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.

Pan, Junhao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 121-135). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis we develop a two component mixture model to perform a Bayesian regression. We implement our model computationally using the Gibbs sampler algorithm and apply it to a dataset of differences in time measurement between two clocks. The dataset has ``good" time measurements and ``bad" time measurements that were associated with the two components of our mixture model. From our theoretical work we show that latent variables are a useful tool to implement our Bayesian normal mixture model with two components. After applying our model to the data we found that the model reasonably assigned probabilities of occurrence to the two states of the phenomenon of study; it also identified two processes with the same slope, different intercepts and different variances. / McAnulty College and Graduate School of Liberal Arts; / Computational Mathematics / MS; / Thesis;

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 215-219).

published_or_final_version / Community Medicine / Doctoral / Doctor of Philosophy

Reliability issues are always salient as behavioral researchers observe human behavior and classify individuals from criterion-referenced test scores. This has created a need for studies to assess agreement between observers, recording the occurrance of various behaviors, to establish the reliability of their classifications. In addition, there is a need for measuring the consistency of dichotomous and polytomous classifications established from criterion-referenced test scores. The development of several log linear univariate models for measuring agreement has partially met the demand for a probability-based measure of agreement with a directly interpretable meaning. However, multi-variate repeated measures agreement produres are necessary because of the development of complex intrasubject and intersubject research designs. The present investigation developed applications of the log linear, latent class, and weighted least squares procedures for the analysis of multivariate repeated measures designs. These computations tested the model-data fit and calculated the multivariate measure of the magnitude of agreement under the quasi-equiprobability and quasi-independence models. Applications of these computations were illustrated with real and hypothetical observational data. It was demonstrated that employing log linear, latent class, and weighted least squares computations resulted in identical multi-variate model-data fits with equivalent chi-square values. Moreover, the application of these three methodologies also produced identical measures of the degree of agreement at each point in time and for the multivariate average. The multivariate methods that were developed also included procedures for measuring the probability of agreement for a single response classification or subset of classifications from a larger set. In addition, procedures were developed to analyze occurrences of systematic observed disagreement within the multivariate tables. The consistency of dichotomous and polytomous classifications over repeated assessments of the identical examinees was also suggested as a means of conceptualizing criterion-referenced reliability. By applying the univariate and multivariate models described, the reliability of these classifications across repeated testings could be calculated. The procedures utilizing the log linear, latent structure, and weighted least squares concepts for the purpose of measuring agreement have the advantages of (1)yielding a coefficient of agreement that varies between zero and one and measures agreement in terms of the probability that the observers' judgements will agree, as estimated under a quasi-equiprobability or quasi-independence model, (2)correcting for the proportion of "chance" agreement, and (3) providing a directly interpretable coefficient of "no agreement." Thus, these multivariate procedures may be regarded as a more refined psychometric technology for measuring inter-observer agreement and criterion-referenced test reliability.

Thesis (Ph. D.)--University of Texas Health Science Center at Houston, School of Public Health, 2007. / Includes bibliographical references (leaves 58-59).

Thesis (Ph. D.)--University of California, San Diego and San Diego State University, 2007. / Title from first page of PDF file (viewed May 29, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 99-105).