Chung Li Wu

Date of Award

Fall 2022

Document Type

Open Access Dissertation


Epidemiology and Biostatistics

First Advisor

James Hardin


A proper study design assures adequate power to detect statistically significant differences. Existing power calculations for multilevel mediation analysis make a strong distributional assumption of normality. However, binary outcomes are commonly seen in real-world study. Motivated by this fact, we conduct a simulation-based power study for a multilevel mediation analysis with binary outcomes. The numbers of participants needed to achieve 80% power are summarized in tables for future reference.

Mixed-effect regression is commonly used in multilevel analysis for panel data. Yet, the estimated coefficients from the random-intercept model could represent either purely between-cluster, purely within-cluster, or weighted-average effects. Therefore, we explore the theory of level-specific estimation (LSE) and evaluate the performance of LSE through extensive simulations. Simulation results show that LSE has good performance. Finally, the application of LSE to data from our smoking project identifies two cognitive elaboration items that act differently at within and between participant level. Also, labeling effects are found significantly transmitted through these two cognitive elaboration items to main behavioral outcomes.

The Sobel test is widely used in estimating indirect effects when conducting mediation analysis. The distribution of the estimated indirect effects by Sobel’s test is derived using multivariate delta method and assumed to be asymptotically normally distributed. However, whether or not the strong distributional assumption of normality is adequate under small sample size requires investigation. Therefore, we examine the normality assumption on the performance of Sobel’s test by comparing it to the indirect distribution estimated by the permutation test. Simulation results in our study show that Sobel’s test has lower power to detect the significant differences.

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