Monte Carlo simulations are computer experiments designed to study the performance of statistical methods under known data-generating conditions (Morris, White, & Crowther, 2019). Methodologists use simulations to examine questions such as: (1) how does ordinary least squares regression perform if errors are heteroskedastic? (2) how does the presence of missing data affect treatment effect estimates from a propensity score analysis? (3) how does cluster robust variance estimation perform when the number of clusters is small? To answer such questions, we conduct experiments by simulating thousands of datasets based on pseudo-random sampling, applying statistical methods, and evaluating how well those statistical methods recover the true data-generating conditions (Morris et al., 2019).

The goal of `simhelpers`

is to assist in running simulation studies. The package includes two main tools. First, it includes a collection of functions to calculate measures of estimator performance such as bias, root mean squared error, rejection rates, and confidence interval coverage. The functions also calculate the associated Monte Carlo standard errors (MCSE) of the performance measures. These functions are divided into three major categories of performance criteria: absolute criteria, relative criteria, and criteria to evaluate hypothesis testing. The functions are designed to play well with `dplyr`

and fit easily into a `%>%`

-centric workflow (Wickham et al., 2019).

In addition to the set of functions that calculates performance measures and MCSE, the package includes some further convenience functions to assist in programming simulations. These include `bundle_sim()`

, which can be used to create a single function for running a simulation from component pieces. The function takes a function for generating data, a function for analyzing the data, and (optionally) a function for summarizing the results, and constructs a single function for running a full simulation given a set of parameter values and optional arguments, or what we call a “simulation driver.” The simulation driver function can then be applied to a parameter set using `evaluate_by_row()`

to execute simulations across multiple conditions.

Finally, the package also includes a function, `create_skeleton()`

, that generates a skeleton outline for a simulation study. Another function, `evaluate_by_row()`

, runs the simulation for each combination of conditions row by row. This function uses `future_pmap()`

from the `furrr`

package, making it easy to run the simulation in parallel (Vaughan & Dancho, 2018). The package also includes several datasets that contain results from example simulation studies.

## Installation

Install the latest release from CRAN:

`install.packages("simhelpers")`

Install the development version from GitHub:

```
# install.packages("devtools")
devtools::install_github("meghapsimatrix/simhelpers")
```

## Related Work

Our explanation of MCSE formulas and our general simulation workflow is closely aligned with the approach described by Morris et al. (2019). We want to recognize several other R packages that offer functionality for conducting Monte Carlo simulation studies. In particular, the `rsimsum`

package (which has a lovely name that makes me hungry) also calculates Monte Carlo standard errors (Gasparini, 2018). The `SimDesign`

package implements a generate-analyze-summarize model for writing simulations, which provided inspiration for our `bundle_sim()`

tools. `SimDesign`

also includes tools for error handling and parallel computing (Chalmers, 2019).

In contrast to the two packages mentioned above, our package is designed to be used with `dplyr`

, `tidyr`

and `purrr`

syntax (Wickham et al., 2019). The functions that calculate MCSEs are easy to run on grouped data. For parallel computing, `evaluate_by_row()`

uses the `furrr`

and `future`

packages (Bengtsson, 2020; Vaughan & Dancho, 2018). Moreover, in contrast to the `rsimsum`

and `SimDesign`

packages, `simhelpers`

provides jack-knife MCSE for variance estimators. It also provides jack-knife MCSE estimates for root mean squared error.

Another related project is `DeclareDesign`

, a suite of packages that allow users to declare and diagnose research designs, fabricate mock data, and explore tradeoffs between different designs (Blair et al., 2019). This project follows a similar model for how simulation studies are instantiated, but it uses a higher-level API, which is tailored for simulating certain specific types of research designs. In contrast, our package is a simpler set of general-purpose utility functions.

Other packages that have similar aims to `simhelpers`

include: MonteCarlo, parSim, simsalapar, simulator, simstudy, simTool, simSummary, and ezsim.

# Acknowledgments

We are grateful for the feedback provided by Danny Gonzalez, Sangdon Lim, Man Chen, and Edouard Bonneville.

# References

Bengtsson, H. (2020). future: Unified parallel and distributed processing in r for everyone. Retrieved from https://CRAN.R-project.org/package=future

Blair, G., Cooper, J., Coppock, A., & Humphreys, M. (2019). Declaring and diagnosing research designs. American Political Science Review, 113(3), 838–859. Retrieved from https://declaredesign.org/paper.pdf

Chalmers, P. (2019). SimDesign: Structure for organizing Monte Carlo simulation designs. Retrieved from https://CRAN.R-project.org/package=SimDesign

Gasparini, A. (2018). rsimsum: Summarise results from Monte Carlo simulation studies. Journal of Open Source Software, 3(26), 739. https://doi.org/10.21105/joss.00739

Morris, T. P., White, I. R., & Crowther, M. J. (2019). Using simulation studies to evaluate statistical methods. Statistics in Medicine, 38(11), 2074–2102.

Vaughan, D., & Dancho, M. (2018). furrr: Apply mapping functions in parallel using futures. Retrieved from https://CRAN.R-project.org/package=furrr

Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L. D., François, R., … Yutani, H. (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686. https://doi.org/10.21105/joss.01686