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Models for establishing substantive theory in behavioral, medical, psychological and sociological sciences usually involve casual effects and correlations among the manifest variables and latent variables that cannot be measured by one single measurement. The aim of this thesis is to give some statistical analyses of some latent variable models. There are seven chapters in this thesis. The first two chapters respectively give an outline of the thesis and present some methodologies. In Chapters 3 and 4, the maximum likelihood and Bayesis estimations of the models for binary data and polytomous data are given respectively, in which some statistical analyses are also discussed. Chapters 5 describes a Bayesian procedure and two maximum likelihood methods to analyze the general nonlinear structural equation models. In Chapter 6, nonlinear structural equation models with continuous and polytomous variables are discussed. Finally, we extend the previous methodology to deal with the multilevel data in Chapter 7. / by Hong-tu Zhu. / "December 1999." / Adviser: Sik-Yum Lee. / Source: Dissertation Abstracts International, Volume: 61-03, Section: B, page: 1479. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 120-135). / 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 dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Lam Yuk Fai. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 50-52). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Includes bibliographical references (p. 112-117).

Latent variables are often included in a model in order to capture the diversity among subjects in a population. Sometimes the distribution of these latent variables are of principle interest. In studies where sequences of observations are taken from subjects, ancillary variables, such as the number of observations provided by each subject, usually also vary between subjects. The goal here is to understand efficient estimation of the expectation of the latent variable in the presence of these subject-specific ancillaries. Unbiased estimation and efficient estimation of the expectation of the latent parameter depend on the dependence structure of these three subject-specific components: latent variable, sequence of observations, and ancillary. This dissertation considers estimation under two dependence configurations. In Chapter 3, efficiency is studied under the model in which no assumptions are made about the joint distribution of the latent variable and the subject-specific ancillary. Chapter 4 treats the setting where the ancillary variable and the latent variable are independent.

Xu Liang. / "June 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 74-82). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Tsang, Yim Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background of the Latent Normal Model and the Latent Growth Curve Model --- p.4 / Chapter 2.1 --- Latent. Variable Growth Curve Modeling --- p.5 / Chapter 2.1.1 --- Two-factor Latent Variable Growth Curve Model for Two Time Points --- p.5 / Chapter 2.1.2 --- The Intercept and Slope Factors --- p.7 / Chapter 2.1.3 --- The Factor Loadings of the Slope Factor --- p.8 / Chapter 2.1.4 --- The Error Variance --- p.9 / Chapter 2.1.5 --- "Expressing Model Parameters as Functions of Measured Means, Variances and Covariances" --- p.10 / Chapter 2.2 --- Maximum Likelihood Estimation of the Latent Normal Model from Ordinal Data --- p.12 / Chapter 2.2.1 --- Model --- p.13 / Chapter 2.2.2 --- The Maximum Likelihood Estimation Function --- p.15 / Chapter 2.2.3 --- Derivation of the Likelihood Equations --- p.16 / Chapter 2.3 --- The Two Approaches for Generalizing the Latent Normal Model for Analyzing Latent Growth Curve Model --- p.17 / Chapter 3 --- Latent Variable Growth Curve Modeling for Ordinal Categorical Data --- p.19 / Chapter 3.1 --- The Model and the Maximum Likelihood Estimation --- p.20 / Chapter 3.1.1 --- The Two-factor Growth Curve Model with Ordinal Variables --- p.20 / Chapter 3.1.2 --- Implementation --- p.23 / Chapter 3.2 --- The Two-Stage Estimation Method --- p.28 / Chapter 3.2.1 --- Maximum Likelihood Estimation of the Latent Normal Method --- p.28 / Chapter 3.2.2 --- Two-factor Latent Growth Curve Model --- p.29 / Chapter 3.3 --- Misleading Result of Using Continuous Assumption for Ordinal Categorical Data --- p.31 / Chapter 3.3.1 --- Latent Growth Curve Modeling Method --- p.32 / Chapter 3.3.2 --- Direct Continuous Assumption to the Ordinal Categorical Data --- p.33 / Chapter 3.3.3 --- Interpretation --- p.35 / Chapter 3.4 --- Simulation Study --- p.36 / Chapter 4 --- Conclusion --- p.40 / Appendices --- p.43 / A Sample Mx Input Script for Latent Growth Curve Analysis of Ordinal Categorical Data --- p.43

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Daniel L. McGee, Sr., Florida State University, College of Arts and Sciences, Dept. of Statistics. Title and description from dissertation home page (viewed Sept. 21, 2006). Document formatted into pages; contains xii, 147 pages. Includes bibliographical references.

Local influence (LI) analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. However, arbitrarily perturbing a model may result in misleading inference about the influential aspects in the model. Hence, an important issue of local influence analysis is to select an appropriate perturbation vector. In this thesis, we develop a general method to select an appropriate perturbation vector as well as second-order local influence measures to address this issue in the context of latent variable models (LVMs). The proposed methodologies are applied to nonlinear structural equation models (NSEMs), generalized linear mixed models (GLMMs), and two-level structural equation models (SEMs) with continuous and ordered categorical data. For nonlinear structural equation models, some perturbation schemes are investigated, including three schemes where simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the causal influential ones. In generalized linear mixed models, perturbation schemes are designed such that the influence of the observations in the clusters can be assessed under some schemes and the influence assessment of the clusters can be obtained under the other schemes. In two-level structural equation models, some perturbation schemes are considered to obtain the influence assessment of the clusters. The proposed procedures are illustrated by simulation studies and real examples. / Chen, Fei. / Adviser: Sik-Yum Lee. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3584. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 73-77). / 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. / Abstracts in English and Chinese. / School code: 1307.

by Ming-long Lam. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 41-43.