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 (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 38-41). Also available in electronic version. Access restricted to campus users.

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.

在許多實驗研究中，實驗數據經常由有序觀測數據組成，這樣的例子很容易在醫學、臨床研究、社會學或心理學的研究中找到。一般有兩種方法可以用來分析有序分類數據。第一種方法是基於Wilcoxon-Mann-Whitney 統計量的非參數方法，第二種方法是把響應變量看成是某個連續潛變量模型的一種表現的潛變量模型。在本論文中，我們主要研究基於潛變量模型對具有一維或二維有序分類響應變量的處理的比較問題，同時解決具有一維有序分類數據的多重比較過程的功效及樣本量的確定問題。 / 潛變量模型已經被應用于對具有一維有序分類觀測數據的含有對照組的多重比較中。這種方法可以很好地應用于臨床研究中對含有對照組的不同治療方法的效用比較問題。在本論文的第一部份中，我們致力於把這種思想推廣到成對多重比較，成對多重比較是臨床研究中另一個很重要的課題。我們通過隨機模擬來對不同的方法在控制整體第一類錯誤和功效的優勢進行評估。在本論文的第二部份，我們主要研究具有二維有序分類響應變量的多重比較過程。在這些過程中，我們把二維有序分類數據看成是某個潛二維變量的一種表現。非參數方法也經常被應用於做兩個處理的比較問題。然而在本文中，我們對非參數方法的劣勢進行了說明。處理具有二維有序分類響應變量的含有對照組的多重比較問題是本論文的研究重點。基於潛變量模型的方法，我們給出了含有對照組的多重比較的若干檢驗過程，包括單步檢驗過程和逐步檢驗過程。在論文的第三部份，我們對具有一維有序分類數據的含有對照組的多重比較過程的功效和樣本量的確定問題進行了討論。基於Lu, Poon and Cheung (2012) 建議的多重比較過程，我們得到了滿足一定功效的樣本量的確定方法，并通過實例進行了說明。 / In many scientific studies, research data are frequently composed of ordered categorical observations. Numerous examples could easily be found in areas including medical and clinical studies, sociology and psychology. There are two popular approaches in analyzing ordered categorical data. One is to employ the non-parametric method based on the Wilcoxon-Mann-Whitney statistics. The other is to use the latent variable model that conceptualizes the responses as manifestations of some underlying continuous variables. In this project, we focus on the comparisons of different populations with either univariate or bivariate ordered categorical observations using a latent variable model. The study of power and sample size requirement for multiple testing with univariate ordered categorical data are also provided in this thesis. / For univariate ordered categorical observations, the latent variable model has been used to compare treatments with a control. The developed methods are useful for applications in clinical studies where one would like to compare the efficacy of different treatments with a given control/placebo. In this thesis, we seek to extend this idea to develop the useful procedures for pairwise multiple comparisons which are often important objectives of clinical trials. Extensive simulation studies regarding overall type I error rate and power are performed to evaluate the merits of different procedures. / The second part of this thesis is devoted to multiple comparison methods with bivariate ordered categorical responses under the assumption that the bivariate ordered categorical data are manifestations of an underlying bivariate normal distribution. To compare two population mean vectors, nonparametric procedures are also frequently being used, but as demonstrated in this thesis, these methods are inferior to testing procedures based on the latent variable model. Hence, by the adoption of the latent variable model, we develop procedures that can be used to conduct multiple comparisons with a control for bivariate categorical responses. Different multiple comparison mechanisms including single-step and stepwise procedures are explored. Numerical examples for illustrative purposes are also given. / For the last part of this thesis, we discuss power and sample size determination for multiple comparisons with control for univariate ordered categorical data. Based on the multiple testing procedures proposed by Lu, Poon and Cheung (2012), we derive the procedure to compute the required sample size that guarantee a pre-specified power level. Numerical examples are also given. / For the last part of this thesis, we discuss power and sample size determination for multiple comparisons with control for univariate ordered categorical data. Based on the multiple testing procedures proposed by Lu, Poon and Cheung (2012), we derive the procedure to compute the required sample size that guarantee a pre-specified power level. Numerical examples are also given. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lin, Yueqiong. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 92-100). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Outline of the thesis --- p.4 / Chapter 2 --- Pairwise Comparisons with Ordered Categorical Responses --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Proportional odds model --- p.8 / Chapter 2.3 --- Latent variable model --- p.11 / Chapter 2.4 --- Pairwise comparisons --- p.15 / Chapter 2.4.1 --- Single-step procedure and the computation of critical values . --- p.15 / Chapter 2.4.2 --- Approximation of critical values --- p.16 / Chapter 2.4.3 --- A single-step conservative testing procedure: the Bonferroni procedure --- p.18 / Chapter 2.4.4 --- A step-wise testing procedure: Hochberg's step-up procedure . --- p.19 / Chapter 2.5 --- Simulation: power comparison --- p.20 / Chapter 2.6 --- Examples --- p.24 / Chapter 2.7 --- Conclusion --- p.28 / Chapter 3 --- Multiple comparison procedures for a latent variable model with bivariate ordered categorical responses --- p.29 / Chapter 3.1 --- Introduction --- p.29 / Chapter 3.2 --- Latent bivariate normal model --- p.31 / Chapter 3.2.1 --- The model --- p.31 / Chapter 3.2.2 --- Model specification --- p.33 / Chapter 3.2.3 --- Test Statistics --- p.35 / Chapter 3.2.4 --- Statistical inference --- p.35 / Chapter 3.3 --- Nonparametric test --- p.37 / Chapter 3.3.1 --- Test statistic --- p.39 / Chapter 3.3.2 --- A Comparison between the latent variable model procedure and nonparametric tests --- p.42 / Chapter 3.4 --- Multiple comparisons of several treatments with a control based on the latent variable model --- p.47 / Chapter 3.5 --- Simulation --- p.51 / Chapter 3.6 --- Examples --- p.56 / Chapter 3.7 --- Conclusion --- p.59 / Chapter 4 --- Sample size determination for multiple comparisons with ordered univariate categorical data --- p.62 / Chapter 4.1 --- Introduction --- p.62 / Chapter 4.2 --- Multiple comparisons of treatments a control with ordered categorical responses --- p.64 / Chapter 4.3 --- Power function --- p.67 / Chapter 4.4 --- Sample size determination and tables --- p.75 / Chapter 4.5 --- Examples --- p.85 / Chapter 4.6 --- Conclusion --- p.88 / Chapter 5 --- Further Research --- p.90 / Bibliography --- p.92 / Appendix / Chapter A --- Procedures to obtain the MLE of parameter θ₀ --- p.101 / Chapter B --- Nonparametric test --- p.105 / Chapter C --- Procedures to obtain the critical value for Dunnett's single-step procedure --- p.109 / Chapter D --- Procedures to obtain the critical value for Dunnett's single-step procedure with balanced homogeneous groups --- p.112

A real empirical study was conducted to illustrate the application of the unconstrained approach. The genuine study focused on the interaction effect of music self-concept and music-domain importance on the global self-concept. The result showed that structural equation analysis was advantageous over the traditional regression analysis, while such superiority of the structural equation modeling approach was more prominent in higher-order structural equation models. As expected, the estimated main and interaction effects in the quasi-standardized solution obtained using the centered data coincided with those using the standardized data in different order structural models. / Concepts and issues related to standardized solutions for the latent interaction model were discussed. Quasi-standardized solution was proposed and formulated by using the estimates of the original solution and the ordinary standardized solution. Some properties of the quasi-standardized solution were mathematically derived and proved, which included the demonstration that the main and interaction effects were scale free, so were the loading and the Chi-square of model fit, while t statistics of main and interaction effects were approximate scale free. / Six simulation studies, four for the latent interaction models, and two for the latent quadratic models were conducted to compare the performances of the four approaches. Results generally showed that the QML approach and the constrained approach behaved similarly, while the performance of the unconstrained approach was close to that of the GAPI approach. Under the normal distribution condition, the QML approach performed the best among the four approaches in terms of lack of bias, precision, and power. However, with moderate and large sample sizes (N=200 or above), the differences among the four approaches were systematically smaller, with similar bias and precision. Under nonnormal conditions, the unconstrained approach was more robust, with a smaller bias and predictable type I error rate (near the significant level), and its precision and power increased as the sample size increased. These results supported the use of the unconstrained approach for the analyses of latent interaction and quadratic models. / The unconstrained approach was extended to estimate interaction effects in latent growth models. With the indicators of the interaction term formed by the products of differences (rather than using the usual indicator product strategy), a simplified full interaction model for the latent growth model was proposed. The model was further simplified when only the interaction between change rates was considered. Importantly, the unconstrained approach was an appropriate method for analyses of such simplified full interaction model for latent growth model, which also constituted a unique contribution of this dissertation. / Through a series of related studies, the research attempted to identify better estimation approaches and modeling techniques for latent interaction and quadratic effects. The literature review provided a conceptual framework for the unconstrained approach which was recommended for its simplicity and robustness. Three other approaches, namely, the constrained, the partially constrained (i.e., the generalized appended product indicator, GAPI), and the quasi-maximum likelihood (QML) approaches were selected and compared with the unconstrained approach. / 溫忠粦. / 論文(哲學博士)--香港中文大學, 2005. / 參考文獻(p. 191-203). / Adviser: Kit-Tai Hau. / Source: Dissertation Abstracts International, Volume: 67-01, Section: A, page: 0160. / 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 also in English. / School code: 1307. / Lun wen (Zhe xue bo shi)--Xianggang Zhong wen da xue, 2005. / Can kao wen xian (p. 191-203). / Wen Zhonglin.

Chen, Qiuting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 71-74). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Bayesian Approach --- p.3 / Chapter 1.3 --- Outline of the thesis --- p.5 / Chapter 2 --- Model Descriptions --- p.6 / Chapter 2.1 --- Basic Latent Curve Models --- p.6 / Chapter 2.2 --- Latent Curve Models with Exogenous Latent Variables --- p.8 / Chapter 2.3 --- Latent Curve Models with both Exogenous Variables and Longitudinal La- tent Variables --- p.9 / Chapter 2.4 --- multisample analysis --- p.12 / Chapter 3 --- Bayesian Estimation and Model Comparison --- p.18 / Chapter 3.1 --- Bayesian analysis for parameter estimation --- p.18 / Chapter 3.2 --- Bayesian model comparison --- p.27 / Chapter 4 --- A simulation study --- p.31 / Chapter 4.1 --- Simulation for parameter estimations --- p.31 / Chapter 4.2 --- Simulation for model comparison using DIC --- p.35 / Chapter 5 --- An illustrative example --- p.47 / Chapter 5.1 --- Background introduction --- p.47 / Chapter 5.2 --- Some firm-specific factors that may affect the capital structure --- p.49 / Chapter 5.3 --- Real data illustration --- p.52 / Chapter 6 --- Conclusion and further discussion --- p.65 / Appendix --- p.67 / Chapter 7 --- Appendix: equation derivation --- p.67 / Bibliography

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Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Laura M. Stapleton. Vita. Includes bibliographical references.

Wing-Yeong Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 73-75). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The observed data --- p.3 / Chapter 1.3 --- Outline of the thesis --- p.8 / Chapter Chapter 2 --- Modeling using Latent Variable --- p.9 / Chapter Chapter 3 --- Imputation Procedure --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- Introduction to Metropolis-Hastings algorithm --- p.18 / Chapter 3.3 --- Introduction to Gibbs sampler --- p.19 / Chapter 3.4 --- Imputation step --- p.21 / Chapter 3.5 --- Initialization of the missing values by regression --- p.23 / Chapter 3.6 --- Initialization of the parameters and creating the latent variable and noises --- p.27 / Chapter 3.7 --- Simulation of Y's --- p.30 / Chapter 3.8 --- Simulation of the parameters --- p.34 / Chapter 3.9 --- Simulation of T by use of the Metropolis-Hastings algorithm --- p.41 / Chapter 3.10 --- Distribution of Vij's given all other values --- p.44 / Chapter 3.11 --- Simulation procedure of Vij's --- p.46 / Chapter Chapter 4 --- Data Analysis of the Pollutant Data --- p.48 / Chapter 4.1 --- Convergence of the process --- p.48 / Chapter 4.2 --- Data analysis --- p.53 / Chapter Chapter 5 --- Conclusion --- p.69 / REFERENCES --- p.73