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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.

Yeung Yuk Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 82-85). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Historical background --- p.2 / Chapter 1.3 --- Outline of this thesis --- p.3 / Chapter 2 --- Mode classifications --- p.5 / Chapter 2.1 --- Fluid modes --- p.6 / Chapter 2.1.1 --- f mode (fundamental mode) --- p.6 / Chapter 2.1.2 --- p mode (pressure mode) --- p.7 / Chapter 2.1.3 --- g mode (gravity mode) --- p.7 / Chapter 2.2 --- w mode (spacetime mode) --- p.8 / Chapter 3 --- Oscillations of neutron stars --- p.10 / Chapter 3.1 --- The equilibrium configurations of neutron star models --- p.10 / Chapter 3.1.1 --- Newtonian stars --- p.10 / Chapter 3.1.2 --- Relativistic stars --- p.11 / Chapter 3.2 --- Perturbation of the star's equilibrium --- p.14 / Chapter 3.2.1 --- Axial perturbation equation --- p.15 / Chapter 3.2.2 --- Boundary conditions --- p.16 / Chapter 3.2.3 --- Numerical techniques --- p.16 / Chapter 3.2.4 --- The Quasinormal modes of stars --- p.18 / Chapter 4 --- Excitation and detection of QNMs --- p.20 / Chapter 4.1 --- Studies of excitation of stellar QNMs --- p.20 / Chapter 4.2 --- Detection of QNM ringing --- p.21 / Chapter 4.3 --- Parameter estimation --- p.23 / Chapter 5 --- Oscillations of realistic neutron stars --- p.28 / Chapter 5.1 --- Motivations of study --- p.28 / Chapter 5.2 --- Realistic equations of state --- p.29 / Chapter 5.3 --- Axial QNM --- p.36 / Chapter 6 --- Logarithmic perturbation method --- p.38 / Chapter 6.1 --- Introduction --- p.38 / Chapter 6.2 --- Logarithmic perturbation theory --- p.39 / Chapter 6.3 --- Evaluation of perturbation formulae --- p.42 / Chapter 6.3.1 --- The first-order perturbation --- p.42 / Chapter 6.3.2 --- The second-order perturbation --- p.47 / Chapter 6.4 --- Comparison of LPT calculations with exact results --- p.47 / Chapter 6.5 --- Discussion --- p.51 / Chapter 7 --- Scaled coordinate logarithmic perturbation method --- p.53 / Chapter 7.1 --- Rescaling of the axial perturbation equations --- p.54 / Chapter 7.1.1 --- The original axial perturbation equations --- p.55 / Chapter 7.1.2 --- The rescaled axial perturbation equations --- p.56 / Chapter 7.2 --- The formalism of SCLPT --- p.57 / Chapter 7.2.1 --- Logarithmic perturbation theory --- p.59 / Chapter 7.2.2 --- First-order perturbation --- p.63 / Chapter 7.2.3 --- Second-order perturbation --- p.65 / Chapter 7.3 --- Comparison of the perturbation calculation with the exact result --- p.67 / Chapter 7.4 --- Discussion --- p.70 / Chapter 8 --- Conclusion --- p.73 / Chapter 8.1 --- Summary --- p.73 / Chapter 8.2 --- Outlook --- p.74 / Chapter A --- Units conventions --- p.76 / Chapter B --- Numerical technique in Leaver's series --- p.77 / Chapter C --- Method of numerical derivatives --- p.80 / Bibliography --- p.82

Thesis (M.S.)--University of Missouri-Columbia, 2003. / Typescript. Includes bibliographical references (leaves 64-66). Also available on the Internet.

Thesis (M.S.)--University of Missouri-Columbia, 2003. / Typescript. Includes bibliographical references (leaves 64-66). Also available on the Internet.

published_or_final_version / Mathematics / Master / Master of Philosophy