scholarly journals Power Analysis for Conditional Indirect Effects: A Tutorial for Conducting Monte Carlo Simulations with Categorical Exogenous Variables

2021 ◽  
Author(s):  
Samuel Donnelly ◽  
Terrence D. Jorgensen ◽  
Cort Rudolph
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Sample Size ◽  
Indirect Effects ◽  
Power Analysis ◽  
Moderated Mediation ◽  
Exogenous Variables ◽  
Sample Size Planning ◽  
Conditional Indirect Effects ◽  
Mediation Models

Conceptual and statistical models that include conditional indirect effects (i.e., so-called “moderated mediation” models) are increasingly popular in the behavioral sciences. Although there is ample guidance in the literature for how to specify and test such models, there is scant advice regarding how to best design studies for such purposes, and this especially includes techniques for sample size planning (i.e., “power analysis”). In this paper, we discuss challenges in sample size planning for moderated mediation models and offer a tutorial for conducting Monte Carlo simulations in the specific case where one has categorical exogenous variables. Such a scenario is commonly faced when one is considering testing conditional indirect effects in experimental research, wherein the (assumed) predictor and moderator variables are manipulated factors and the (assumed) mediator and outcome variables are observed/measured variables. To support this effort, we offer example data and reproducible R code that constitutes a “toolkit” to aid researchers in the design of research to test moderated mediation models.

Using Monte Carlo simulations to determine power and sample size for planned missing designs

2014 ◽  
Vol 38 (5) ◽  
pp. 471-479 ◽  
Author(s):  
Alexander M. Schoemann ◽  
Patrick Miller ◽  
Sunthud Pornprasertmanit ◽  
Wei Wu
Keyword(s):  
Monte Carlo ◽  
Missing Data ◽  
Monte Carlo Simulations ◽  
Sample Size ◽  
Power Analysis ◽  
Sample Size Determination ◽  
Quality Of Data ◽  
Planned Missing Data ◽  
Planned Missing

Planned missing data designs allow researchers to increase the amount and quality of data collected in a single study. Unfortunately, the effect of planned missing data designs on power is not straightforward. Under certain conditions using a planned missing design will increase power, whereas in other situations using a planned missing design will decrease power. Thus, when designing a study utilizing planned missing data researchers need to perform a power analysis. In this article, we describe methods for power analysis and sample size determination for planned missing data designs using Monte Carlo simulations. We also describe a new, more efficient method of Monte Carlo power analysis, software that can be used in these approaches, and several examples of popular planned missing data designs.

Determining Power and Sample Size for Simple and Complex Mediation Models

2017 ◽  
Vol 8 (4) ◽  
pp. 379-386 ◽  
Author(s):  
Alexander M. Schoemann ◽  
Aaron J. Boulton ◽  
Stephen D. Short
Keyword(s):  
Monte Carlo ◽  
Confidence Interval ◽  
Sample Size ◽  
Indirect Effect ◽  
Power Analysis ◽  
New Method ◽  
Computational Time ◽  
Personality Psychology ◽  
Mediation Analyses ◽  
Mediation Models

Mediation analyses abound in social and personality psychology. Current recommendations for assessing power and sample size in mediation models include using a Monte Carlo power analysis simulation and testing the indirect effect with a bootstrapped confidence interval. Unfortunately, these methods have rarely been adopted by researchers due to limited software options and the computational time needed. We propose a new method and convenient tools for determining sample size and power in mediation models. We demonstrate our new method through an easy-to-use application that implements the method. These developments will allow researchers to quickly and easily determine power and sample size for simple and complex mediation models.

scholarly journals Erratum to: Power Analysis and Sample Size Planning in Ancova Designs

Psychometrika ◽  
2021 ◽  
Author(s):  
Gwowen Shieh
Keyword(s):  
Sample Size ◽  
Power Analysis ◽  
Sample Size Planning

A Correction to this paper has been published: https://doi.org/10.1007/s11336-019-09692-3

scholarly journals MANOVA: POWER ANALYSIS OF MODELS OF SUDOKU SQUARE DESIGNS

2020 ◽  
Vol 4 (2) ◽  
pp. 350-364
Author(s):  
A. Shehu ◽  
N. S. Dauran
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Sample Size ◽  
Power Analysis ◽  
Design Models ◽  
Power Test ◽  
Power Difference ◽  
The Difference ◽  
Interval Value

This paper assesses the performance of multivariate treatment tests (Wilk’s Lambda, Hoteling-lawley, Roy’s largest root and Pillai) on multivariate Sudoku square design models in terms of power analysis. Monte carlo simulation was conducted to compare the power of these four tests for the four multivariate Sudoku square design models. This study used  0.062 as interval value for Power difference between two tests of the same sample size. The test is considered powerful or having advantage, if the difference between the powers of the tests is   . The results of Power test show that Hoteling-lawley has advantage over three other tests at P=2 while at P=3 Wilk’s lambda test has power advantage over other tests in all the multivariate Sudoku models.

Economical Optimization of Microgrids: A Non-Causal Model

2015 ◽  
Author(s):  
Kevin Milis ◽  
Herbert Peremans
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Optimization Model ◽  
Causal Model ◽  
Operating Cost ◽  
Electricity Prices ◽  
Exogenous Variables ◽  
Electricity Grid ◽  
Uncertain Future ◽  
Economical Optimization

In this paper we present an economical optimization model for a microgrid connected to the general electricity grid by minimizing the total operating cost over a given period in the presence of uncertain future grid electricity prices. The microgrid is modeled to consist of five distinct blocks, four of which make up the microgrid and the fifth one being the connection to the general electricity grid. Each of these components has various adjustable attributes, allowing for the simulation of different kinds of consumers as well as different storage and generation technologies. Consumption and intermittent generation are exogenous variables derived from existing datasets. Under uncertain future grid electricity prices, the storage component introduces a non-causal dependency into the model, to cope with this non-causality, we present various storage use strategies and analyze the resulting cost patterns using real electricity price data and Monte Carlo simulations.

scholarly journals Estimating Sample Size Required to Establish an Association Between Walnut Intake and Cognitive Change in Older Adults: An Application of Monte Carlo Power Analysis

2020 ◽  
Vol 4 (Supplement_2) ◽  
pp. 10-10
Author(s):  
Nicholas Bishop
Keyword(s):  
Older Adults ◽  
Monte Carlo ◽  
Cognitive Function ◽  
Sample Size ◽  
Power Analysis ◽  
Observational Studies ◽  
Cognitive Change ◽  
Cognitive Status ◽  
Parameter Estimates ◽  
Detailed Measurement

Abstract Objectives Observational studies support a cross-sectional association between walnut intake and cognitive function among older adults, but few of these studies identify walnut intake as a predictor of cognitive change. This project estimates the sample size required to establish a statistically significant association between walnut intake and cognitive change in an observational study using Monte Carlo power analysis. Methods Initial observations were drawn from the 2012, 2014, and 2016 Health and Retirement Study (HRS) and the 2013 Health Care and Nutrition Study (HCNS; age ≥ 65, n = 3632). Global cognitive function was measured using the Telephone Interview for Cognitive Status and two operationalizations of walnut intake were investigated (none, low intake (.01 – .08 servings/day), and moderate intake (> .08 servings/day); no intake vs. any intake). Latent growth models adjusting for covariates and complex sample design were used to estimate age-based developmental trajectories of TICS scores as a function of walnut intake. Parameter estimates from these models were used as starting values in Monte Carlo simulation models replicated for sample sizes from 1000–50,000. Results Model estimation required around 1200 hours of processing time. When measured as a trichotomous variable, the observed association between walnut intake and cognitive change was weak (for moderate intake, b = −0.030, SE = .03) and would require at least 42,000 observations to reduce the standard error to a level where 80% or more of random samples would identify the effect as statistically significant (P < .05). When measured as a dichotomous variable, the observed effect was small (b = −0.013, SE = 0.025) and required a sample size of at least 39,000 observations to identify power above .80. Conclusions Given that the HRS and HCNS are nationally-representative studies, the population size from which an adequate sample would need to be drawn to identify walnut intake as a significant predictor of cognitive decline would exceed the number of adults age 65 and older currently living in the US. Rather than increase sample size of observational studies, researchers should apply quasi-experimental methods and detailed measurement of walnut intake to establish an association between walnut intake and cognitive change. Funding Sources This research was funded by the California Walnut Commission.

Accommodating binary and count variables in mediation

2017 ◽  
Vol 42 (2) ◽  
pp. 300-308 ◽  
Author(s):  
G. John Geldhof ◽  
Katherine P. Anthony ◽  
James P. Selig ◽  
Carolyn A. Mendez-Luck
Keyword(s):  
Indirect Effects ◽  
Relevant Literature ◽  
Research Literature ◽  
Simple Extension ◽  
Data Types ◽  
Endogenous Variables ◽  
Nonlinear Associations ◽  
Conditional Indirect Effects ◽  
Diverse Data ◽  
Mediation Models

The existence of several accessible sources has led to a proliferation of mediation models in the applied research literature. Most of these sources assume endogenous variables (e.g., M, and Y) have normally distributed residuals, precluding models of binary and/or count data. Although a growing body of literature has expanded mediation models to include more diverse data types, the nonlinearity of these models presents a substantial hurdle to their implementation and interpretation. The present study extends the existing literature (e.g., Hayes & Preacher, 2010; Stolzenberg, 1980) to propose conditional indirect effects as a useful tool for understanding mediation models that include paths estimated using the Generalized Linear Model (e.g., logistic regression, Poisson regression). We briefly review the relevant literature, culminating in a discussion of conditional indirect effects and their importance when examining nonlinear associations. We present a simple extension of the equations presented by Hayes and Preacher (2010) and provide an applied example of the technique.

Evaluation methods for estimation of Weibull parameters used in Monte Carlo simulations for safety analysis of pressure vessels

2021 ◽  
Vol 63 (4) ◽  
pp. 379-385
Author(s):  
Bin Wang ◽  
Faisal Islam ◽  
Georg W. Mair
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Monte Carlo Simulations ◽  
Sample Size ◽  
Least Squares ◽  
Test Data ◽  
Pressure Vessels ◽  
Small Sample ◽  
Least Squares Regression ◽  
Weibull Parameters

Abstract The test data for static burst strength and load cycle fatigue strength of pressure vessels can often be well described by Gaussian normal or Weibull distribution functions. There are various approaches which can be used to determine the parameters of the Weibull distribution function; however, the performance of these methods is uncertain. In this study, six methods are evaluated by using the criterion of OSL (observed significance level) from Anderson-Darling (AD) goodness of Fit (GoF), These are: a) the norm-log based method, b) least squares regression, c) weighted least squares regression, d) a linear approach based on good linear unbiased estimators, e) maximum likelihood estimation and f) method of moments estimation. In addition, various approaches of ranking function are considered. The results show that there are no outperforming methods which can be identified clearly, primarily due to the limitation of the small sample size of the test data used for Weibull analysis. This randomness resulting from the sampling is further investigated by using Monte Carlo simulations, concluding that the sample size of the experimental data is more crucial than the exact method used to derive Weibull parameters. Finally, a recommendation is made to consider the uncertainties of the limitations due to the small size for pressure vessel testing and also for general material testing.

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