Statistics and Probability Commons^™

Estimating Cumulative Incidence Rate On Interval Censored Data In An Illness-Death Model., Chen Qian

Electronic Theses and Dissertations

Phase IV clinical trials are designed to monitor long-term side effects caused overtime by the medical treatment. For instance, in advanced primary cancer treatment, childhood cancer survivors are often at risk of developing undesired events, such as cardiotoxicity, during their adulthood. Such problems could be due to their cancer or the treatment they received for their cancer such as radiation or intensive chemotherapy. Cardiotoxicity can be diagnosed with electrophysiology with measurements of fraction shortening, afterload, etc. Often the primary focus of a study could be on estimating the cumulative incidence of a particular outcome of interest such as cardiotoxicity. However, …

Observational Studies In Group Testing And Potential Applications., Alexander Christopher Noll

Electronic Theses and Dissertations

The use of group testing to identify individuals with targeted outcomes in a population can greatly improve the efficiency, speed, and cost effectiveness of testing a population for an outcome, or at least for identifying the prevalence of an outcome in a population. The implementation of causal inference techniques can provide the basis for an observational study that would allow an investigator to gather estimates for treatment effectiveness if group testing was conducted on the population in a certain way. This thesis examines a simulation of the above outlined principles in order to demonstrate a potential application for determining treatment …

Performance Comparison Of Multiple Imputation Methods For Quantitative Variables For Small And Large Data With Differing Variability, Vincent Onyame

Electronic Theses and Dissertations

Missing data continues to be one of the main problems in data analysis as it reduces sample representativeness and consequently, causes biased estimates. Multiple imputation methods have been established as an effective method of handling missing data. In this study, we examined multiple imputation methods for quantitative variables on twelve data sets with varied sizes and variability that were pseudo generated from an original data. The multiple imputation methods examined are the predictive mean matching, Bayesian linear regression and linear regression, non-Bayesian in the MICE (Multiple Imputation Chain Equation) package in the statistical software, R. The parameter estimates generated from …

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …

Moving Past ‘One Size Fits All’: Developing A Trajectory Deviance Index For Dynamic Measurement Modeling, Yixiao Dong

Electronic Theses and Dissertations

Dynamic Measurement Modeling (DMM) is a recently developed measurement framework for gauging developing constructs (e.g., learning capacity) that conventional single-timepoint tests cannot assess. Like most measurement models, overall model fit indices of DMM do not indicate the measurement appropriateness for each included student. For this reason, other measurement modeling paradigms (e.g., Item-Response Theory; IRT) utilize person-fit or model appropriateness statistics to indicate whether a measurement model appropriately describes the data from each individual student. However, within the extant DMM framework, no statistical index has yet been developed for this purpose. Thus, the current project advanced a person-specific DMM Trajectory Deviance …

Evaluation Of The Effect Of The Clinical-Decision-Support Systems On Diabetes Management: A Multivariate Meta-Analysis Comparison With Univariate Meta-Analysis, Abdelfattah Elbarsha

Electronic Theses and Dissertations

The advantage of using meta-analysis lies in its ability in providing a quantitative summary of the findings from multiple studies. The aim of this dissertation was first to conduct a simulation study in order to understand what factors (sample size, between-study correlation, and percent of missing data) have a significant effect on meta-analysis estimates and whether using univariate or multivariate meta-analysis would produce different estimates.

The second goal of this study was to evaluate the effect of clinical decision support systems CDSS on diabetes care management by conducting three separate univariate meta-analyses and one multivariate meta-analysis. CDSS are health information …

Statistical Modeling Of Positive Peer Support On Longitudinal Adolescent Substance Use, Kady Rost

Electronic Theses and Dissertations

To evaluate this study’s research question of ”Does the latent construct of Positive Peer Support (PPS) relate to the construct of Adolescent Substance Use (ASU) over time, controlling for neighborhood safety, race, and sex?”, Structural Equation (SEM) and Latent Growth Curve Modeling (LGCM) were used to investigate trajectories. Secondary longitudinal data from Zimmerman (2014) of 604 students enrolled for four consecutive years in public schools located in Flint, Michigan. In the secondary data resource, students who participated were declared “at risk” by GPA. Significant relationships were found in SEM: Positive Peer Support to Adolescent Substance Use, All Control Variables to …

The Combined Impact Of Continuous And Ordinal Auxiliary Variables On Missing Data Imputation In Sem, Salina Wu Whitaker

Electronic Theses and Dissertations

“Modern” methods of addressing missing data using full-information maximum-likelihood (FIML) have become mainstays in SEM analyses. FIML allows the inclusion of auxiliary variables which carry information that is related to missing values and can reduce bias in parameter estimates. Past research has illustrated the benefits of auxiliary variable inclusion under different missingness conditions (MCAR and MNAR; e.g., Enders, 2008), missingness proportions (e.g., Collins et al., 2001), and although limited, missingness patterns (e.g., Yoo, 2009) in FIML analyses. While past studies have focused on the effects of either continuous or ordinal auxiliary variables, no study has included both types in their …

Use Of Research Tradition And Design In Program Evaluation: An Explanatory Mixed Methods Study Of Practitioners’ Methodological Choices, Margaret Schultz Patel

Electronic Theses and Dissertations

The goal of this explanatory sequential mixed method study was to assess whether there were observable trends, associations, or group differences in evaluation methodology by settings and content area in published evaluations from the past ten years (quantitative), to illuminate how evaluation practitioners selected these methodologies (qualitative), and assess how emergent findings from each phase fit together or helped contextualize each other. In this study, methodology was operationalized as research tradition and method was operationalized as research design. For phase one (quantitative), a systematized ten-year review of five peer-reviewed evaluation journals was conducted and coded by journal, research tradition, research …

Assessing The Variations Of Educational Attainment At National And Subnational Levels Using Hierarchical Linear Models, Bingxin Qi

Electronic Theses and Dissertations

Education is a human right, and equal access to education is not only crucial for an individual’s well-being, but also essential for eradicating poverty, ensuring long-term prosperity for all, transforming the society, and achieving sustainable development. Measuring education development, especially the variations of educational attainment, in a timely and accurate manner can help educators, practitioners, scientists, and policymakers compare and evaluate various education indicators at both subnational and national levels. This research presents an approach that combines multi-source and multidimensional data including population distribution, human settlement, and education data to assess and explore educational attainment trajectories at both national and …

A Grounded Theory Inquiry Into The Pedagogical Socialization Of Graduate Students Within Graduate Quantitative Methods Courses, Amanda Kay Thomas

Electronic Theses and Dissertations

Quantitative methods are one of the most highly technical fields of study within social sciences graduate programs. Although classroom pedagogy is an important factor connected to student success within graduate quantitative methods courses little is known on the pedagogical socialization experiences of masters and doctoral students. The purpose of this grounded theory inquiry was to discover graduate students perspectives on their pedagogical socialization experiences and the norms, values and role expectations transmitted during the teaching and learning of quantitative methods. Narrative data was collected from in-depth interviews among a theoretical sample of 31 masters and doctoral students enrolled in introductory, …

Comparison Of Software Packages For Detecting Differentially Expressed Genes From Single-Sample Rna-Seq Data, Rong Zhou

Electronic Theses and Dissertations

RNA-sequencing (RNA-seq) has rapidly become the tool in many genome-wide transcriptomic studies. It provides a way to understand the RNA environment of cells in different physiological or pathological states to determine how cells respond to these changes. RNA-seq provides quantitative information about the abundance of different RNA species present in a given sample. If the difference or change observed in the read counts or expression level between two experimental conditions is statistically significant, the gene is declared as differentially expressed. A large number of methods for detecting differentially expressed genes (DEGs) with RNA-seq have been developed, such as the methods …

Development Of A Probabilistic Multi-Class Model Selection Algorithm For High-Dimensional And Complex Data, Madeline Anne Ausdemore

Electronic Theses and Dissertations

The development of quantifiable measures of uncertainty in forensic conclusions has resulted in the debut of several ad-hoc methods for approximating the weight of evidence (WoE). In particular, forensic researchers have attempted to use similarity measures, or scores, to approximate the weight of evidence characterized by highdimensional and complex data. Score-based methods have been proposed to approximate theWoE for numerous evidence types (e.g., fingerprints, handwriting, inks, voice analysis). In general, scorebased methods consider the score as a projection onto the real line. For example, the score-based likelihood ratio evaluates and compares the likelihoods of a score calculated between two objects …

Development And Properties Of The Roc-Abc Bayes Factor For The Quantification Of The Weight Of Forensic Evidence, Jessie Hendricks

Electronic Theses and Dissertations

Many scholars have proposed the use of a Bayes factor to quantify the weight of forensic evidence. However, due to the complex and high-dimensional nature of pattern evidence, likelihood functions are intractable and thus, Bayes factors cannot be assigned using traditional methods. Approximate Bayesian Computation (ABC) model selection algorithms provide likelihood-free methods to assign Bayes factors. ABC Bayes factors leverage the use of the scoring functions commonly used in recent years in forensic statistics in a rigorous statistical manner. However, traditional methods for assigning ABC Bayes factors are subject of several criticisms. In this dissertation, one of the main criticisms …

Methods For High-Dimensional Spatial Data: Dimension Reduction And Covariance Approximation, Paul May

Electronic Theses and Dissertations

In spatial statistics, because quantities are correlated based on their relative positions in space, data is modeled as a single realization of a multivariate stochastic process. Spatial data can be high-dimensional either through a large number of observed variables per location, or through a large number of observed locations. The two are often handled differently, with the former addressed through dimension reduction and the latter addressed through appropriate modeling of the spatial correlation between locations. The main body of this dissertation is a three-part work. Parts 2 and 3 pertain to the "many variables" problem, proposing novel methods of dimension …

Modified-Half-Normal Distribution And Different Methods To Estimate Average Treatment Effect., Jingchao Sun

Electronic Theses and Dissertations

This dissertation consists of three projects related to Modified-Half-Normal distribution and causal inference. In my first project, a new distribution called Modified-Half-Normal distribution was introduced. I explored a few of its distributional properties, the procedures for generating random samples based on Bayesian approaches, and the parameter estimation based on the method of moments. The second project deals with the problem of selection bias of average treatment effect (ATE) if we use the observational data. I combined the propensity score based inverse probability of treatment weighting (IPTW) method and the directed acyclic graph (DAG) to solve this problem. The third project …

Statistical Approaches Of Gene Set Analysis With Quantitative Trait Loci For High-Throughput Genomic Studies., Samarendra Das

Electronic Theses and Dissertations

Recently, gene set analysis has become the first choice for gaining insights into the underlying complex biology of diseases through high-throughput genomic studies, such as Microarrays, bulk RNA-Sequencing, single cell RNA-Sequencing, etc. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results. Further, the statistical structure and steps common to these approaches have not yet been comprehensively discussed, which limits their utility. Hence, a comprehensive overview of the available gene set analysis approaches used for different high-throughput genomic studies is provided. The analysis of gene sets is usually carried out based on …

Aspects Of Causal Inference., John A. Craycroft

Electronic Theses and Dissertations

Observational studies differ from experimental studies in that assignment of subjects to treatments is not randomized but rather occurs due to natural mechanisms, which are usually hidden from researchers. Yet objectives of the two studies are frequently the same: identify the causal – rather than merely associational – relationship between some treatment or exposure and an outcome. The statistical issues that arise in properly analyzing observational data for this goal are numerous and fascinating, and these issues are encompassed in the domain of causal inference. The research presented in this dissertation explores several distinct aspects of causal inference. This dissertation …

The Influence Of Environmental Variables On The Height Growth Of Loblolly Pine (Pinus Taeda) In The Western Gulf, Osakpamwan Edo-Iyasere

Electronic Theses and Dissertations

Understanding the effects of environmental factors on stand growth is important in optimizing forest management plans. This study investigated the effects of soil and climate factors on the height growth (site index) of loblolly pine (Pinus Taeda L.) using data collected from permanent plots established in intensively-managed plantations across East Texas and Western Louisiana. The Chapman-Richards model was selected as the base model to describe the height-age relationships and important soil and climate variables were incorporated into the models as model parameter coefficient adjustors. Our results showed that the most important factors for predicting site index were nitrogen …

Linear Methods For Regression With Small Sample Sizes Relative To The Number Of Variables., Rajesh Sikder

Electronic Theses and Dissertations

In data sets where there are a small number of observations but a large number of variables observed for each observation, ordinary least squares estimation cannot be used for regression models. There are many alternative including stepwise regression, penalized methods such as ridge regression and the LASSO, and methods based on derived inputs such as principal components regression and partial least squares regression. In this thesis, these five methods are described. K-fold cross validation is also discussed as a way for determining regularization parameters for each method. The performance of these methods in estimation and prediction is also examined through …

Marginal Methods And Software For Clustered Data With Cluster- And Group-Size Informativeness., Mary Elizabeth Gregg

Electronic Theses and Dissertations

Clustered data result when observations have some natural organizational association. In such data, cluster size is defined as the number of observations belonging to a cluster. A phenomenon termed informative cluster size (ICS) occurs when observation outcomes vary in a systematic way related to the cluster size. An additional form of informativeness, termed informative within-cluster group size (IWCGS), arises when the distribution of group-defining categorical covariates within clusters similarly carries information related to outcomes. Standard methods for the marginal analysis of clustered data can produce biased estimates and inference when data have informativeness. A reweighting methodology has been developed that …

Chemostratigraphy Of Carbonate Gravity Flows Of The Wolfcamp Formation In Crockett County, Midland Basin, Texas, Alex Blizzard, Julie Bloxson

Electronic Theses and Dissertations

Sediment gravity flows into deep-water environments are important stratigraphic traps in lithologically diverse reservoirs generating multiple plays for hydrocarbon exploration. These highly heterogeneous deposits can be studied by utilizing chemostratigraphy and higher-order sequence stratigraphy; being an accurate method for reservoir characterization. Studying these gravity flows along a carbonate platform’s slope can further expand an understanding of the stratigraphy that is filling adjacent basins. The application of elemental analyses can support in identifying mineralogy that impact reservoir quality, especially when conventional testing cannot be applied.

This study utilizes five cores containing the Wolfcamp Formation from the southeastern slope of the Central …

Using Saddlepoint Approximations And Likelihood-Based Methods To Conduct Statistical Inference For The Mean Of The Beta Distribution, Bryn Brakefield

Electronic Theses and Dissertations

The prevalence of conducting statistical inference for the mean of the beta distribution has been rising in various fields of academic research, such as in immunology that analyzes proportions of rare cell population subsets. For our purposes, we will address this statistical inference problem by using likelihood-based applications to hypothesis testing, along with a relatively new statistical method called saddlepoint approximations. Through simulation work, we will compare the performance of these statistical procedures and provide both the statistical and scientific communities with recommendations on best practices.

Novel Bayesian Methodology For The Analysis Of Single-Cell Rna Sequencing Data., Michael Sekula

Electronic Theses and Dissertations

With single-cell RNA sequencing (scRNA-seq) technology, researchers are able to gain a better understanding of health and disease through the analysis of gene expression data at the cellular-level; however, scRNA-seq data tend to have high proportions of zero values, increased cell-to-cell variability, and overdispersion due to abnormally large expression counts, which create new statistical problems that need to be addressed. This dissertation includes three research projects that propose Bayesian methodology suitable for scRNA-seq analysis. In the first project, a hurdle model for identifying differentially expressed genes across cell types in scRNA-seq data is presented. This model incorporates a correlated random …

Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya

Electronic Theses and Dissertations

Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …

The Effects Of Adverse Childhood Experiences On Behavioral Outcomes, Jennifer Thomas

Electronic Theses and Dissertations

This study intends to explore the intersection of two vulnerable populations, early childhood development and risks associated with exposure to adverse childhood experiences (ACEs). This study examines how age plays a role in the long-term relationship between ACEs and internal and external behaviors. This study seeks to answer the question of: How does age influence the relationship between number of ACEs and internal and external behaviors? The participants in this study include those aged 0 – 16 from the National Survey of Child and adolescent Well-Being (NSCAW) dataset. The NSCAW study consists of five waves of data where Wave I …

Is The Reliability Of Objective Originality Scores Confounded By Elaboration?, Shannon Marie Maio

Electronic Theses and Dissertations

The increased use of text-mining models as a scoring mechanism for divergent thinking (DT) tasks has sparked concerns about the ways in which automated Originality scores may be influenced by other dimensions of DT, especially Elaboration. The debate centers around the question of whether too much variance in automated Originality scores is accounted for by the number of words a participant uses in a response (i.e., Elaboration), and, thus, how the influence of Elaboration can affect the reliability of Originality scores. Here, a partial correlation analysis, in conjunction with text-mining and psychometric modeling, is conducted to test the degree to …

Measuring The Connective Action Of Black Lives Matter Activists: A Psychometric Investigation Into Twitter Data, Paige Alfonzo

Electronic Theses and Dissertations

Many protest movements from the last twenty-first century have become increasingly networked and personalized. Several scholars have tapped into this change coining terms such as participatory action, digitally mediated action, computer-mediated communication, issue-based organization, and what I focus on in this project, connective action. Building on the ideas percolating across the literary landscape at the time, Bennett and Segerberg (2012) introduced the logic of connective action based on emergent characteristics they observed in post-2010 large-scale social movements. Both the logic of connective action and related work have become deeply ingrained in today's social movement scholarship. As such, I felt it …

Comprehensive Research Synthesis: An Approach To Mixed Methods Research Syntheses, Lilian Linialy Chimuma

Electronic Theses and Dissertations

Mixed methods research synthesis (MMRS) is an emerging application of both mixed-methods research (MMR) and review research. MMRS promises to comprehensively address intricate contemporary research and evaluation questions given diverse evidence sources (across quantitative, qualitative, and MMR primary studies). The significance of concurrently addressing methodological issues for new research developments is widely noted in the literature. Current efforts attempt to streamline methodological practices along with application of the MMRS approach. Researchers have proposed conceptual frameworks to guide the application and practice of MMRS studies. Despite these efforts, complications and disagreements persist. In response to these concerns, this study developed a …

The Experiences Of Ncaa Student-Athletes With An Eating Disorder Or Disordered Eating, Rachel E. Taylor

Electronic Theses and Dissertations

The purpose of this study was to explore the experiences of student-athletes who had an eating disorder or disordered eating (ED/DE) while competing for the National Collegiate Athletic Association (NCAA). Integrating criticism and connoisseurship and critical evocative portraiture, four post-collegiate women who participated in cross country and track, who were either clinically diagnosed with an ED/DE or who self-diagnosed, participated in two interviews to describe their experiences with and the impact of ED/DE on their athletic pursuits, academic pursuits, as well as their relationships with coaches, teammates, and family. The analysis of these interviews showed the complexity of this topic. …