Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed June 17, 2008). PDF text: vii, 137 p. : ill. (some col.) ; 1 Mb. UMI publication number: AAT 3288807. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph. D.)--Florida State University, 2005. / Advisor: Dr. Richard Tate, Florida State University, College of Education, Dept. of Educational Psychology and Learning Systems. Title and description from dissertation home page (viewed June 14, 2005). Document formatted into pages; contains xiii, 163 pages. Includes bibliographical references.

Keywords: General transformation model, Model Misspecification, Marginal likelihood, Markov chain Monte Carlo, Stochastic approximation, Mixed-effects model, Consistency, Asymptotic normality, Discretization technique. / Part II of this thesis concerns studies of mixed-effects general transformation models, i.e. general transformation models incorporating both fixed and random effects, to analyze grouped or clustered data. Rank-based marginal likelihood estimation is proposed. The estimation procedure is baseline-free, a good property enjoyed by the Cox partial likelihood. A three-stage Markov chain Monte Carlo stochastic approximation (MCMC-SA) algorithm is developed to find the maximum marginal likelihood estimation (MMLE). The asymptotic normality is obtained via a discretization procedure. Monte Carlo simulation shows that the MMLE has a good small- and moderate-sample behavior. In the end we illustrate an application of the proposed method to Hong Kong horse racing data. / Since it was first proposed by Dabrowska and Doksum in 1988, there is an explosive growth in both studies and applications of transformation model. Transformation model has many naturally endowed merits such as flexibility and conciseness in modeling lifetime or duration and ranking data involving covariates. However, like many other statistical models, transformation model may suffer the problem of misspecification due to falsely specified error term distribution or omitted covariates. The author investigates the large sample behavior of the rank-based quasi maximum marginal likelihood estimator (QMMLE) when transformation model is misspecified, and shows that owing to model misspecification, the QMMLE converges not to the true value of the parameter of interest, but to a "pseudo-true value" which minimizes the Kullback-Leibler divergence between the true model and the misspecified working model. A robust "sandwich" estimate of variance is proposed. The asymptotic normality of the QMMLE is also proved. Following the steps of White (1982), the appropriate Wald test statistic, Lagrange Multiplier test statistic and Information matrix specification test statistic are proposed. / Ni, Zhongxin. / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3587. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 86-99). / 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.

Thesis (Ph. D.)--Georgia State University, 2008. / Title from file title page. Carolyn F. Furlow, committee chair; Phillip Gagne, T. Chris Oshima, Christopher Domaleski, committee members. Electronic text (113 p.) : digital, PDF file. Description based on contents viewed June 24, 2008. Includes bibliographical references (p. 96-101).

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009. / Title from title screen (site viewed January 5, 2010). PDF text: xii, 190 p. : col. ill. ; 1 Mb. UMI publication number: AAT 3365711. Includes bibliographical references. Also available in microfilm and microfiche formats.

The overall theme of this thesis focuses on methods for functional regression and nonlinear mixed-effects models with applications to PET data. The first part considers the problem of variable selection in regression models with functional responses and scalar predictors. We pose the function-on-scalar model as a multivariate regression problem and use group-MCP for variable selection. We account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance. Our method is illustrated by the application to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control. The second part introduces a functional data analytic approach for the estimation of the IRF, which is necessary for describing the binding behavior of the radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which shrinkage and roughness penalties are incorporated to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data. The third part discusses a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a compartment model. The traditional NLS estimators of the population parameters are applied in a two-stage analysis, which brings instability issue and neglects the variation in rate parameters. In contrast, we propose to estimate the rate parameters by fitting nonlinear mixed-effects (NLME) models, in which all the subjects are modeled simultaneously by allowing rate parameters to have random effects and population parameters can be estimated directly from the joint model. Simulations are conducted to compare the power of detecting group effect in both rate parameters and summarized measures of tests based on both NLS and NLME models. We apply our NLME approach to clinical PET data to illustrate the model building procedure.

In the last three decades recursive residuals and estimation have received extensive attention as important and powerful tools in providing a diagnostic test of the structural change and functional misspecification in regression models. Recursive residuals and their relationship with recursive estimation of regression parameters have been developed for fixed effect models. Such residuals and estimation have been used to test the constancy of regression models over time and their usage has been suggested for almost all areas of regression model validation. These recursive techniques have not been developed for some of the more recent generalisations of Linear Models such as Linear Mixed Models (LMM) and their important extension to Generalised Linear Mixed Models (GLMM) which provide a suitable framework to analyse a variety of special problems in an unified way. The aim of this thesis is to extend the idea of recursive residuals and estimation to Mixed Models particularly for LMM and GLMM. Recurrence formulae are developed and recursive residuals are defined. / Doctor of Philosophy (PhD)

Title from PDF of title page (University of Missouri--Columbia, viewed on March 10, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Thesis advisor: Dr. Steve Osterlind. Includes bibliographical references.

Thesis (M.A.)--University of Toronto, 2005.

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2006. / Includes bibliographical references (p. 69-72).