Interest in mediation analysis has increased over time, with particular excitement in the social and behavioral sciences. A mediator is defined as an intermediate in the causal sequence between an independent and dependent variable. Previous research has demonstrated that the cross-sectional form of mediation analysis is inherently flawed, evidenced by the inability of the cross-sectional mediation model to account for temporal precedence and estimation of the indirect effect being biased in nearly all situations. For these reasons, a longitudinal model is recommended. However, a method for determining the exact time points to measure the variables used in mediation analysis has not been adequately examined. In this study, we examined methods for determining an appropriate time lag when designing a mediation study. The methods implemented include correlation analysis, the quadratic and exponential forms of the lag as a moderator approach, and knot estimation using basis splines. The data for the study was simulated for three distinct trends generated using a linear piecewise model, a sigmoid model, and a sigmoid piecewise model. Additionally, two sampling approaches, an intense sampling approach and a three-measure approach, were examined as well as six sample sizes and three effect sizes for the total effect on the outcome. The estimation methods were additionally compared by considering different types of error structures used in data generation as well as by examining equal and unequal time lag lengths between the predictor and mediator, and the mediator and outcome. The intent of the study is to provide methods so that researchers can estimate the best time to evaluate mediator and outcome measurements that will be used in mediation analysis. The results from this study showed that the best estimation method varied depending on the lag being estimated, the sampling approach, and the length of the lag. However, the knot estimation approach worked reasonably well in most scenarios considered even with small sample sizes of 5 or 10 per group. The findings from this study have the potential to improve study design for research implementing longitudinal mediation analysis by reducing bias in the estimate of the indirect effect when adequate time points are used.

abstract: Methods to test hypotheses of mediated effects in the pretest-posttest control group design are understudied in the behavioral sciences (MacKinnon, 2008). Because many studies aim to answer questions about mediating processes in the pretest-posttest control group design, there is a need to determine which model is most appropriate to test hypotheses about mediating processes and what happens to estimates of the mediated effect when model assumptions are violated in this design. The goal of this project was to outline estimator characteristics of four longitudinal mediation models and the cross-sectional mediation model. Models were compared on type 1 error rates, statistical power, accuracy of confidence interval coverage, and bias of parameter estimates. Four traditional longitudinal models and the cross-sectional model were assessed. The four longitudinal models were analysis of covariance (ANCOVA) using pretest scores as a covariate, path analysis, difference scores, and residualized change scores. A Monte Carlo simulation study was conducted to evaluate the different models across a wide range of sample sizes and effect sizes. All models performed well in terms of type 1 error rates and the ANCOVA and path analysis models performed best in terms of bias and empirical power. The difference score, residualized change score, and cross-sectional models all performed well given certain conditions held about the pretest measures. These conditions and future directions are discussed. / Dissertation/Thesis / Masters Thesis Psychology 2015