Bayesian Generalized Structured Component Analysis

"Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM) that postulates and examines various directional relationships among latent and observed variables. GSCA constructs components or weighted composites of observed variables as proxies for latent variables. It combines three sub-models, such as measurement, structural, and weighted relation models, into a unified formulation, and estimates all model parameters simultaneously via least squares. Over the past decade, GSCA has been extended to deal with a wider range of data types including discrete, multilevel, or intensive longitudinal data, as well as to accommodate a more variety of complex analyses such as latent moderation analysis, the capturing of cluster-level heterogeneity, and regularized analysis. To date, nonetheless, there has been no attempt to generalize the scope of GSCA into the Bayesian framework. In this dissertation, a novel extension of GSCA, called Bayesian GSCA, is proposed that estimates parameters within the Bayesian framework. Bayesian GSCA can be more attractive than GSCA in numerous respects. Firstly, it infers the probability distributions of parameters, treating the parameters as random variables, which in turn facilitates the interpretation of the parameters. Secondly, it permits specifying various structures of error terms in the measurement model, which are left unspecified in GSCA. Thirdly, it provides additional fit measures for model assessment and comparison from the Bayesian perspectives. Lastly, it allows directly incorporating external information on parameters, which may be obtainable from past research, expert opinions, subjective beliefs or knowledge on the parameters, as the form of prior distributions in the modelling process. Bayesian GSCA adopts a Markov Chain Monte Carlo method, i.e., Gibbs Sampler, to update the posterior distributions for parameters. The dissertation begins by describing two building blocks of Bayesian GSCA - GSCA and Bayesian inference, and subsequently discusses the technical underpinnings of Bayesian GSCA. It also demonstrates the usefulness of Bayesian GSCA based on the analyses of both simulated and real data. " --