A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can be taken advantage of to improve estimation, especially for those probabilities with little associated data. The transition probabilities are estimated using MCMC and the Metropolis-Hastings algorithm.

Array comparative genomic hybridization (aCGH) is a technique for identifying duplications and deletions of DNA at specific locations across a genome. Potential objectives of aCGH analysis are the identification of (1) altered regions for a given subject, (2) altered regions across a set of individuals, and (3) clinically relevant clusters of hybridizations. aCGH analysis can be particularly useful when it identifies previously unknown clusters with clinical relevance. This project focuses on the assessment of existing aCGH clustering methodologies. Three methodologies are considered: hierarchical clustering, weighted clustering of called aCGH data, and clustering based on probabilistic recurrent regions of alteration within subsets of individuals. Assessment is conducted first through the analysis of aCGH data obtained from patients with ovarian cancer and then through simulations. Performance assessment for the data analysis is based on cluster assignment correlation with clinical outcomes (e.g., survival). For each method, 1,000 simulations are summarized with Cohen's kappa coefficient, interpreted as the proportion of correct cluster assignments beyond random chance. Both the data analysis and the simulation results suggest that hierarchical clustering tends to find more clinically relevant clusters when compared to the other methods. Additionally, these clusters are composed of more patients who belong in the clusters to which they are assigned.

<p> Hierarchical leadership structures were once the primary paradigm for leadership in the church. In a contemporary world where culture has shifted and the rise of the scepticism of authority has eroded hierarchies, the church must embrace a new paradigm. Flat leadership is a structure that is being embraced in both the secular world and the church. In this thesis we interpret the shifts in culture and how they have altered the landscape of leadership. We also assess flat leadership as an effective approach to leadership in response to our shifting culture.</p> <p> Flat leadership is a biblical approach to leading. This thesis will engage with Scripture and highlight its support for leading through a sharing of power and authority. Finally, we offer some thoughts on how to begin to move churches from hierarchies to flat structures. Flat leadership represents a Biblical approach to church organizational structures. Utilizing this approach can help churches avoid many of the common pitfalls of ministry and can promote healthier structures for congregational life to thrive.</p> / Thesis / Master of Theological Studies (MTS)

Malaysia’s preferential policies have reduced the educational attainment gap between ethnic groups. However, we know less about their effects on ethnic differences in academic achievement. With this point in mind, the overall goal of this study is to examine inter-ethnic differences in mathematics and science achievement based on the cohort of eighth grade (Form 2) Malaysian students who participated in the Third International Mathematics and Sciences Study Repeat Project (TIMMS-R). It sought to determine the extent to which theoretical propositions of the structural and cultural perspectives developed to explain achievement differences in the United States are applicable in Malaysia. Malaysia is an interesting setting for the purpose of the present study for three reasons. First, the interethnic differences in educational outcomes were historically linked to occupational structure and class-and ethnicity-based residential segregation during the Brisish colonial rule. Second, Malaysia is one of the few countries (i.e. Fiji, Nigeria, Sri Lanka, Uganda, India, and New Zealand) that have strong public policies to rectify the historical ethnic inequalities in access to education. However, the difference between Malaysia and these countries seems to be in the relative status of the formerly disadvantaged ethnic group in question. Finally, as a new member of the New Industrialized Countries (NICs), Malaysia is in the process of making the transition from an agricultural economy to an indutrialized nation. As such, the importance of mathematics and science education increases along with socioeconomic and technological advance and the discrepancies in mathematics and science achievement can have important implications on socioeconomic disparity among ethnic groups. The primary contribution of this dissertation is that it holistically examines how individual, family and school characteristics affect mathematics and science achievement of the eighth graders in Malaysia. The multilevel modeling analyses showed that Non-Malay students performed significantly better in mathematics achievement than Malay students, even after controlling for family and school characteristics as well as students’ perceived importance of mathematics and educational expectations. Overall, the results suggest that the structural and cultural perspectives work differently for Malay and Non-Malay students.

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This study examined the relationship between self-leadership and personality through an analysis and comparison of hierarchical factor structures. More specifically, this study examined the relationships between the self-leadership dimensions of behavior-focused strategies, natural reward strategies, and constructive thought strategies, and the personality dimensions of extraversion, emotional stability, and conscientiousness. The results of the study provide evidence that the self-leadership dimensions are distinct from, yet related to, the specified personality traits. The hypothesis that self-leadership strategies are distinct from the selected personality traits was supported through structural equations modeling analyses examining competing models combining the hierarchical factor structures of self-leadership and personality. Model fit increased significantly through a progression of models that showed increasingly greater distinction between self-leadership dimensions and personality traits. The best fitting model in the progression, in harmony with both self-leadership and trait personality theory, consisted of a hierarchical factor structure with three first order self-leadership factors, three first order personality factors, and two correlated second order factors (i.e., self-leadership and personality). Furthermore, intercorrelations were greater within the self-leadership dimensions than between the self-leadership dimensions and the personality traits, thus providing additional evidence of differentiation. Although the evidence indicates that self-leadership skill dimensions are unique with respect to personality traits, these results also suggest that self-leadership and personality factors are nevertheless significantly related. Specifically, both extraversion and conscientiousness were significantly related to all three self-leadership dimensions, while emotional stability was significantly related only to the natural rewards strategies dimension. In summation, the results of this study suggest that self-leadership represents a distinct constellation of strategies that are significantly related to certain key personality traits. The implications of these results for future self-leadership research and practice are discussed. / Ph. D.

Environmental studies often employ data collected over large spatial regions. Although it is convenient, the conventional single model approach may fail to accurately describe the relationships between variables. Two alternative modeling approaches are available: one applies separate models for different regions; the other applies hierarchical models. The separate modeling approach has two major difficulties: first, we often do not know the underlying clustering structure of the entire data; second, it usually ignores possible dependence among clusters. To deal with the first problem, we propose a model-based clustering method to partition the entire data into subgroups according to the empirical relationships between the response and the predictors. To deal with the second, we propose Bayesian hierarchical models. We illustrate the use of the Bayesian hierarchical model under two situations. First, we apply the hierarchical model based on the empirical clustering structure. Second, we integrate the model-based clustering result to help determine the clustering structure used in the hierarchical model. The nature of the problem is classification since the response is categorical rather than continuous and logistic regression models are used to model the relationship between variables. / Ph. D.

Change in educational settings is a complex and multifaceted process that commonly implies change in teaching practices. Different initiatives have shown the significance of teachers and their perceptions when change in teaching practices is intended. Additionally, various factors may influence change in teaching practices at three different moments: before it happens, during, and after its implementation. Considering teachers' perceptions, I studied different factors that may be related to positive change in teaching practices. I studied the relationship between three groups of factors and positive change in teaching practices: motivational factors, including teachers' self-efficacy and autonomy; learning opportunities that include professional development, feedback, and leadership; and the academic and community domains as part of the school climate factor. In particular, I answered the following research question: To what extent do learning opportunities, teacher motivational factors, and school climate predict positive change in teaching practices? In this study I posited that teacher factors such as self-efficacy and school factors such as leadership influence positive change in teaching practices. I also posited that school factors influence the relationship between teacher factors and positive change in teaching practices. To study these relationships, I analyzed data from the Teaching and Learning International Survey (TALIS). This survey provides clustered data: teachers are clustered by schools and schools by countries. I used multilevel modeling statistical methods (i.e., a two-level hierarchical linear model) to examine the Colombian and United Stated datasets. Before estimating the hierarchical linear models, I conducted an exploratory factor analysis (EFA) to identify the teacher-level variables. One follow-up EFA focused on teacher self-efficacy yielded three variables that allowed me to focus on three specific teaching tasks: managing student behavior, motivating students, and varying instructional strategies. I found that learning opportunities, motivational factors, and school climate predict positive change in teaching practices. Learning opportunities, such as feedback from the principal has a stronger effect than feedback from colleagues. The impact of feedback from the principal has significant unnoticeable variability across schools, and it is negatively influenced by the feedback received by the teachers at the same school. Additionally, teachers' self-efficacy in different teaching tasks predicts positive change, however, these relationships differ by country. Finally, distributed leadership as part of school climate is a significant predictor of positive change that also affects it by influencing teacher interactions positively. Implications of these findings are also discussed as it relates to the existing literature and the educational system in each of the two countries. / Doctor of Philosophy / Over many decades there have been different initiatives in education to improve teaching. Unfortunately, many of those efforts have had unsuccessful results, although they are solid proposals. Thus, change itself has become a focus of study. My study focuses on factors that may influence positive change in teaching practices. I focus on three groups of factors: learning opportunities, motivational factors, and school climate. For learning opportunities, I studied the participation of teachers in professional development, feedback to teachers from different educational community members, and interactions between teachers. For motivational factors, I focused on teachers' autonomy and self-efficacy. Finally, for school climate, I studied factors associated with leadership, interactions between teachers at the same school, and participation of teachers from the same school in professional development. I analyzed data from the Teaching and Learning International Survey (TALIS). TALIS is an international survey administered to teachers and principals worldwide. I considered TALIS data from Colombia and the US. Within each country, teachers are grouped by schools, that is, teacher are nested within schools. In this study, teachers are considered the level-one unit, and schools, the level-two units. Therefore, I analyzed the data using a statistical method known as Hierarchical Linear Modelling. This method allowed me to identify different relationships: between teacher-level factors and positive change, between school-level factors and positive change, and between school-level factors and the relationship between teacher factors and positive change. I was also able to partition the variance associated with these relationships between teachers and between schools. I found that learning opportunities, motivational factors, and school climate are predictors of positive change in teaching practices. This means that teachers are more likely to implement changes in their teaching practices if they: participate in professional development, interact with their colleagues, receive feedback from the principal and their colleagues, have a high level of self-efficacy for different teaching tasks, and belong to a school where leadership is well distributed among different stakeholders. In particular, feedback could have a stronger impact if it is based on different sources of information. Finally, I discuss the implications of these findings and conclusions that lead to a better understanding of these relationships.