0.0004188285 -0.0001647625 0.001830696
```

metaSEM documentation built on Oct. 18, 2018, 9:03 a.m.