abstract: Mediation analysis is used to investigate how an independent variable, X, is related to an outcome variable, Y, through a mediator variable, M (MacKinnon, 2008). If X represents a randomized intervention it is difficult to make a cause and effect inference regarding indirect effects without making no unmeasured confounding assumptions using the potential outcomes framework (Holland, 1988; MacKinnon, 2008; Robins & Greenland, 1992; VanderWeele, 2015), using longitudinal data to determine the temporal order of M and Y (MacKinnon, 2008), or both. The goals of this dissertation were to (1) define all indirect and direct effects in a three-wave longitudinal mediation model using the causal mediation formula (Pearl, 2012), (2) analytically compare traditional estimators (ANCOVA, difference score, and residualized change score) to the potential outcomes-defined indirect effects, and (3) use a Monte Carlo simulation to compare the performance of regression and potential outcomes-based methods for estimating longitudinal indirect effects and apply the methods to an empirical dataset. The results of the causal mediation formula revealed the potential outcomes definitions of indirect effects are equivalent to the product of coefficient estimators in a three-wave longitudinal mediation model with linear and additive relations. It was demonstrated with analytical comparisons that the ANCOVA, difference score, and residualized change score models’ estimates of two time-specific indirect effects differ as a function of the respective mediator-outcome relations at each time point. The traditional model that performed the best in terms of the evaluation criteria in the Monte Carlo study was the ANCOVA model and the potential outcomes model that performed the best in terms of the evaluation criteria was sequential G-estimation. Implications and future directions are discussed. / Dissertation/Thesis / Doctoral Dissertation Psychology 2018

Multicollinearity can be present in the propensity score model when estimating average treatment effects (ATEs). In this thesis, logistic ridge regression (LRR) and principal components logistic regression (PCLR) are evaluated as an alternative to ML estimation of the propensity score model. ATE estimators based on weighting (IPW), matching and stratification are assessed in a Monte Carlo simulation study to evaluate LRR and PCLR. Further, an empirical example of using LRR and PCLR on real data under multicollinearity is provided. Results from the simulation study reveal that under multicollinearity and in small samples, the use of LRR reduces bias in the matching estimator, compared to ML. In large samples PCLR yields lowest bias, and typically was found to have the lowest MSE in all estimators. PCLR matched ML in bias under IPW estimation and in some cases had lower bias. The stratification estimator was heavily biased compared to matching and IPW but both bias and MSE improved as PCLR was applied, and for some cases under LRR. The specification with PCLR in the empirical example was usually most sensitive as a strongly correlated covariate was included in the propensity score model.

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