Bayesian Generalized Structured Component Analysis
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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. " --
Generalized Structured Component Analysis
Developed by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured component analysis allows researchers to evaluate the adequacy of a model as a whole, compare a model to alternative specifications, and conduct complex analyses in a straightforward manner. Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling provides a detailed account of this novel statistical methodology and its various extensions. The authors present the theoretical underpinnings of generalized structured component analysis and demonstrate how it can be applied to various empirical examples. The book enables quantitative methodologists, applied researchers, and practitioners to grasp the basic concepts behind this new approach and apply it to their own research. The book emphasizes conceptual discussions throughout while relegating more technical intricacies to the chapter appendices. Most chapters compare generalized structured component analysis to partial least squares path modeling to show how the two component-based approaches differ when addressing an identical issue. The authors also offer a free, online software program (GeSCA) and an Excel-based software program (XLSTAT) for implementing the basic features of generalized structured component analysis.
Bayesian Psychometric Modeling
A Single Cohesive Framework of Tools and Procedures for Psychometrics and Assessment Bayesian Psychometric Modeling presents a unified Bayesian approach across traditionally separate families of psychometric models. It shows that Bayesian techniques, as alternatives to conventional approaches, offer distinct and profound advantages in achieving many goals of psychometrics. Adopting a Bayesian approach can aid in unifying seemingly disparate—and sometimes conflicting—ideas and activities in psychometrics. This book explains both how to perform psychometrics using Bayesian methods and why many of the activities in psychometrics align with Bayesian thinking. The first part of the book introduces foundational principles and statistical models, including conceptual issues, normal distribution models, Markov chain Monte Carlo estimation, and regression. Focusing more directly on psychometrics, the second part covers popular psychometric models, including classical test theory, factor analysis, item response theory, latent class analysis, and Bayesian networks. Throughout the book, procedures are illustrated using examples primarily from educational assessments. A supplementary website provides the datasets, WinBUGS code, R code, and Netica files used in the examples.