Statistics and Probability Commons^™

Causal Mediation Analysis For Difference-In-Difference Design And Panel Data, Pei-Hsuan Hsia, An-Shun Tai, Chu-Lan Michael Kao, Yu-Hsuan Lin, Sheng-Hsuan Lin

Harvard University Biostatistics Working Paper Series

Advantages of panel data, i.e., difference in difference (DID) design data, are a large sample size and easy availability. Therefore, panel data are widely used in epidemiology and in all social science fields. The literatures on causal inferences of panel data setting or DID design are growing, but no theory or mediation analysis method has been proposed for such settings. In this study, we propose a methodology for conducting causal mediation analysis in DID design and panel data setting. We provide formal counterfactual definitions for controlled direct effect and natural direct and indirect effect in panel data setting and DID …

Addressing The Ecological Fallacy With Lagrangian Inference, Michael Schwob

Calvert Undergraduate Research Awards

Most epidemiologists elect to use statistical models that use population-level data to make inference on the spread of some virus or disease. This has become commonplace in the fields of epidemiology and biostatistics since most data used to construct and verify epidemic models are recorded at the population-level. Obtaining inference from a population-level model may be beneficial in studying the spread of disease in a homogeneous population, but the use of such models to describe a heterogeneous population results in inadequate inference. The inaccuracy of these models is further amplified when one tries to make individual-level inference from these population-level …

Principal Components Analysis Corrects Collider Bias In Polygenic Risk Score Effect Size Estimation, Nathaniel S. Thomas, Peter B. Barr, Fazil Aliev, Sally I. Kuo, Danielle M. Dick, Jessica E. Salvatore

Graduate Research Posters

BACKGROUND: Genome-wide polygenic scoring has emerged as a way to predict psychiatric and behavioral outcomes and identify environments that promote the expression of genetic risks. An increasing number of studies demonstrate that the effects of polygenic risk scores (PRS) may be biased by the inclusion of heritable environments as covariates when the environment is influenced by unmeasured confounding variables, an example of collider bias. Inclusion of the principal components of observed confounders as covariates may correct for the effect of unmeasured confounders.

METHODS: A simulation study was conducted to test principal components analysis (PCA) as a correction for collider bias. …

Modeling Longitudinal Change In Cervical Length Across Pregnancy, Hope M. Wolf, Shawn J. Latendresse, Jerome F. Strauss Iii, Timothy P. York

Graduate Research Posters

Introduction: A short cervix (cervical length < 25 mm) in the mid-trimester (18 to 24 weeks) of pregnancy is a powerful predictor of spontaneous preterm delivery (gestational age at delivery < 37 weeks). Although the biological mechanisms of cervical remodeling have been the subject of extensive investigation, very little is known about the rate of change in cervical length over the course of a pregnancy, or the extent to which rapid cervical shortening increases maternal risk for spontaneous preterm delivery.

Methods: A cohort of 5,160 unique women carrying 5,971 singleton pregnancies provided two or more measurements of cervical length during pregnancy. Cervical length was measured in millimeters using a transvaginal 12-3 MHz ultrasound endocavity probe (SuperSonic Imagine). Maternal characteristics, including relevant medical history and birth outcome data, were collected for each participant. Gestational age at delivery was measured from the first day of each woman’s last menstrual period and confirmed by ultrasound. Repeated measurements of cervical length during pregnancy were modeled as a longitudinal, multilevel growth curve in MPlus. A three-level variance structure was …

Studying The Relationship Between Financial Risk Aversion And Income With The Jeopardy! Daily Double, Miles Johnson

Mahurin Honors College Capstone Experience/Thesis Projects

It has long been up for debate as to whether there is a link between financial risk aversion and income. This study’s purpose is to, using data from the game show Jeopardy!, investigate this question through analytical research. This study made use of multiple regression analyses in order to examine the relationship between income and risk aversion in Jeopardy! contestants who appeared on the show between January 2019 and October 2020. Specifically, this study looked to isolate the potential impact a contestant’s estimated annual income had on their willingness to bet on the Jeopardy! Daily Double question. It was …

Biofilm And Cell Adhesion Strength On Dental Implant Surfaces Via The Laser Spallation Technique, James D. Boyd, Arnold J. Stromberg, Craig S. Miller, Martha E. Grady

Statistics Faculty Publications

OBJECTIVE: The aims of this study are to quantify the adhesion strength differential between an oral bacterial biofilm and an osteoblast-like cell monolayer to a dental implant-simulant surface and develop a metric that quantifies the biocompatible effect of implant surfaces on bacterial and cell adhesion.

METHODS: High-amplitude short-duration stress waves generated by laser pulse absorption are used to spall bacteria and cells from titanium substrates. By carefully controlling laser fluence and calibration of laser fluence with applied stress, the adhesion difference between Streptococcus mutans biofilms and MG 63 osteoblast-like cell monolayers on smooth and rough titanium substrates is obtained. The …

A Time Series Analysis Approach To Forecasting Covid-19 Cases And Deaths: An Analysis Of Covid-19 Data In Colombia, Andrea Jackson-Sagredo

Graduate Research Theses & Dissertations

The novel Coronavirus, known as COVID-19 is a highly contagious and transmissible infectious disease that has taken a toll throughout the entire world for over a year. The inner workings and long term effects of COVID-19 continue to be misunderstood. While COVID-19 has impacted all countries tremendously, Latin American countries and specifically Colombia have been impacted significantly by the virus. This thesis investigates the potential to forecast COVID-19 cases and deaths using Time Series Analysis methods and models for the South American country of Colombia. Time series analysis on Colombian COVID-19 data begins with data processing on a data set …

Optimization Of Dynamic Objective Functions Using Path Integrals, Paramahansa Pramanik

Graduate Research Theses & Dissertations

Path integrals are used to find an optimal strategy for a firm under a Walrasian system. We define dynamic optimal strategies and develop an integration method to capture all non-additive non-convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry …

A Unified Approach For Constructing Confidence Intervals And Hypothesis Tests Using H-Function, Weizhen Wang

Mathematics and Statistics Faculty Publications

We introduce a general method, named the h-function method, to unify the con- structions of level- exact test and 1− exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, including a point estimator, is modified to an exact interval; ii) an exact interval is refined to be an interval that is a subset of the previous one. Two real datasets are used to illustrate the method.

Coloring Permutation-Gain Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Correspondence colorings of graphs were introduced in 2018by Dvoˇr ́ak and Postle as a generalization of list colorings of graphswhich generalizes ordinary graph coloring. Kim and Ozeki observed thatcorrespondence colorings generalize various notions of signed-graph col-orings which again generalizes ordinary graph colorings. In this notewe state how correspondence colorings generalize Zaslavsky’s notionof gain-graph colorings and then formulate a new coloring theory ofpermutation-gain graphs that sits between gain-graph coloring and cor-respondence colorings. Like Zaslavsky’s gain-graph coloring, our newnotion of coloring permutation-gain graphs has well defined chromaticpolynomials and lifts to colorings of the regular covering graph of apermutation-gain graph

Stochastic Infection In Network Models With Applications To Pollution Analysis, Alexander Thor Wold

Graduate Research Theses & Dissertations

The continued adoption and escalation of commercial surface extraction techniques threatens to contaminate adjacent river networks across the coal mining landscape. We look to simulate the movement of this pollution across connected graph structures using stochastic block model methodologies, fueled from work and theory derived from exponential random graph models. We begin our study by applying our virtual experiment to the motivating material, later offering an exhaustive walk through of the simulation itself. Afterwards, we present our findings and their implications to water pollution analysis, emphasizing a need for this research and expanding on some inferential statistics left for later …

A Bayesian Hierarchical Mixture Model With Continuous-Time Markov Chains To Capture Bumblebee Foraging Behavior, Max Thrush Hukill

Honors Projects

The standard statistical methodology for analyzing complex case-control studies in ethology is often limited by approaches that force researchers to model distinct aspects of biological processes in a piecemeal, disjointed fashion. By developing a hierarchical Bayesian model, this work demonstrates that statistical inference in this context can be done using a single coherent framework. To do this, we construct a continuous-time Markov chain (CTMC) to model bumblebee foraging behavior. To connect the experimental design with the CTMC, we employ a mixture model controlled by a logistic regression on the two-factor design matrix. We then show how to infer these model …

Novel Methods For Characterizing Conditional Quantiles In Zero-Inflated Count Regression Models, Xuan Shi

Theses and Dissertations--Statistics

Despite its popularity in diverse disciplines, quantile regression methods are primarily designed for the continuous response setting and cannot be directly applied to the discrete (or count) response setting. There can also be challenges when modeling count responses, such as the presence of excess zero counts, formally known as zero-inflation. To address the aforementioned challenges, we propose a comprehensive model-aware strategy that synthesizes quantile regression methods with estimation of zero-inflated count regression models. Various competing computational routines are examined, while residual analysis and model selection procedures are included to validate our method. The performance of these methods is characterized through …

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 …

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, …

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 …

Carbon Dioxide And Particulate Matter Concentration On Hampton Roads Air Quality, Gregory Hubbard

OUR Journal: ODU Undergraduate Research Journal

Hampton Roads has been a maritime crossroads for the last 400 years. Industrialization has impacted the coastal region for the last 250 years. The expansion of the Port of Virginia in 2019 has created dense traffic in the region resulting in impacts to air quality. Two waste products that affect humans are particulate matter and carbon dioxide. Both respective emissions can cause adverse effects on humans, such as asthma, some lung cancers, and other respiratory distress. Scientists and health practitioners are studying the effects of particulate matter on human health. Hampton Roads, in particular, because of its unique location on …