### Abstract

One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.

Original language | English (US) |
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Pages (from-to) | 194-205 |

Number of pages | 12 |

Journal | Structural Equation Modeling |

Volume | 23 |

Issue number | 2 |

DOIs | |

State | Published - Mar 3 2016 |

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### Keywords

- confidence interval
- mediation analysis
- Monte Carlo

### ASJC Scopus subject areas

- Modeling and Simulation
- Decision Sciences(all)
- Economics, Econometrics and Finance(all)
- Sociology and Political Science

### Cite this

**Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects.** / Tofighi, Davood; Mackinnon, David.

Research output: Contribution to journal › Article

*Structural Equation Modeling*, vol. 23, no. 2, pp. 194-205. https://doi.org/10.1080/10705511.2015.1057284

}

TY - JOUR

T1 - Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects

AU - Tofighi, Davood

AU - Mackinnon, David

PY - 2016/3/3

Y1 - 2016/3/3

N2 - One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.

AB - One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.

KW - confidence interval

KW - mediation analysis

KW - Monte Carlo

UR - http://www.scopus.com/inward/record.url?scp=84957435808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957435808&partnerID=8YFLogxK

U2 - 10.1080/10705511.2015.1057284

DO - 10.1080/10705511.2015.1057284

M3 - Article

AN - SCOPUS:84957435808

VL - 23

SP - 194

EP - 205

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

IS - 2

ER -