Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2009. / Includes bibliographical references (p. 95-99).

Structural Equation Modeling is a common name for the statistical analysis of Structural Equation Models. Structural Equation Models are models that specify relationships between a set of variables and can be specified by means of path diagrams. A number of Structural Equation Modeling programs have been developed. These include, amongst others, AMOS, EQS, LISREL, Mx, RAMONA and SEPATH. A number of studies have been published on the use of some of the applications mentioned above. They include, amongst others, Brown (1986), Waller (1993) and Kano (1997). Structural Equation Models are increasingly being used in the social, economic and behavioral sciences. More and more people are therefore making use of one or more of the Structural Equation Modeling applications on the market. This study is performed with the aim of using each of the Structural Equation Modeling applications AMOS, EQS, LISREL, Mx, RAMONA and SEPATH for the first time and document the experience, joy and the difficulties encountered while using them. This treatise is different from the comparisons already published in that it is based on the use of AMOS, EQS, LISREL, Mx, RAMONA and SEPATH to fit a Structural Equation Model for peer influences on ambition, which is specified for data obtained by Duncan, Haller and Portes (1971), by myself as a first time user of each of the programs mentioned. The impressive features as well as the difficulties encountered are listed for each application. Recommendations for possible improvements to the various applications are also proposed. Finally, recommendations for future studies on the use of Structural Equation Modeling programs are made.

Recently there has been a renewed interest in formative measurement and its role in properly specified models. Formative measurement models are difficult to identify, and hence to estimate and test. Existing solutions to the identification problem are shown to not adequately represent the formative constructs of interest. We propose a new two-step approach to operationalize a formatively measured construct that allows a closely matched common factor equivalent to be included in any structural equation model. We provide an artificial example and an original empirical study of privacy to illustrate our approach. Detailed proofs are given in an appendix.

Broadly speaking, cluster analysis is the organization of a data set into meaningful groups and mixture model-based clustering is recently receiving a wide interest in statistics. Historically, the Gaussian mixture model has dominated the model-based clustering literature. When model-based clustering is performed on a large number of observed variables, it is well known that Gaussian mixture models can represent an over-parameterized solution. To this end, this thesis focuses on the development of novel non-Gaussian mixture models for high-dimensional continuous and categorical data. We developed a mixture of joint generalized hyperbolic models (JGHM), which exhibits different marginal amounts of tail-weight. Moreover, it takes into account the cluster specific subspace and, therefore, limits the number of parameters to estimate. This is a novel approach, which is applicable to high, and potentially very- high, dimensional spaces and with arbitrary correlation between dimensions. Three different mixture models are developed using forms of the mixture of latent trait models to realize model-based clustering of high-dimensional binary data. A family of mixture of latent trait models with common slope parameters are developed to reduce the number of parameters to be estimated. This approach facilitates a low-dimensional visual representation of the clusters. We further developed the penalized latent trait models to facilitate ultra high dimensional binary data which performs automatic variable selection as well. For all models and families of models developed in this thesis, the algorithms used for model-fitting and parameter estimation are presented. Real and simulated data sets are used to assess the clustering ability of the models. / Thesis / Doctor of Philosophy (PhD)

Diplomová práce se zabývá problémem strojového učení nepozorovaných úrovní abstrakce mělké sémantické reprezentace. Odstraňujeme předpoklady, které se při sémantické anotaci lingvistických zdrojů obvykle činí, např. pevný počet sémantických rolí v PropBanku, a učíme se klíčové lingvistické prvky této ano- tace (sémantické rámce, slovesa, lexikální a syntaktické třídy) s různou mírou ab- strakce. Model implementujeme pomocí latentních gramatik a získané struktury je možné použít pro úlohu značkování sémantických rolí (semantic role labeling, SRL) v několika jazycích s přesností srovnatelnou s jinými současnými přístupy. Navíc ukazujeme, že tyto struktury jsou velmi blízké abstrakcím, které je možné pozorovat ve FrameNetu. Celkovým výsledkem je tak jazykově-nezávislý model sémantické informace bez rysů, který produkuje interpretovatelné struktury a jeho použitelnost je na úloze SRL empiricky ověřena.

Latent variable models play an important role in psychological and educational measurement, which attempt to uncover the underlying structure of responses to test items. This thesis focuses on the development of statistical learning methods based on latent variable models, with applications to psychological and educational assessments. In that connection, the following problems are considered. The first problem arises from a key assumption in latent variable modeling, namely the local independence assumption, which states that given an individual's latent variable (vector), his/her responses to items are independent. This assumption is likely violated in practice, as many other factors, such as the item wording and question order, may exert additional influence on the item responses. Any exploratory analysis that relies on this assumption may result in choosing too many nuisance latent factors that can neither be stably estimated nor reasonably interpreted. To address this issue, a family of models is proposed that relax the local independence assumption by combining the latent factor modeling and graphical modeling. Under this framework, the latent variables capture the across-the-board dependence among the item responses, while a second graphical structure characterizes the local dependence. In addition, the number of latent factors and the sparse graphical structure are both unknown and learned from data, based on a statistically solid and computationally efficient method. The second problem is to learn the relationship between items and latent variables, a structure that is central to multidimensional measurement. In psychological and educational assessments, this relationship is typically specified by experts when items are written and is incorporated into the model without further verification after data collection. Such a non-empirical approach may lead to model misspecification and substantial lack of model fit, resulting in erroneous interpretation of assessment results. Motivated by this, I consider to learn the item - latent variable relationship based on data. It is formulated as a latent variable selection problem, for which theoretical analysis and a computationally efficient algorithm are provided.

This dissertation encompasses three studies on issues of model-data fit methods for latent variable models implemented in modern educational measurement. The first study proposes a new statistic to test the mean-difference of the ability distributions estimated based on the responses of a group of examinees, which can be used to detect aberrant responses of a group of test-takers. The second study is a review of the current model-data fit indexes used for cognitive diagnostic models. Third study introduces a modified version of an existing item fit statistic so that the modified statistic has a known chi-square distribution. Lastly, a discussion of the three studies is given, including the studies’ limitations and thoughts on the direction of future research.

In medical, behavioral, and social-psychological sciences, latent variable models are useful in handling variables that cannot be directly measured by a single observed variable, but instead are assessed through a number of observed variables. Traditional latent variable models are usually based on parametric assumptions on both relations between outcome and explanatory latent variables, and error distributions. In this thesis, semiparametric models with Bayesian P-splines are developed to relax these rigid assumptions. / In the fourth part of the thesis, the methodology developed in the third part is further extended to a varying coefficient model with latent variables. Varying coefficient model is a class of flexible semiparametric models in which the effects of covariates are modeled dynamically by unspecified smooth functions. A transformation varying coefficient model can handle arbitrarily distributed dynamic data. A simulation study shows that our proposed method performs well in the analysis of this complex model. / In the last part of the thesis, we propose a finite mixture of varying coefficient models to analyze dynamic data with heterogeneity. A simulation study demonstrates that our proposed method can explore possible existence of different groups in a dynamic data, where in each group the dynamic influences of covariates on the response variables have different patterns. The proposed method is applied to a longitudinal study concerning the effectiveness of heroin treatment. Distinct patterns of heroin use and treatment effect in different patient groups are identified. / In the second part of the thesis, a latent variable model is proposed to relax the first assumption, in which unknown additive functions of latent variables in the structural equation are modeled by Bayesian P-splines. The estimation of nonparametric functions is based on powerful Markov chain Monte Carlo (MCMC) algorithm with block update scheme. A simulation study shows that the proposed method can handle much wider situation than traditional models. The proposed semiparametric latent variable model is applied to a study on osteoporosis prevention and control. Some interesting functional relations, which may be overlooked by traditional parametric latent variable models, are revealed. / In the third part of the thesis, a transformation model is developed to relax the second assumption, which usually assumes the normality of observed variables and random errors. In our proposed model, the nonnormal response variables are transformed to normal by unknown functions modeled with Bayesian P-splines. This semiparametric transformation model is shown to be applicable to a wide range of statistical analysis. The model is applied to a study on the intervention treatment of polydrug use in which the traditional model assumption is violated because many observed variables exhibit serious departure from normality. / Lu, Zhaohua. / Adviser: Xin-Yuan Song. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 119-130). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Bin Lu. / "September 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 118-126) / 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.

Lam, Kwok Hap. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 68-72). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Two-level NSEM with outcomes from Exponential Family --- p.6 / Chapter 2.1 --- Basic Model Description --- p.7 / Chapter 2.2 --- Generalization from Normal Distribution to Exponential Family Distributions --- p.9 / Chapter 2.3 --- Bayesian Analysis of the Model --- p.10 / Chapter 2.3.1 --- Posterior Analysis and Gibbs Sampler --- p.10 / Chapter 2.3.2 --- Prior Distributions --- p.11 / Chapter 2.3.3 --- Bayesian Estimation --- p.13 / Chapter 2.3.4 --- Bayesian Model Selection --- p.14 / Chapter 2.4 --- A Simulation Study --- p.15 / Chapter 3 --- Two-level NSEM with mixed continuous and ordered categorical data --- p.28 / Chapter 3.1 --- Model Description --- p.29 / Chapter 3.2 --- Bayesian Analysis of the Model --- p.30 / Chapter 3.2.1 --- Posterior Analysis and Gibbs Sampler --- p.30 / Chapter 3.2.2 --- Bayesian Estimation --- p.31 / Chapter 3.3 --- A Simulation Study --- p.31 / Chapter 4 --- "Two-level NSEM with mixed continuous, count and binomial data" --- p.36 / Chapter 4.1 --- Model Description --- p.37 / Chapter 4.2 --- Bayesian Estimation --- p.38 / Chapter 4.3 --- A Simulation Study --- p.39 / Chapter 5 --- Two-level NSEM with mixed continuous and unordered categorical data --- p.43 / Chapter 5.1 --- Basic Model Description --- p.44 / Chapter 5.2 --- Bayesian Analysis of the Model --- p.47 / Chapter 5.2.1 --- Posterior Analysis and Gibbs Sampler --- p.47 / Chapter 5.2.2 --- Prior Distributions --- p.48 / Chapter 5.3 --- A Simulation Study --- p.49 / Chapter 6 --- Conclusion and Discussion --- p.53 / Chapter A --- Technical Details for Chapter 2 --- p.56 / Chapter A.1 --- Full conditional distributions --- p.56 / Chapter A.2 --- Implementation of the Metropolis-Hastings (MH) Algorithm --- p.59 / Chapter A.3 --- Gelman-Rubin statistic --- p.61 / Chapter B --- Technical Details for Chapter 3 --- p.63 / Chapter B.1 --- Full conditional distributions --- p.63 / Chapter B.2 --- Implementation of the Metropolis-Hastings (MH) Algorithm --- p.64 / Chapter C --- Technical Details for Chapter 5 --- p.66 / Chapter C.l --- Full conditional distributions --- p.66 / Bibliography --- p.68