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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.

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.

by Mannon Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 42-47). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Maximum Likelihood Estimations of Polyserial Correlations --- p.7 / Chapter 3 --- Normal Curvature and the Conformal Normal Curvature of Lo- cal Influence --- p.12 / Chapter 3.1 --- Normal Curvature --- p.14 / Chapter 3.2 --- Conformal Normal Curvature as an Influential Measure --- p.16 / Chapter 4 --- Influential Observations in the Estimations of Polyserial Corre- lations and the Thresholds --- p.18 / Chapter 4.1 --- Case-weights perturbation --- p.18 / Chapter 4.2 --- "Observations Influencing the Estimates of = (μ, Σ, ε，T)" --- p.20 / Chapter 4.3 --- "Observations Influencing the Estimates of θ1 = （(μ, Σ)" --- p.25 / Chapter 4.4 --- Observations Influencing the Estimates of θ2 = （(ε，T) --- p.27 / Chapter 5 --- Examples --- p.28 / Chapter 5.1 --- Cox's Data --- p.28 / Chapter 5.2 --- Aids Data --- p.32 / Chapter 5.3 --- Simulation Data --- p.35 / Chapter 6 --- Discussion --- p.38 / Chapter 7 --- References --- p.42 / Chapter A --- Appendix I --- p.48 / Chapter B --- Appendix II --- p.50 / Chapter C --- Appendix III --- p.73

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