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

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.

In this report we give a brief introduction to Item Response Theory models and multilevel models. The general assumptions of two classical Item Response Theory, 1PL and 2PL models are discussed. We follow the discussion by introducing a multilevel level framework for these two Item Response Theory Models. We explain Bock and Aitkin's (1981) work to estimate item parameters for these two models. Finally we illustrate these models with a LSAT exam data and two statistical softwares; R project and Stata. / text

Statistics / M. Sc. (Statistics)

There were two purposes set out in this study, first to identify the principal associations with educational performance of Scottish students as reported in the 2007 wave of the Trends in International Mathematics and Science Study (TIMSS2007), and second to evaluate methods of data analysis where sample surveys use plausible value (PV) methodology. Four sets of data were used for the secondary analysis of TIMSS2007, with student's responses to cognitive items and questionnaire data emanating from two stages (G$ and G*) that each addressed two disciplines (mathematics and science). Explanatory models for each stage and discipline were analysed using hierarchical linear modelling techniques to accommodate the cluster sample design of the survey. Guided by existing literature in STEM education the study examined elements of students' learning experiences that fell within a social constructivist theory of learning to ascertain whether the empirical data supported current claims on effective practice. A number of control variables were included in the analyses, some well-established constructs and others derived from background questionnaires. Overall, the results showed that selected background characteristics were consistently related to mathematics and science achievement. The strength of association with home resources, and although girls were generally associated with lower achievement scores, that gender association was strongest in G4 mathematics achievement. The findings suggest there is limited support for current claims in respect of a reform agenda that privileges discussion and collaborative group work. Other policy initiatives on assessment for learning and using technologies in class are not supported in the data, with either no evidence of association or a significant negative effect in the models of mathematics and science achievement. Aspects of practical work and scientific enquiry are positively associated with G4 science achievement, with particular credence given to 'doing' and 'watching' experiments or investigations, buy there is no association with achievement scores at G8 for any of planning, watching or conducting experiments. This latter finding provides empirical evidence of difference across stages on an aspect of practice that is heavily debated. The primary method of analysis utilised a four-level structure, with PV as the unit of analysis. Substantive findings were compared with alternative methods: first making the dependent variable an average of the five PVs; second using one PV as the response variable; and third computing statistics from all five PVs and merging results using Rubin's Rules for combining multilevel method underestimates standard errors in the model in the same way as witnessed for the average of PVs. This leads to the conclusion that the only valid route to analysing imputed data is through Rubin's method of combining results from all five PVs.

No description available.

This thesis includes three parts. The overarching theme is how to analyze structured hierarchical data, with applications to astronomy and sociology. The first part discusses how expectation propagation can be used to parallelize the computation when fitting big hierarchical bayesian models. This methodology is then used to fit a novel, nonlinear mixture model to ultraviolet radiation from various regions of the observable universe. The second part discusses how the Stan probabilistic programming language can be used to numerically integrate terms in a hierarchical bayesian model. This technique is demonstrated on supernovae data to significantly speed up convergence to the posterior distribution compared to a previous study that used a Gibbs-type sampler. The third part builds a formal latent kernel representation for aggregate relational data as a way to more robustly estimate the mixing characteristics of agents in a network. In particular, the framework is applied to sociology surveys to estimate, as a function of ego age, the age and sex composition of the personal networks of individuals in the United States.

There is a growing awareness that informal supports such as family-supportive supervision are critical in assuring the success of work-life policies and benefits. Furthermore, it is believed that family-supportive supervision may have positive effects regardless of the number or quality of work-life polices and benefits an organization has in place. Given this recognition, work-life experts have emphasized the need for supervisor training to increase family-supportive supervision. To date however, there has been a paucity of research on the predictors of family-supportive supervision which could be used as the target of such a training intervention. This dissertation had three major aims: 1) to investigate which supervisor-level (e.g., reward system, productivity maintenance, salience of changing workforce, belief in business case, awareness of organizational policies and benefits, role-modeling) and employee-level (e.g., support sought) factors are most strongly related to family-supportive supervision; 2) to explore whether supervisor factors moderate the relationship between support sought and family-supportive supervision; 3) and to use a multilevel design to confirm the association between family-supportive supervision and work-family conflict. This study used a cross-sectional, two-level (e.g., supervisor, and employee) hierarchical design. The data were collected from supervisors (Nurse Managers N=67) and employees (Nurses N=757) at five hospitals in the Pacific Northwest. All of the major analyses were conducted using multi-level regression in HLM. The results indicated that family-supportive supervision was higher for employees who worked for managers with a stronger belief in the business case and for employees who sought support. None of the other supervisor-level factors were found to be significant predictors of family supportive supervision. There was no evidence that supervisor-level factors moderated that relationship between support sought and family-supportive supervision. Higher levels of family-supportive supervision were related to lower work-to-family conflict. These findings suggest that organizations seeking to reduce work-family conflict and increase family supportive supervision should consider intervening at multiple levels. This dissertation reviews a rich body of evidence demonstrating the business case for offering work-life supports that could serve as a starting point for developing a training to increase supervisors' belief in the business case. In addition, strategies for organizations to increase support seeking, which has been shown to be an important coping mechanism, are discussed. The multi-level design of this dissertation also contributes to the literature by demonstrating that the largest proportion of variability in family-supportive supervision is at the employee-level. This finding suggests the importance of measuring family-supportive supervision at the employee-level and suggests that future research should focus on the employee-level predictors of family-supportive supervision.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 264-275).