Bayesian Structural Equation Modeling of Time Series Data and Longitudinal Data
| Autor: | Yi-Fu Wang, 王義富 |
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| Rok vydání: | 2011 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 99 Structural equation models (SEM) have been extensively used in behavioral, social, and psychological research to model relations between latent variables and observations. Most softwares for fitting SEM rely on frequentist methods. However, traditional models and softwares are not appropriate to analyze dependent observations such as the time-series data and multidimensional longitudinal data. We first introduce a structural equation model with time series feature via Bayesian approach with the aid of the Markov chain Monte Carlo method. Bayesian inference as well as prediction of the proposed time series structural equation model will be developed which can also reveal certain unobserved relationship among the observations. The approach is successfully employed using real Asian, American and European stock return data. Moreover, we consider to deal with the multidimensional longitudinal myopia data with correlation between both eyes. Myopia is becoming a significant public health problem, affecting more and more people. Motivated by the increase in the number of people affected by this problem, the primary focus is to utilize mathematical methods to gain further insight into their relationship with myopia. Accordingly, utilizing multidimensional longitudinal myopia data with correlation between both eyes, a Bayesian structural equation model including random effects is developed. Four observed factors, including intraocular pressure, anterior chamber depth, lens thickness and axial length, are considered. The results indicate that the genetic effect has much greater influence on myopia than the environmental effects. We also consider to apply the model selection problem with mixture prior to the SEMs. To put the reasonable mixture prior on the specific parameter which describes the doubting relationship in the SEMs, the model posterior probability can be computed via the MCMC iterations and viewed as a Bayesian model selection criterion. An advantage of the method using mixture priors is that it can automatically identify the predictors having non-zero fixed effect coefficients or non-zero random effects variance in the MCMC procedure. Specifically, we will focus on the multidimensional longitudinal myopia data to reduce the dimensionality of the parameter space and to select the simpler model. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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