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A Bayesian Synthesis approach to data fusion using augmented data-dependent priors

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The process of combining data is one in which information from disjoint datasets sharing at least a number of common variables is merged. This process is commonly referred to as

The process of combining data is one in which information from disjoint datasets sharing at least a number of common variables is merged. This process is commonly referred to as data fusion, with the main objective of creating a new dataset permitting more flexible analyses than the separate analysis of each individual dataset. Many data fusion methods have been proposed in the literature, although most utilize the frequentist framework. This dissertation investigates a new approach called Bayesian Synthesis in which information obtained from one dataset acts as priors for the next analysis. This process continues sequentially until a single posterior distribution is created using all available data. These informative augmented data-dependent priors provide an extra source of information that may aid in the accuracy of estimation. To examine the performance of the proposed Bayesian Synthesis approach, first, results of simulated data with known population values under a variety of conditions were examined. Next, these results were compared to those from the traditional maximum likelihood approach to data fusion, as well as the data fusion approach analyzed via Bayes. The assessment of parameter recovery based on the proposed Bayesian Synthesis approach was evaluated using four criteria to reflect measures of raw bias, relative bias, accuracy, and efficiency. Subsequently, empirical analyses with real data were conducted. For this purpose, the fusion of real data from five longitudinal studies of mathematics ability varying in their assessment of ability and in the timing of measurement occasions was used. Results from the Bayesian Synthesis and data fusion approaches with combined data using Bayesian and maximum likelihood estimation methods were reported. The results illustrate that Bayesian Synthesis with data driven priors is a highly effective approach, provided that the sample sizes for the fused data are large enough to provide unbiased estimates. Bayesian Synthesis provides another beneficial approach to data fusion that can effectively be used to enhance the validity of conclusions obtained from the merging of data from different studies.

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  • 2017

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Handling sparse and missing data in functional data analysis: a functional mixed-effects model approach

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This paper investigates a relatively new analysis method for longitudinal data in the framework of functional data analysis. This approach treats longitudinal data as so-called sparse functional data. The first

This paper investigates a relatively new analysis method for longitudinal data in the framework of functional data analysis. This approach treats longitudinal data as so-called sparse functional data. The first section of the paper introduces functional data and the general ideas of functional data analysis. The second section discusses the analysis of longitudinal data in the context of functional data analysis, while considering the unique characteristics of longitudinal data such, in particular sparseness and missing data. The third section introduces functional mixed-effects models that can handle these unique characteristics of sparseness and missingness. The next section discusses a preliminary simulation study conducted to examine the performance of a functional mixed-effects model under various conditions. An extended simulation study was carried out to evaluate the estimation accuracy of a functional mixed-effects model. Specifically, the accuracy of the estimated trajectories was examined under various conditions including different types of missing data and varying levels of sparseness.

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  • 2016

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Statistical properties of the single mediator model with latent variables in the bayesian framework

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Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of

Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of the single mediator model with manifest and latent variables have been studied using simulation studies. However, the single mediator model with latent variables in the Bayesian framework with various accurate and inaccurate priors for structural and measurement model parameters has yet to be evaluated in a statistical simulation. This dissertation outlines the steps in the estimation of a single mediator model with latent variables as a Bayesian structural equation model (SEM). A Monte Carlo study is carried out in order to examine the statistical properties of point and interval summaries for the mediated effect in the Bayesian latent variable single mediator model with prior distributions with varying degrees of accuracy and informativeness. Bayesian methods with diffuse priors have equally good statistical properties as Maximum Likelihood (ML) and the distribution of the product. With accurate informative priors Bayesian methods can increase power up to 25% and decrease interval width up to 24%. With inaccurate informative priors the point summaries of the mediated effect are more biased than ML estimates, and the bias is higher if the inaccuracy occurs in priors for structural parameters than in priors for measurement model parameters. Findings from the Monte Carlo study are generalizable to Bayesian analyses with priors of the same distributional forms that have comparable amounts of (in)accuracy and informativeness to priors evaluated in the Monte Carlo study.

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  • 2017