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.

In this report we give a brief introduction to the multilevel models, provide a brief summary of the need for using the multilevel model, discuss the assumptions underlying use of multilevel models, and present by means of example the necessary steps involved in model building. This introduction is followed by a discussion of power and sample size determination in multilevel designs. Some formulae are discussed to provide insight into the design aspects that are most influential in terms of power and calculation of standard errors. Finally we conclude by discussing and reviewing the simulation study performed by Maas and Hox (2005) about the influence of different sample sizes at individual as well as group level on the accuracy of the estimates (regression coefficients and variances) and their standard errors. / text

The majority of research on suicide has focused on the role of direct risk factors in the development of suicidal intent, including personal characteristics and psychiatric illness. While research on the wider influence of socio-economic circumstances is not uncommon, most research has considered single risk factors, and often limits the scope of the research to small groups or small areas. This research attempted to provide a unified and comprehensive analysis, and used mainly aggregate data to consider the extent to which socio-economic factors explain geographic and temporal variations in suicide. Variations in suicide over the local authority districts of England and Wales were found to be significantly associated with several ecological predictors, including male unemployment, lone households, low social class and divorce. The importance of the predictors varied according to age and sex, and the results corresponded well to those from individual level studies. The research also considered the geographical differences between suicide and undetermined death verdicts, and found that the latter have a significant urban bias. These cross- 3ectional results were used as the basis for a study of the changes that took place in suicide rates during the 1980s, to determine the extent to which changes in the area characteristics that were significant at a given point in time accounted for changes in suicide rates over time. Particular attention was given to the dramatic rise in rates among younger males (aged 15-44). Little evidence was found at the ecological level to support the hypothesis that changes in unemployment and/or deprivation, the proportion of people living alone, or the divorce rate might have been responsible for the increase in suicide among younger men, while the rates for all other groups declined. Individual data for Norfolk were also used, and the predictors of geographic variation were found to be very similar for Norfolk and England and Wales. Furthermore, although the sexand age-specific changes in rates during the 1980s were also similar, the ecological variable~ again failed to adequately predict the changes. Analysis did not support the hypothesis tha1 suicide rates increased solely because of the increased availability of motor vehicle exhaus1 fumes as a suicide method, though there was some suggestion that this may have contributec to the trends. Further analysis of individual deaths found strong evidence to suggest the urbar bias of undetennined death to be an artifact of the reporting of suicide, whereby mon equivocal methods, more likely to lead to an undetermined death verdict, tend to be use( more often in urban areas. Two main conclusions are reached. First, the extent of the urban-rural variation between tbl verdicts was such that studies using different definitions of suicide over the same study are; could possibly derive diifering conclusions. Combining the verdicts is therefore encouragec Second, while the geography of suicide may be explained in tenns of socio-economic facton changes in suicide rates appear to have little or no geographic and socio-economi manifestation. Detennining the role of cultural change, presently the only theory t adequately account for the divergence in rates, requires more psychologically and socially orientated research.

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.

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

The estimation of variance components serves as an integral part of the evaluation of variation, and is of interest and required in a variety of applications (Hugo, 2012). Estimation of the among-group variance components is often desired for quantifying the variability and effectively understanding these measurements (Van Der Rijst, 2006). The methodology for determining Bayesian tolerance intervals for the one – way random effects model has originally been proposed by Wolfinger (1998) using both informative and non-informative prior distributions (Hugo, 2012). Wolfinger (1998) also provided relationships with frequentist methodologies. From a Bayesian point of view, it is important to investigate and compare the effect on coverage probabilities if negative variance components are either replaced by zero, or completely disregarded from the simulation process. This research presents a simulation-based approach for determining Bayesian tolerance intervals in variance component models when negative variance components are either replaced by zero, or completely disregarded from the simulation process. This approach handles different kinds of tolerance intervals in a straightforward fashion. It makes use of a computer-generated sample (Monte Carlo process) from the joint posterior distribution of the mean and variance parameters to construct a sample from other relevant posterior distributions. This research makes use of only non-informative Jeffreys‟ prior distributions and uses three Bayesian simulation methods. Comparative results of different tolerance intervals obtained using a method where negative variance components are either replaced by zero or completely disregarded from the simulation process, is investigated and discussed in this research.