Physical Sciences and Mathematics Commons^™

Atrial Fibrillation Management In Hispanic Adults, Tania Borja

Dissertations

Background: Research has found atrial fibrillation (AF) to be the primary or a contributing cause of death on 183,321 death certificates, and an underlying cause of death for 26,535 Americans in 2019. Findings indicate an increased AF diagnosis in White people compared to racial and ethnic minorities, contrasting widespread findings of increased prevalence of cardiovascular disease and ischemic strokes in minorities. Significant disparities—by race and socioeconomic status in disease distribution and access to testing and lifesaving treatments—have been documented, specifically associated with social determinants of health (SDOH); i.e., the conditions in which people are born, grow, live, work, and age. …

Nonparametric Tests For Replicated Latin Squares, Joseph Yang

Dissertations

Two classes of nonparametric procedures for a replicated Latin square design that test for both general and increasing alternatives are developed. The two classes of procedures are similar in the sense that both transform the data so that existing well-known tests for randomized complete block designs can be utilized. On the other hand, the two classes differ in the way that the data is transformed - one class essentially aggregates the data while the other class aligns the data. Within these contexts, the exact distributions and asymptotic distributions are discussed, when applicable. The exact distributions are easily computed using the …

Learning Finite Mixture Of Ising Graphical Models, Chong Gu

Dissertations

The Ising model is valuable in examining complex interactions within a system, but its estimation is challenging. In this work, we proposed penalized likelihood procedures to infer conditional dependence structure when observed data come from heterogeneous resources in high-dimensional setting. The proposed method can be efficiently implemented by taking advantage of coordinate-ascent, minorization–maximization principles and EM algorithm. A BIC-type criterion will be utilized for the selection of the tuning parameter in the penalized likelihood approaches. The effectiveness of the proposed method is supported by simulation studies and a real-world example.

Evaluating The Performance Of Estimators In Sem And Irt With Ordinal Variables, Bo Klauth

Dissertations

In conducting confirmatory factor analysis with ordered response items, the literature suggests that when the number of responses is five and item skewness (IS) is approximately normal, researchers can employ maximum likelihood with robust standard errors (MLR). However, MLR can yield biased factor loadings (FL) and FL standard errors (FLSE) when the variables are ordinal. Other estimators are available. Unweighted least squares and weighted least squares with adjusted mean and variance (ULSMV and WLSMV) are known as the estimators for CFA with ordinal variables (CFA-OV). Another estimator, marginal maximum likelihood (MML), is used in the item response theory (IRT), specifically …

Functional Generalized Linear Mixed Models, Harmony Luce

Dissertations

With the advancements in data collection technologies, researchers in various fields such as epidemiology, chemometrics, and environmental science face the challenges of obtaining useful information from more detailed, complex, and intricately-structured data. Since the existing methods often are not suitable for such data, new statistical methods are developed to accommodate the complicated data structures.

As a part of such efforts, this dissertation proposes Functional Generalized Linear Mixed Model (FGLMM), which extends classical generalized linear mixed models to include functional covariates. Functional Data Analysis (FDA) is a rapidly developing area of statistics for data which can be naturally viewed as smooth …

Utilizing New Technologies To Measure Therapy Effectiveness For Mental And Physical Health, Jonathan Ossie

Dissertations

Mental health is quickly becoming a major policy concern, with recent data reporting increasing and disproportionately worse mental health outcomes, including anxiety, depression, increased substance abuse, and elevated suicidal ideation. One specific population that is especially high risk for these issues is the military community because military conflict, deployment stressors, and combat exposure contribute to the risk of mental health problems.

Although several pharmacological approaches have been employed to combat this epidemic, their efficacy is mixed at best, which has led to novel nonpharmacological approaches. One such approach is Operation Surf, a nonprofit that provides nature-based programs advocating the restorative …

Special Education: Inclusion And Exclusion In The K-12 U.S. Educational System, Erik Brault

Dissertations

The U.S. Department of Education defines students with disabilities as those having a physical or mental impairment that substantially limits one or more life activities. Previous research has found that students with disabilities placed in inclusive environments perform better academically and socially compared to students with disabilities who are placed in segregated environments. Yet, we know that inclusion in K-12 general education classrooms across the country is not consistently implemented.

The purpose of this study was to better understand the effects, if any, of general education high school teachers’ personal and professional experiences and knowledge on their attitudes toward educating …

High-Dimensional Variable Selection Via Knockoffs Using Gradient Boosting, Amr Essam Mohamed

Dissertations

As data continue to grow rapidly in size and complexity, efficient and effective statistical methods are needed to detect the important variables/features. Variable selection is one of the most crucial problems in statistical applications. This problem arises when one wants to model the relationship between the response and the predictors. The goal is to reduce the number of variables to a minimal set of explanatory variables that are truly associated with the response of interest to improve the model accuracy. Effectively choosing the true influential variables and controlling the False Discovery Rate (FDR) without sacrificing power has been a challenge …

Statistical Clustering Of Networks With Additional Information, Paul Atandoh

Dissertations

As the online market grows rapidly, many companies and researchers are interested in analyzing product review dataset which includes ratings and text review data. In the first project, we mainly focus on analyzing the text review data. In the current literature, it is common to use only text analysis tools to analyze review dataset. But in our work, we propose a method that utilizes both a text analysis method such as topic modeling and a statistical network model to build network among individuals and find interesting communities. We introduce a promising framework that incorporates topic modeling technique to define the …

Mixture Of Functional Graphical Models, Qihai Liu

Dissertations

With the development of data collection technologies that use powerful monitoring devices and computational tools, many scientific fields are now obtaining more detailed and more complicatedly structured data, e.g., functional data. This leads to increasing challenges of extracting information from the large complex data. Making use of these data to gain insight into complex phenomena requires characterizing the relationships among a large number of functional variables. Functional data analysis (FDA) is a rapidly developing area of statistics for data which can be naturally viewed as a smooth curve or function. It is a method that changes the frame of data …

Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan

Dissertations

Stochastic gradient descent (SGD) is a popular iterative method for model parameter estimation in large-scale data and online learning settings since it goes through the data in only one pass. While SGD has been well studied for independent data, its application to spatially-correlated data largely remains unexplored. This dissertation develops SGD-based parameter estimation and statistical inference algorithms for the spatial autoregressive (SAR) model, a common model for spatial lattice data.

This research contains three parts. (I) The first part concerns SGD estimation and inference for the SAR mean regression model. A new SGD algorithm based on maximum likelihood estimator (MLE) …

Dependent Censoring In Survival Analysis, Zhongcheng Lin

Dissertations

This dissertation mainly consists of two parts. In the first part, some properties of bivariate Archimedean Copulas formed by two time-to-event random variables are discussed under the setting of left censoring, where these two variables are subject to one left-censored independent variable respectively. Some distributional results for their joint cdf under different censoring patterns are presented. Those results are expected to be useful in both model fitting and checking procedures for Archimedean copula models with bivariate left-censored data. As an application of the theoretical results that are obtained, a moment estimator of the dependence parameter in Archimedean copula models is …

Estimation Of Odds Ratio In 2 X 2 Contingency Tables With Small Cell Counts, Guohao Zhu

Dissertations

This study is focusing on properties of estimators of odds ratio or its logarithm in case of 2x2 tables with small counts. The odds ratio represents the odds that an outcome of interest will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure. Both parameters are often used to quantify the strength of association of two binary variables and are common measurements reported in case-control, cohort, and cross-sectional studies.

Because of their wide applicability, both parameters, odds ratio, and its logarithm, have been intensively studied in the literature. However, most …

Novel Statistical Modeling Methods For Traffic Video Analysis, Hang Shi

Dissertations

Video analysis is an active and rapidly expanding research area in computer vision and artificial intelligence due to its broad applications in modern society. Many methods have been proposed to analyze the videos, but many challenging factors remain untackled. In this dissertation, four statistical modeling methods are proposed to address some challenging traffic video analysis problems under adverse illumination and weather conditions.

First, a new foreground detection method is presented to detect the foreground objects in videos. A novel Global Foreground Modeling (GFM) method, which estimates a global probability density function for the foreground and applies the Bayes decision rule …

Ensemble Data Fitting For Bathymetric Models Informed By Nominal Data, Samantha Zambo

Dissertations

Due to the difficulty and expense of collecting bathymetric data, modeling is the primary tool to produce detailed maps of the ocean floor. Current modeling practices typically utilize only one interpolator; the industry standard is splines-in-tension.

In this dissertation we introduce a new nominal-informed ensemble interpolator designed to improve modeling accuracy in regions of sparse data. The method is guided by a priori domain knowledge provided by artificially intelligent classifiers. We recast such geomorphological classifications, such as ‘seamount’ or ‘ridge’, as nominal data which we utilize as foundational shapes in an expanded ordinary least squares regression-based algorithm. To our knowledge …

Asymmetric Multivariate Archimedean Copula Models And Semi-Competing Risks Data Analysis, Ziyan Guo

Dissertations

Many multivariate models have been proposed and developed to model high dimensional data when the dimension of a data set is greater than 2 (d ≥ 3). The existing multivariate models often force the “exchangeable” structure for part or the whole model, are not very flexible which tends to be of limited use in practice. There is a demand for developing and studying multivariate models with any pre-specified bivariate margins.

Suppose there exists such a class of flexible models with any pre-specified bivariate margins. Given a multivariate data, what is the distribution function and how to easily estimate the parameters …

On Simes’S Second Conjecture: An Extended Single-Step Simes Test Procedure For Multiple Testing, Matthew G. Hudson

Dissertations

One of the major concerns with multiple tests of significance is controlling the family wise error rate. Various methods have been developed to ensure that the false positive rate be maintained at some prespecified level. One of the most well know being the Bonferroni procedure. Simes presented an improved Bonferroni procedure for testing the global hypothesis that is more powerful and less conservative, especially with positively correlated tests. While Simes’s procedure is more powerful, it does not allow for making inferences on the individual hypotheses. However, the Simes procedure has since become the foundation of many p-value based multiple testing …

A Management Strategy Evaluation Of The Impacts Of Interspecific Competition And Recreational Fishery Dynamics On Vermilion Snapper (Rhomboplites Aurorubens) In The Gulf Of Mexico, Megumi C. Oshima

Dissertations

In the Gulf of Mexico (GOM), Vermilion Snapper (Rhomboplites auroruben), are believed to compete with Red Snapper directly for prey and habitat. The two species share similar diets and have significant spatial overlap in the Gulf. Red Snapper are thought to be the dominate competitor, forcing Vermilion Snapper to feed on less nutritious prey when local resources are depleted. In addition to ecological pressures, GOM Vermilion Snapper support substantial commercial and recreational fisheries. Over the past decade, recreational landings have steadily increased, reaching a historical high in 2018. One cause may be stricter regulations for similar target species such as …

Machine Learning Approaches For Improving Prediction Performance Of Structure-Activity Relationship Models, Gabriel Idakwo

Dissertations

In silico bioactivity prediction studies are designed to complement in vivo and in vitro efforts to assess the activity and properties of small molecules. In silico methods such as Quantitative Structure-Activity/Property Relationship (QSAR) are used to correlate the structure of a molecule to its biological property in drug design and toxicological studies. In this body of work, I started with two in-depth reviews into the application of machine learning based approaches and feature reduction methods to QSAR, and then investigated solutions to three common challenges faced in machine learning based QSAR studies.

First, to improve the prediction accuracy of learning …

Statistical Properties And Applications Of Press Statistic, Ida Marie Alcantara

Dissertations

The most popularly used statistic R^₂ has a fundamental weakness in model building: it favors adding more predictors to the model because R² can only increase. In effect, the additional predictors start fitting the noise in data. Other criterion in selecting a regression model such as R² _adj , AIC, SBC, and Mallow’s C_p does not guarantee the model selected will also make better prediction of future values. To avoid this, data scientists withhold a percentage of the data for validation purposes. The PRESS statistic does something similar by withholding each observation in calculating its own …

Statistical Machine Learning Methods For Mining Spatial And Temporal Data, Fei Tan

Dissertations

Spatial and temporal dependencies are ubiquitous properties of data in numerous domains. The popularity of spatial and temporal data mining has thus grown with the increasing prevalence of massive data. The presence of spatial and temporal attributes not only provides complementary useful perspectives, but also poses new challenges to the representation and integration into the learning procedure. In this dissertation, the involved spatial and temporal dependencies are explored with three genres: sample-wise, feature-wise, and target-wise. A family of novel methodologies is developed accordingly for the dependency representation in respective scenarios.

First, dependencies among discrete, continuous and repeated observations are studied …

Statistical Models For Correlated Data, Xiaomeng Niu

Dissertations

Correlated data arise frequently in many studies where multiple response variables or repeatedly measured responses within subjects are correlated. My dissertation topic lies broadly in developing various statistical methodologies for correlated types of data such as longitudinal data, clustered data, and multivariate data.

Multiple response variables might be relevant within subjects. A univariate procedure fitting each response separately does not take into account the correlation among responses. To improve estimation efficiency for the regression parameter, this study proposes two estimation procedures by accommodating correlations among the response variables. The proposed procedures do not require knowledge of the true correlation structure …

Statistical Properties Of Population Stability Index, Bilal Yurdakul

Dissertations

Population stability is an important concept in model management. It is crucial to monitor whether the current population has changed from the population used during development of a model. For example, has the distribution of credit scores changed, and is the existing credit score model still valid? Population change may occur for many reasons–change in the economic environment, strategic change in the business, policy changes within the company, or changes in regulatory environment.

The population stability index (PSI) is a statistic that measures how much a variable has shifted over time, and is used to monitor applicability of a statistical …

Denoising Large Neuroimage Mri Data Using Spatial Random Effect Models, Leonard Chukuma Johnson

Dissertations

Spatial smoothing in Magnetic Resonance image (MRI) involves applying a filter to remove high frequency information and consequently improves signal-to-noise ratio that can greatly aid neurosurgeons in pre-surgical planning stages of tumor resection. This immensely reduces the time spent on Electrical stimulation mapping (ESM) prior to surgery. MRI's three-dimensional data provides voxel intensities with complex spatial relationship. The standard de facto spatial smoothing method, Gaussian Kernel smoothing, is satisfactory since a uniform smoothing is done for the whole brain. Secondly, the kernel smoothing technique assumes normality for the voxel intensity, but there is ample evidence in current research that indicates …

Statistical And Clinical Equivalence Of Measurements, Puntipa Wanitjirattikal

Dissertations

This study proposes a test for statistical equivalence of two measurements. Typically, a new measurement process Υ is compared to an existing or standard measurement process Χ. We are assuming that Χ and Υ are measurements on the same scale. The paired t-test may be used to check for significant difference between (Χ, Υ) pairs. However, the paired t-test is intended to detect shift-type relationships of the form Υ=Χ+δ1 and may have low power for scale-type relations of the form Υ=γΧ.

We propose a test that has reasonable power to …

Diagnostics For Choosing Between Stratified Logrank And Stratified Wilcoxon, Jhoanne Marsh C. Gatpatan

Dissertations

Martinez and Naranjo (2010) proposed a pretest for choosing between Logrank or Wilcoxon test in a two - sample case. However, in the presence of covariates, comparing two populations without adjusting for covariates would yield misleading results. In this study, we propose several pretests that will help the analyst decide to use stratified Logrank or stratified Wilcoxon tests in comparing two survival curves after covariates have been taken into account. Power performance of each adaptive test was done through simulations under PH and non-PH cases.

Development Of Traditional And Rank-Based Algorithms For Linear Models With Autoregressive Errors And Multivariate Logistic Regression With Spatial Random Effects, Shaofeng Zhang

Dissertations

Linear models are the most commonly used statistical methods in many disciplines. One of the model assumptions is that the error terms (residuals) are independent and identically distributed. This assumption is often violated and autoregressive error terms are often encountered by researchers. The most popular technique to deal with linear models with autoregressive errors is perhaps the autoregressive integrated moving average (ARIMA). Another common approach is generalized least squares, such as Cochrane-Orcutt estimation and Prais-Winsten estimation. However, these usually have poor behaviors when fitting small samples. To address this problem, a double bootstrap method was proposed by McKnight et al. …

Spatial Analysis Of Time Between Two Consecutive Dental And Two Consecutive Well-Child Visits For Foster Care Youth, Chenyang Shi

Dissertations

Foster care youth is a medically vulnerable population. Poor dental health and irregular well-child visits may cause serious health-related issues, such as mental disorder, nutrition imbalance, tooth damage, etc. Michigan requires all youth in foster care to receive annual dental and well-child visits. Usually, the study of foster care well-child and dental visits include two parts: time between two consecutive visits (gap time) and number of visits. For this study, a longitudinal-spatial model that has the flexibility to analyze the well-child/dental gap times and number of visits was developed. The longitudinal data (2009-2012) on Michigan foster care youth from 10 …

Subgroup Analysis And Growth Curve Models For Longitudinal Data, Nichole Andrews

Dissertations

In clinical trials and biomedical studies, treatments are compared to determine which one is effective against illness. Growth curve analysis can be beneficial in longitudinal biomedical studies, as we can evaluate the treatment effect on the response over time. The generalized growth curve model using polynomial regression is proposed for longitudinal data. An optimal degree for the polynomial is obtained using the BIQIF, an adaptation of the Bayesian information criterion. Quadratic inference functions are used to estimate the parameters of the model, which takes into account the fact that repeated measurements from the same subject are more likely to be …

Some Nonparametric Ordered Restricted Inference Problems In The Context Of A Statistical Education Study, Bradford M. Dykes

Dissertations

Over the past 10 years, the Department of Statistics at Western Michigan University has developed a question generating system that can be used for creating multiple forms of exams, quizzes and homework for online and face-to-face use. This system can also be used to provide students with a form of instantaneous feedback. With the goal of analyzing how different levels of feedback in an online learning environment impacts students' performance on assignments, this study presents data collected on two semesters of students enrolled in three different meeting types (strictly online, typical face-to-face, and honors face-to-face) of an introductory Statistics course. …