The goal of my proposed research is to develop Bayesian techniques to test mediational effects in cluster randomized designs with multiple measurement waves. Mediational analysis studies the processes through which interventions achieve their effects through intervening variables that are targeted for change. Because the widely used maximum likelihood approach relies on large samples and normal theory to produce valid results, Bayesian techniques are expected to show superior performance in small to moderate sample sizes particularly with the non-normal data common in substance abuse prevention trials. In addition, Bayesian methods can incorporate information from previous studies further adding to their efficiency.
Aim 1 will develop Bayesian techniques to test mediation effects in cluster randomized and longitudinal models that can incorporate information from previous experiments and handle non-normal data. The resulting estimates can potentially lead to more reliable estimates and greater statistical power than current approaches.
Aim 2 develops Markov Chain Monte Carlo (MCMC) methods to estimate Bayesian mediation models. Also, computer code to implement MCMC methods in publicly free software packages (e.g., R, WinBUGS) will be written, making this work accessible to other researchers.
Aim 3 conducts a simulation study to compare the performance of the Bayesian and maximum likelihood estimators using data structures that mimic existing drug prevention cluster randomized trials and longitudinal studies. Of most interest, cluster size, number of clusters, and degree of non-normality will be varied.
Aim 4 applies both Bayesian and existing frequent is to multilevel methods to three existing data sets on drug prevention to compare the performance of the point and interval estimators of the mediation effects from each model. A Monte Carlo comparison of the performance of maximum likelihood and Bayesian approaches as a function of sample size will be conducted using repeated random samples from a large existing data set. The proposal aims to improve statistical methodology in analyzing data from randomized control trials with multiple waves of measurement in the drug prevention areas. The proposed methodology offers new methods when the number of participants is not large and enhances validity of existing statistical methods and the interpretability of the results in drug prevention and health science. My ultimate career goal is to become a faculty member in psychology, education, or the health sciences. I wish to develop and extend quantitative methods that have application in basic psychosocial research and randomized trials on substance abuse prevention. I hope to contribute to the statistical and methodological foundation that will be useful to prevention researchers in understanding the processes through which preventive interventions achieve their effects.
My immediate goals for this fellowship are twofold. First, I will further strengthen my understanding of Bayesian statistics and mediational models. I will continue to do supervised reading under the direction of my committee, notably my co-chairs professors David MacKinnon and Stephen West who are experts in mediation models, longitudinal data analysis, and research design and Professor Roy Levy who is an expert on Bayesian statistics. I have proposed and my committee has approved a comprehensive examination proposal for an extensive paper on Bayesian approaches to mediation which will further strengthen my preparation for the proposed project. I expect to complete my comprehensive examination paper reviewing Bayesian statistical approaches by May, 2009, prior to the beginning of the funding cycle. Second, I will further enhance my training in prevention research, including classes on prevention research methods approaches to prevention and the development of preventive interventions
| Tofighi, Davood; West, Stephen G; MacKinnon, David P (2013) Multilevel mediation analysis: The effects of omitted variables in the 1-1-1 model. Br J Math Stat Psychol 66:290-307 |
| Tofighi, Davood; MacKinnon, David P (2011) RMediation: an R package for mediation analysis confidence intervals. Behav Res Methods 43:692-700 |
