Monte Carlo Simulation Power Analysis Using Mplus and R

Planning effective research investigations requires sophisticated power analysis techniques. This book provides readers with clearly explained tools for using Monte Carlo simulations to estimate the needed sample sizes for adequate statistical power for a variety of modern research designs. Featuring step-by-step instructions, chapters move from simpler cross-sectional designs and path tracing rules to advanced longitudinal designs, while incorporating mediation, moderation, and missing data considerations. Worked-through applied examples with annotated Mplus and R syntax scripts, sample power analysis write-ups, and end-of-chapter suggested readings are also included. The companion website offers Mplus and R code for four additional power analysis models--latent variable moderation, discrete- and continuous-time survival analyses, cross-sectional and longitudinal two-level models, and moderated mediation--as well as supplemental computational materials.

I. Cross-Sectional Power Analyses
1. Introduction
- Statement of the Problem: Statistical Power in the Empirical Literature
- What Does This Mean?
- Why Monte Carlo Simulation Power Analyses?
- Software to Conduct Power Analyses
- Why Use the Approach Shown in This Book?
- Proof of Concept: Why and How the Assumption of Standardization Simplifies
- A Relationship Research Question Power Analysis
- Mplus Monte Carlo Power Analysis: Bivariate Regression
- R Monte Carlo Power Analysis: Bivariate Regression using lavaan and simsem
- A Comparison Research Question Power Analysis
- Mplus Monte Carlo Power Analysis: Two-Group Comparison
- R Monte Carlo Power Analysis: Two-Group Comparison
- Conclusion
- Suggested Readings & Resources
- Appendix 1.1: Chapter Addendum: The Fundamentals
2. A Multivariate, Two-Group, Pretest-Posttest Power Analysis
- Mplus Monte Carlo Power Analysis: Multivariate Two-Group Comparison
- R Monte Carlo Power Analysis: Multivariate Two-Group Comparison
- Simulation Power Analysis Write-Up: Multivariate Two-Group Comparison
- Suggested Readings
3. Path Analysis
- Mplus Monte Carlo Power Analysis: Mediated Path Analysis
- R Monte Carlo Power Analysis: Mediated Path Analysis
- Simulation Power Analysis Write-Up: Mediated Path Analysis
- Suggested Readings
4. Structural Equation Model
- Measurement Model: CFA
- SEM: Predictive Relationships Among CFA Models
- R Code for SEM Model-Reproduced Correlation Matrix
- Mplus Monte Carlo Power Analysis: SEM
- R Monte Carlo Power Analysis: SEM
- Impacts of Unreliability on SEM Power Estimates
- Mplus Syntax for Lower Reliability SEM Power Analysis
- R Syntax for Lower Reliability SEM Power Analysis
- Simulation Power Analysis Write-Up: SEM
- Suggested Readings
5. Logistic Regression
- The Logistical Foundation: Probabilities, Odds and Log Odds (Logits)
- Logistic Regression Power Analysis: Vakhitova and Alston-Knox (2018)
- Mplus Monte Carlo Power Analysis: Logistic Regression
- Simulation Power Analysis Write-Up: Logistic Regression
- Problems Using R packages lavaan or simsem for Logistic Regression Power Analysis
- Suggested Readings
6. Missing Data in Monte Carlo Simulation Power Analyses
- Missing Data in Mplus
- Missing Data in R Using simsem and lavaan Packages
- A Univariate Example of MCAR
- A Simple Regression MAR Example
- Monte Carlo Simulation Power Estimates and Missing Data
- Multivariate Two-Group Power Analysis Using Mplus
- Multivariate Two-Group Power Analysis Using R
- Multivariate Two-Group Simulation Power Analysis with Missing Data Write-Up
- Structural Equation Model
- Structural Equation Model Power Analysis Using Mplus
- Structural Equation Model Power Analysis Using R
- Structural Equation Model Simulation Power Analysis with Missing Data Write-Up
- Missing Data Concluding Remarks
- Suggested Readings
II. Longitudinal Power Analyses
7. Unconditional Latent Growth Curve
- The Metric of Time: Scaling and Centering
- An Unconditional Latent Growth Curve Model Power Analysis
- Mplus Monte Carlo Simulation Power Analysis
- R Monte Carlo Simulation Power Analysis
- Unconditional Latent Growth Curve Model Simulation Power Analysis Write-Up
- Latent Growth Curve Models: Moving Forward
- Suggested Readings
8. Time-Invariant Covariates
- A Tauber et al. (2021) Replication Power Analysis
- Mplus Monte Carlo Power Analysis: Longitudinal RCT Pilot
- R Monte Carlo Power Analysis: Longitudinal RCT Pilot
- Longitudinal RCT Pilot Model Simulation Power Analysis Write-Up
- But, What If…?
- Mplus Monte Carlo Power Analysis: Longitudinal Treatment Effect
- R Monte Carlo Power Analysis: Longitudinal Treatment Effect
- Longitudinal RCT Treatment Effect Model Simulation Power Analysis Write-Up
- Ok, BUT…?
- Mplus Monte Carlo Power Analysis: Longitudinal RCT Covariate
- R Monte Carlo Power Analysis: Longitudinal RCT Covariate Issues
- Longitudinal RCT Covariate Simulation Power Analysis Write-Up
- Just One More Thing
- Mplus Monte Carlo Power Analysis: Longitudinal RCT Moderation Model
- R Monte Carlo Power Analysis: Longitudinal RCT Moderation Model Issues
- Longitudinal RCT Moderation Model Simulation Power Analysis Write-Up
- A Final Note
- Suggested Readings
- Appendix 8.1: “Old School†Power Analyses Using “Old School†Methods
- Mixed-Factorial ANOVA Design Matrices
- A Mixed-Factorial ANOVA Model Simulation Power Analysis Write-Up
9. Adding Time-Varying Covariates
- Mplus Monte Carlo Power Analysis: Adding Time-Varying Covariates
- R Monte Carlo Power Analysis: Adding Time-Varying Covariates Issues
- Longitudinal Time-Varying Covariates Simulation Power Analysis Write-Up
- Mplus Monte Carlo Power Analysis: A Random Effect Model
- R Monte Carlo Power Analysis: Random Effect Model Issues
- Longitudinal Random Effect Model Simulation Power Analysis Write-Up
- Suggested Readings
10. Parallel-Process Mediation
- A Parallel-Process Power Analysis Based on Becker et al. (2016)
- Mplus Monte Carlo Power Analysis for Parallel-Process Mediation
- R Monte Carlo Power Analysis for Parallel-Process Mediation
- Parallel-Process Simulation Power Analysis Write-Up
- Suggested Readings
11. Power Analysis for Complex Longitudinal Designs
- A Complex Longitudinal Power Analysis Based on Beal et al. (2020)
- Maltreatment Predicting CDI Trajectory Variance
- CDI Trajectory and Maltreatment Predict Quality of Life (QOL)
- CDI Trajectory and Maltreatment Predict Biomarkers
- Logistic Prediction of Opioid Use Disorder
- Prediction of Opioid Misuse Disorder
- Assembling the Mplus Syntax
- A Note on RSyntax for this Design
- Complex Longitudinal Simulation Power Analysis Write-Up
- Suggested Readings
III. Conclusion
12. Statistical Power in a “Post-p < .05†World
- Ringing the Alarm Bell
- Possible Paths Toward a “Post-p < .05†World
- What Does All of This Mean?
- Suggested Readings
References
Author Index
Subject Index
About the Author

Online-Only Appendices:
Appendix A. Statistical Power for Latent Variable Moderation
Appendix B. Part 1: Statistical Power for Survival Analysis
Appendix B. Part 2: Continuous-Time Survival Analysis
Appendix C. Monte Carlo Simulation Power for Two-Level Models (Arend and Schafer, 2019)
Appendix D. Statistical Power for Moderated Mediation

Kaylee Litson, PhD, is Assistant Professor in the Department of Psychology at the University of Houston. As an interdisciplinary quantitative psychologist, they have a particular interest in the link between statistical model estimation and theory-driven interpretation, especially in the context of complex, multimethod, and longitudinal research design. Dr. Litson's work highlights the translation of quantitative psychology methods to applied research in fields such as cognition and educational psychology. Their publications have appeared in applied and quantitative journals.

Power analysis is vitally important for designing strong studies and convincing grant panels that a study is fundable, yet it is rarely (if ever) part of formal quantitative methods courses or training sequences. This book empowers researchers by providing an accessible explanation of Monte Carlo approaches to power analysis, which are particularly useful for modern, mainstream multivariate statistical models popular in the behavioral sciences. The book walks through the mechanics of Monte Carlo studies and deftly explains how to write corresponding code in Mplus and R, interpret the output, and understand implications for sample size. This is an indispensable resource for behavioral scientists and methodologists seeking to design studies and craft effective grant proposals.--Daniel McNeish, PhD, Department of Psychology, Arizona State University

Drawing on nearly 20 years of teaching graduate-level quantitative methods, this text is an exceptional resource for lessons in power analysis across courses in multiple linear and logistic regression, multilevel modeling, and introductory and advanced latent/structural equation modeling. Beyond power analysis, the book can also be used for instruction in how missingness and incorrect model specification can impact parameter point and interval estimates. The progression of concepts and the writing style are easy to follow, and the companion code is invaluable. I will most certainly use this book for my classes.--Elizabeth A. Sanders, PhD, Professor and Director, Measurement and Statistics Program, College of Education, University of Washington, Seattle

This book fills a critical gap for researchers. Typical textbook examples for power analysis usually refer to relatively simple models with complete data sets, whereas the reality of models and data is often much messier. The topics and simulation approach outlined here address this reality, by providing researchers guidance and accessible software to run Monte Carlo power analyses for complex models with multilevel and missing data. Using this book, research faculty and graduate students alike will be better equipped to conduct more solid research and to write grant proposals with more realistic sample size estimates.--Frederick L. Oswald, PhD, Professor and Herbert S. Autrey Chair in Social Sciences, Department of Psychological Sciences, Rice University

Power analysis is essential for designing robust and replicable studies, yet it can seem daunting and complex. Peugh and Litson demystify the process, offering a step-by-step guide that encourages researchers to engage deeply with their data and avoid the pitfalls of underpowered studies. The included Mplus and R syntax go well beyond basic models, and the authors’ clear explanations make simulation-based power analysis both approachable and immediately applicable.--Francis Huang, PhD, College of Education and Human Development, University of Missouri–Columbia

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