Latent variable models (LVMS) are widely appreciated multivariate methods to explore variables that are related to the observed variables, and assessing the relationships among them. One of most widely used latent variable models is structural equation model (SEM). Based on more than a dozen standard packages for fitting SEMs, such as LISREL VIII (Jorskog and Sorbom, 1996), and EQS (Bentler, 2004), these models have been widely appreciated in behavioral, educational, medical, social, and psychological research. The statistical theories and methods in these packages are based on the normal distribution; hence, they are vulnerable to outliers and the non-normal assumption. As outliers and non-normal data set are commonly encountered in substantive research, this fundamental problem has received much attention in the field. However, almost all existing methods are developed via the covariance structure analysis approach that heavily depends on the asymptotical properties of the sample covariance matrices S. Hence, this approach cannot be applied to the more complex SEMs and/or SEMs with more complex data structure such as missing data, because under these more complicated situations S is complicated, and its asymptotical properties are not well known. The objectives of this thesis are to develop novel robust methods for analyzing complex SEMs and/or more data structures, including but not limited to nonlinear SEMs with missing data. Both maximum likelihood (ML) and Bayesian approaches for estimation, hypothesis testing and model comparison will be investigated. Efficient algorithm for computing the results for statistical inference will be developed through unitization and modification of the advanced tools in statistical computing, for example the Monte Carlo Expectation-Maximization algorithm, and the Markov Chains Monte Carlo methods. Asymptotical properties of some statistics are derived. Simulation studies and real examples are conducted to reveal the empirical performance of the Bayesian and ML approaches. The newly developed methodologies will be very useful for analyzing complex data in the substantive research. / Xia Yemao. / "October 2005." / Adviser: S. Y. Lee. / Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3883. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 105-114). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343682 |
| Date | January 2005 |
| Contributors | Xia, Yemao., Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (xiii, 127 p. : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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