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https://github.com/jeksterslab/semmcci
semmcci: Monte Carlo Confidence Intervals in Structural Equation Modeling
https://github.com/jeksterslab/semmcci
confidence-intervals monte-carlo r r-package structural-equation-modeling
Last synced: 21 days ago
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semmcci: Monte Carlo Confidence Intervals in Structural Equation Modeling
- Host: GitHub
- URL: https://github.com/jeksterslab/semmcci
- Owner: jeksterslab
- License: other
- Created: 2021-03-16T12:56:55.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-04-08T17:47:15.000Z (7 months ago)
- Last Synced: 2024-04-08T21:33:09.696Z (7 months ago)
- Topics: confidence-intervals, monte-carlo, r, r-package, structural-equation-modeling
- Language: TeX
- Homepage: https://jeksterslab.github.io/semmcci/
- Size: 44.9 MB
- Stars: 2
- Watchers: 4
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
- Citation: CITATION.cff
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README
semmcci
================
Ivan Jacob Agaloos Pesigan
2024-10-22
[](https://cran.r-project.org/package=semmcci)
[](https://jeksterslab.r-universe.dev/semmcci)
[](https://doi.org/10.3758/s13428-023-02114-4)
[](https://github.com/jeksterslab/semmcci/actions/workflows/make.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/check-full.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/test-coverage.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/lint.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/pkgdown-gh-pages.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/latex.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/shellcheck.yml)
[](https://github.com/jeksterslab/semmcci/actions/workflows/pages/pages-build-deployment)
[](https://codecov.io/gh/jeksterslab/semmcci)
## Installation
You can install the CRAN release of `semmcci` with:
``` r
install.packages("semmcci")
```
You can install the development version of `semmcci` from
[GitHub](https://github.com/jeksterslab/semmcci) with:
``` r
if (!require("remotes")) install.packages("remotes")
remotes::install_github("jeksterslab/semmcci")
```
## Description
In the Monte Carlo method, a sampling distribution of parameter
estimates is generated from the multivariate normal distribution using
the parameter estimates and the sampling variance-covariance matrix.
Confidence intervals for defined parameters are generated by obtaining
percentiles corresponding to 100(1 - α)% from the generated sampling
distribution, where α is the significance level.
Monte Carlo confidence intervals for free and defined parameters in
models fitted in the structural equation modeling package `lavaan` can
be generated using the `semmcci` package. The package has three main
functions, namely, `MC()`, `MCMI()`, and `MCStd()`. The output of
`lavaan` is passed as the first argument to the `MC()` function or the
`MCMI()` function to generate Monte Carlo confidence intervals. Monte
Carlo confidence intervals for the standardized estimates can also be
generated by passing the output of the `MC()` function or the `MCMI()`
function to the `MCStd()` function. A description of the package and
code examples are presented in Pesigan and Cheung (2023:
).
## Example
A common application of the Monte Carlo method is to generate confidence
intervals for the indirect effect. In the simple mediation model,
variable `X` has an effect on variable `Y`, through a mediating variable
`M`. This mediating or indirect effect is a product of path coefficients
from the fitted model.
``` r
library(semmcci)
library(lavaan)
```
### Data
``` r
summary(df)
#> X M Y
#> Min. :-2.76266 Min. :-3.21655 Min. :-3.04206
#> 1st Qu.:-0.74750 1st Qu.:-0.66996 1st Qu.:-0.62765
#> Median :-0.06346 Median :-0.05311 Median : 0.01924
#> Mean :-0.05342 Mean :-0.03643 Mean : 0.02026
#> 3rd Qu.: 0.60882 3rd Qu.: 0.66178 3rd Qu.: 0.67857
#> Max. : 3.06685 Max. : 3.09347 Max. : 2.84476
#> NA's :100 NA's :100 NA's :100
```
### Model Specification
The indirect effect is defined by the product of the slopes of paths `X`
to `M` labeled as `a` and `M` to `Y` labeled as `b`. In this example, we
are interested in the confidence intervals of `indirect` defined as the
product of `a` and `b` using the `:=` operator in the `lavaan` model
syntax.
``` r
model <- "
Y ~ cp * X + b * M
M ~ a * X
X ~~ X
indirect := a * b
direct := cp
total := cp + (a * b)
"
```
### Monte Carlo Confidence Intervals
We can now fit the model using the `sem()` function from `lavaan`. We
use full-information maximum likelihood to deal with missing values.
``` r
fit <- sem(data = df, model = model, missing = "fiml")
```
The `fit` `lavaan` object can then be passed to the `MC()` function to
generate Monte Carlo confidence intervals.
``` r
mc <- MC(fit, R = 20000L, alpha = 0.05)
mc
#> Monte Carlo Confidence Intervals
#> est se R 2.5% 97.5%
#> cp 0.2833 0.0309 20000 0.2228 0.3444
#> b 0.4577 0.0298 20000 0.3983 0.5157
#> a 0.4891 0.0306 20000 0.4293 0.5494
#> X~~X 0.9396 0.0437 20000 0.8532 1.0259
#> Y~~Y 0.5328 0.0260 20000 0.4812 0.5829
#> M~~M 0.7392 0.0357 20000 0.6702 0.8099
#> Y~1 0.0507 0.0247 20000 0.0023 0.0991
#> M~1 -0.0166 0.0285 20000 -0.0729 0.0390
#> X~1 -0.0484 0.0317 20000 -0.1112 0.0133
#> indirect 0.2238 0.0201 20000 0.1860 0.2641
#> direct 0.2833 0.0309 20000 0.2228 0.3444
#> total 0.5072 0.0294 20000 0.4501 0.5655
```
### Monte Carlo Confidence Intervals - Multiple Imputation
The `MCMI()` function can be used to handle missing values using
multiple imputation. The `MCMI()` accepts the output of `mice::mice()`,
`Amelia::amelia()`, or a list of multiply imputed data sets. In this
example, we impute multivariate missing data under the normal model.
``` r
mi <- mice::mice(
df,
method = "norm",
m = 100,
print = FALSE,
seed = 42
)
```
We fit the model using lavaan using the default listwise deletion.
``` r
fit <- sem(data = df, model = model)
```
The `fit` `lavaan` object and `mi` object can then be passed to the
`MCMI()` function to generate Monte Carlo confidence intervals.
``` r
mcmi <- MCMI(fit, mi = mi, R = 20000L, alpha = 0.05, seed = 42)
mcmi
#> Monte Carlo Confidence Intervals (Multiple Imputation Estimates)
#> est se R 2.5% 97.5%
#> cp 0.2810 0.0317 20000 0.2189 0.3432
#> b 0.4576 0.0304 20000 0.3983 0.5172
#> a 0.4903 0.0307 20000 0.4299 0.5508
#> X~~X 0.9413 0.0443 20000 0.8540 1.0276
#> Y~~Y 0.5316 0.0262 20000 0.4805 0.5832
#> M~~M 0.7403 0.0354 20000 0.6699 0.8094
#> indirect 0.2244 0.0207 20000 0.1848 0.2655
#> direct 0.2810 0.0317 20000 0.2189 0.3432
#> total 0.5054 0.0293 20000 0.4482 0.5629
```
### Standardized Monte Carlo Confidence Intervals
Standardized Monte Carlo Confidence intervals can be generated by
passing the result of the `MC()` function or the `MCMI()` function to
`MCStd()`.
``` r
MCStd(mc, alpha = 0.05)
#> Standardized Monte Carlo Confidence Intervals
#> est se R 2.5% 97.5%
#> cp 0.2849 0.0304 20000 0.2253 0.3446
#> b 0.4661 0.0282 20000 0.4095 0.5211
#> a 0.4829 0.0265 20000 0.4300 0.5342
#> X~~X 1.0000 0.0000 20000 1.0000 1.0000
#> Y~~Y 0.5733 0.0260 20000 0.5213 0.6236
#> M~~M 0.7668 0.0255 20000 0.7146 0.8151
#> indirect 0.0526 0.0185 20000 0.1893 0.2621
#> direct -0.0169 0.0304 20000 0.2253 0.3446
#> total -0.0499 0.0256 20000 0.4588 0.5589
```
``` r
MCStd(mcmi, alpha = 0.05)
#> Standardized Monte Carlo Confidence Intervals
#> est se R 2.5% 97.5%
#> cp 0.2793 0.0315 20000 0.2209 0.3444
#> b 0.4706 0.0291 20000 0.4097 0.5235
#> a 0.4593 0.0268 20000 0.4300 0.5349
#> X~~X 1.0000 0.0000 20000 1.0000 1.0000
#> Y~~Y 0.5798 0.0259 20000 0.5226 0.6240
#> M~~M 0.7891 0.0258 20000 0.7139 0.8151
#> indirect 0.2161 0.0191 20000 0.1888 0.2638
#> direct 0.2793 0.0315 20000 0.2209 0.3444
#> total 0.4954 0.0257 20000 0.4567 0.5581
```
## Documentation
See [GitHub Pages](https://jeksterslab.github.io/semmcci/index.html) for
package documentation.
## Citation
To cite `semmcci` in publications, please cite Pesigan & Cheung (2023).
## References
MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence
limits for the indirect effect: Distribution of the product and
resampling methods. *Multivariate Behavioral Research*, *39*(1), 99–128.
Pesigan, I. J. A., & Cheung, S. F. (2023). Monte Carlo confidence
intervals for the indirect effect with missing data. *Behavior Research
Methods*, *56*(3), 1678–1696.
Preacher, K. J., & Selig, J. P. (2012). Advantages of Monte Carlo
confidence intervals for indirect effects. *Communication Methods and
Measures*, *6*(2), 77–98.
Tofighi, D., & Kelley, K. (2019). Indirect effects in sequential
mediation models: Evaluating methods for hypothesis testing and
confidence interval formation. *Multivariate Behavioral Research*,
*55*(2), 188–210.
Tofighi, D., & MacKinnon, D. P. (2015). Monte Carlo confidence intervals
for complex functions of indirect effects. *Structural Equation
Modeling: A Multidisciplinary Journal*, *23*(2), 194–205.