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

One of the fundamental tasks in science is to find explainable relationships between observed phenomena. Recent work has addressed this problem by attempting to learn the structure of graphical models - especially Gaussian models - by the imposition of sparsity constraints. The graphical lasso is a popular method for learning the structure of a Gaussian model. It uses regularisation to impose sparsity. In real-world problems, there may be latent variables that confound the relationships between the observed variables. Ignoring these latents, and imposing sparsity in the space of the visibles, may lead to the pruning of important structural relationships. We address this problem by introducing an expectation maximisation (EM) method for learning a Gaussian model that is sparse in the joint space of visible and latent variables. By extending this to a conditional mixture, we introduce multiple structures, and allow side information to be used to predict which structure is most appropriate for each data point. Finally, we handle non-Gaussian data by extending each sparse latent Gaussian to a Gaussian copula. We train these models on a financial data set; we find the structures to be interpretable, and the new models to perform better than their existing competitors. A potential problem with the mixture model is that it does not require the structure to persist in time, whereas this may be expected in practice. So we construct an input-output HMM with sparse Gaussian emissions. But the main result is that, provided the side information is rich enough, the temporal component of the model provides little benefit, and reduces efficiency considerably. The GWishart distribution may be used as the basis for a Bayesian approach to learning a sparse Gaussian. However, sampling from this distribution often limits the efficiency of inference in these models. We make a small change to the state-of-the-art block Gibbs sampler to improve its efficiency. We then introduce a Hamiltonian Monte Carlo sampler that is much more efficient than block Gibbs, especially in high dimensions. We use these samplers to compare a Bayesian approach to learning a sparse Gaussian with the (non-Bayesian) graphical lasso. We find that, even when limited to the same time budget, the Bayesian method can perform better. In summary, this thesis introduces practically useful advances in structure learning for Gaussian graphical models and their extensions. The contributions include the addition of latent variables, a non-Gaussian extension, (temporal) conditional mixtures, and methods for efficient inference in a Bayesian formulation.

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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Travel Demand Management (TDM) is now considered one of the most important aspects of transportation planning and operation. The prime objective of TDM is to develop a sustainable transportation system utilizing the existing infrastructure. It is now a well known fact that excessive use of single occupancy vehicle causes numerous problems like traffic congestion, environmental pollution etc. Thus, from TDM perspective, it is of great importance to analyze travel behaviour in order to influence people to reduce car use and choose more sustainable modes such as carpool, public transit, park & ride, walk, bike etc. This study attempts an in-depth analysis of commuting mode choice behaviour using workplace commuter survey data from the City of Edmonton. Unlike traditional mode choice models, this study uses both instrumental and latent variables to better understand the choice process and analyzes their sensitivities with respect to TDM policies. / Transportation Engineering

Thesis (Ph.D.)--McMaster University, 2004. / Supervisors: John F. MacGregor, Theodora Kourti. Includes bibliographical references (leaves 221-227). Also available via World Wide Web.

Thesis (Ph.D.) -- McMaster University, 1998. / Includes bibliographical references (leaves 169-173). Also available via World Wide Web.

abstract: Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of the single mediator model with manifest and latent variables have been studied using simulation studies. However, the single mediator model with latent variables in the Bayesian framework with various accurate and inaccurate priors for structural and measurement model parameters has yet to be evaluated in a statistical simulation. This dissertation outlines the steps in the estimation of a single mediator model with latent variables as a Bayesian structural equation model (SEM). A Monte Carlo study is carried out in order to examine the statistical properties of point and interval summaries for the mediated effect in the Bayesian latent variable single mediator model with prior distributions with varying degrees of accuracy and informativeness. Bayesian methods with diffuse priors have equally good statistical properties as Maximum Likelihood (ML) and the distribution of the product. With accurate informative priors Bayesian methods can increase power up to 25% and decrease interval width up to 24%. With inaccurate informative priors the point summaries of the mediated effect are more biased than ML estimates, and the bias is higher if the inaccuracy occurs in priors for structural parameters than in priors for measurement model parameters. Findings from the Monte Carlo study are generalizable to Bayesian analyses with priors of the same distributional forms that have comparable amounts of (in)accuracy and informativeness to priors evaluated in the Monte Carlo study. / Dissertation/Thesis / Doctoral Dissertation Psychology 2017

In this thesis, we focus on the the comparison of treatments with ordered categorical responses. The three cases of treatment comparisons will all be studied. The main objective of this thesis is to develop more effective comparison methods for treatments with ordinal responses and to address some important issues involved in different comparison problems. Our major statistical approach is to consider ordinal responses as manifestations of some underlying continuous random variables. / The comparison of treatments to detect possible treatment effects is a very important topic in statistical research. It has been drawing significant interests from both academicians and practitioners. Important research work on treatment comparisons dates back several decades. For treatment comparisons, the following three cases are very common: the comparison of two independent treatments; the comparison of treatments with repeated measurements; and the multiple comparison of several treatments. For different cases, the involved research issues are usually different. In many fields of study, the level of measurement for responses of the treatments is ordinal. Many examples can be found in areas such as biostatistics, psychology, sociology, and market research, where the ordered categorical variables play an important role. / This thesis consists of three main parts. In the first part, we consider the modeling of treatments with longitudinal ordinal responses by a latent growth curve. On the basis of such a latent growth curve, we achieve a comprehensive flexible model with straightforward interpretations and a variety of applications including treatment comparison, the analysis of covariates, and equivalence test of treatments. In the second part, we consider the comparison of several treatments with a control for ordinal responses. By considering the ordinal responses as manifestations of some underlying normal random variables, a latent normal distribution model is utilized and the corresponding parameter estimation method is proposed. Further, we also derive testing procedures that compare several treatments with a control under an analytical framework. Both single-step and stepwise procedures are introduced, and these procedures are compared in terms of average power based on a simulation study. In the last part of this thesis, we establish a unified framework for treatment comparisons with ordinal responses, which allows various treatment comparison methods be comprehended using a unified perspective. The latent variable model is also utilized, but the underlying random variables are allowed to have any member of the location-scale distribution family. This latent variable model under such a specification of underlying distributions subsumes many existing models in the literature. A two-step procedure to identify the model and produce the parameter estimates is proposed. Based on this procedure, many important statistical inferences can be conveniently conducted. Furthermore, the sample size determination method based on the latent variable method is also proposed. The proposed latent variable method is compared with the existing methods in terms of power and sample size. / Lu, Tongyu. / Adviser: Wai-Yin Poon. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 94-101). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.