Longitudinal Data Analysis and Time Series Commons^™

An Association Test For Ordinal Outcomes In Clustered Data With Informative Cluster Size, Hasika K. Wickrama Senevirathne, Sandipan Dutta

Mathematics & Statistics Faculty Publications

In cluster-correlated data, the number of observations in a cluster can be associated with the outcome from that cluster. This phenomenon is known as informative cluster size which can occur in cluster-randomized clinical trial data. Several studies have found that ignoring the issue of informative cluster size can produce biased results in the analysis of clustered data. Most of the existing methods for addressing informative cluster size are suited to continuous outcomes. However, ordinal outcomes and covariates are often encountered in clustered data obtained from large clinical studies. The existing methods for ordinal association testing in clustered data can produce …

Multiple Changepoint Detection For Non-Gaussian Time Series, Robert Lund, Thomas J. Fisher, Norou Diawara, Michael Wehner

Mathematics & Statistics Faculty Publications

This article combines methods from existing techniques to identify multiple changepoints in non‐Gaussian autocorrelated time series. A transformation is used to convert a Gaussian series into a non‐Gaussian series, enabling penalized likelihood methods to handle non‐Gaussian scenarios. When the marginal distribution of the data is continuous, the methods essentially reduce to the change of variables formula for probability densities. When the marginal distribution is count‐oriented, Hermite expansions and particle filtering techniques are used to quantify the scenario. Simulations demonstrating the efficacy of the methods are given and two data sets are analyzed: 1) the proportion of home runs hit by …

Copula Based Models For Bivariate Zero-Inflated Count Time Series Data, Dimuthu Fernando

Mathematics & Statistics Theses & Dissertations

Count time series data have multiple applications. The applications can be found in areas of finance, climate, public health and crime data analyses. In most scenarios, time is an important part of the data. Time series counts then come as multivariate vectors that exhibit not only serial dependence within each time series but also with cross-correlation among the series. When considering these observed counts, and when a value, say zero, occurs more often than usual, analysis presents crucial challenges. There is presence of zeroinflation in the data. The literature on bivariate or multivariate count time series, as well as zero-inflated …

Gpu Utilization: Predictive Sarimax Time Series Analysis, Dorothy Dorie Parry

Modeling, Simulation and Visualization Student Capstone Conference

This work explores collecting performance metrics and leveraging the output for prediction on a memory-intensive parallel image classification algorithm - Inception v3 (or "Inception3"). Experimental results were collected by nvidia-smi on a computational node DGX-1, equipped with eight Tesla V100 Graphic Processing Units (GPUs). Time series analysis was performed on the GPU utilization data taken, for multiple runs, of Inception3’s image classification algorithm (see Figure 1). The time series model applied was Seasonal Autoregressive Integrated Moving Average Exogenous (SARIMAX).

The Effectiveness Of Visualization Techniques For Supporting Decision-Making, Cansu Yalim, Holly A. H. Handley

Modeling, Simulation and Visualization Student Capstone Conference

Although visualization is beneficial for evaluating and communicating data, the efficiency of various visualization approaches for different data types is not always evident. This research aims to address this issue by investigating the usefulness of several visualization techniques for various data kinds, including continuous, categorical, and time-series data. The qualitative appraisal of each technique's strengths, weaknesses, and interpretation of the dataset is investigated. The research questions include: which visualization approaches perform best for different data types, and what factors impact their usefulness? The absence of clear directions for both researchers and practitioners on how to identify the most effective visualization …

Copula-Based Models For Bivariate And Multivariate Zero-Inflated Count Time Series Data, Dimuthu Fernando, Norou Diawara

College of Sciences Posters

Count time series data have multiple applications. The applications can be found in areas of finance, climate, public health and crime data analyses. In some scenarios, count time series come as multivariate vectors that exhibit not only serial dependence within each time series but also with cross correlation among the series. When considering these observed counts, analysis presents crucial challenges when a value, say zero, occurs more often than usual. There is presence of zero-inflation in the data.

In this presentation, we mainly focus on modeling bivariate zero-inflated count time series model based on a joint distribution of the two …

Institutional Context Drives Mobility: A Comprehensive Analysis Of Academic And Economic Factors That Influence International Student Enrollment At United States Higher Education Institutions, Natalie Cruz

College of Education & Professional Studies (Darden) Posters

International student enrollment (ISE) has become a hallmark of world-class higher education institutions (HEIs). Although the U.S. has welcomed the largest numbers of international students since the 1950s, ISE shrunk by 10% in the previous three years from an all-time high of 903,127 students in 2016/2017 (IIE, 2019). Research studies about international student mobility and enrollment highlights the significant role that academic and economic rationales play for international students. This quantitative, ex post facto study focused on the influence of ranking, tuition, Optional Practical Training, Gross Domestic Product, and the unemployment rate on ISE at 2,884 U.S. HEIs from 2008 …

Unsupervised Multivariate Time Series Clustering, Md Monibor Rahman, Lasitha Vidyaratne, Alex Glandon, Khan Iftekharuddin

College of Engineering & Technology (Batten) Posters

Clustering is widely used in unsupervised machine learning to partition a given set of data into non-overlapping groups. Many real-world applications require processing more complex multivariate time series data characterized by more than one dependent variables. A few works in literature reported multivariate classification using Shapelet learning. However, the clustering of multivariate time series signals using Shapelet learning has not explored yet. Shapelet learning is a process of discovering those Shapelets which contain the most informative features of the time series signal. Discovering suitable Shapelets from many candidates Shapelet has been broadly studied for classification and clustering of univariate time …

D-Vine Pair-Copula Models For Longitudinal Binary Data, Huihui Lin

Mathematics & Statistics Theses & Dissertations

Dependent longitudinal binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. A popular method for analyzing such data is the multivariate probit (MP) model. The motivation for this dissertation stems from the fact that the MP model fails even the binary correlations are within the feasible range. The reason being the underlying correlation matrix of the latent variables in the MP model may not be positive definite. In this dissertation, we study alternatives that are based on D-vine pair-copula models. We consider both the serial dependence modeled by the first order autoregressive (AR(1)) and …

Copula-Based Zero-Inflated Count Time Series Models, Mohammed Sulaiman Alqawba

Mathematics & Statistics Theses & Dissertations

Count time series data are observed in several applied disciplines such as in environmental science, biostatistics, economics, public health, and finance. In some cases, a specific count, say zero, may occur more often than usual. Additionally, serial dependence might be found among these counts if they are recorded over time. Overlooking the frequent occurrence of zeros and the serial dependence could lead to false inference. In this dissertation, we propose two classes of copula-based time series models for zero-inflated counts with the presence of covariates. Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP) distributed marginals of the …

Rates Of Relative Sea Level Rise Along The United States East Coast, Jesse N. Beckman, Joseph E. Garcia

Virginia Journal of Science

Recent studies have indicated that some coastal areas, including the East Coast of the United States, are experiencing higher rates of sea level rise than the global average. Rates of relative sea level rise are affected by changes in ocean dynamics, as well as by surface elevation fluctuations due to local land subsidence or uplift. In this study, we derived long-term trends in annual mean relative sea level using tide gauge data obtained from the Permanent Service for Mean Sea Level for stations along the United States East Coast. Stations were grouped by location into the Northeast, Mid-Atlantic, and Southeast …

New Approaches To Model Simulated Spatio-Temporal Moran's Index, Nhan Bu, Jennifer Lorio, Norou Diawara, Kumar Das, Lance Waller

Mathematics & Statistics Faculty Publications

The Moran's index is a statistic that measures spatial autocorrelation; it quantifies the degree of dispersion (or clustering) of objects in space. However, when investigating data over a general area, a single global Moran statistic may not give a sufficient summary of the spread, behavior, features or latent surfaces shared by neighboring areas; rather, by partitioning the area and taking the Moran statistic of each divided subareas, we can discover patterns of the local neighbors not otherwise apparent. In this paper, we present a simulation experiment where the local Moran values are computed and a time variable is added to …

Longitudinal Tidal Dispersion Coefficient Estimation And Total Suspended Solids Transport Characterization In The James River, Beatriz Eugenia Patino

Civil & Environmental Engineering Theses & Dissertations

The longitudinal dispersion coefficient is a parameter used to evaluate the effect of cross-sectional variations on substance mixing mechanisms in estuaries influenced by tide, wind and internal density variations. Considering a two dimensional approach, this study aims at evaluating a tidal area of the lower James River at approximately 19 miles upstream from the mouth at the Chesapeake Bay, in the City of Newport News, and applies an experimental procedure based on in-situ salinity concentrations to estimate the dispersion coefficient in the area where receives a discharge from the HRSD James River Wastewater Treatment Plant, and further characterizes Total Suspended …

Key Factors Driving Personnel Downsizing In Multinational Military Organizations, Ilksen Gorkem, Resit Unal, Pilar Pazos

Engineering Management & Systems Engineering Faculty Publications

Although downsizing has long been a topic of research in traditional organizations, there are very few studies of this phenomenon in military contexts. As a result, we have little understanding of the key factors that drive personnel downsizing in military setting. This study contributes to our understanding of key factors that drive personnel downsizing in military organizations and whether those factors may differ across NATO nations’ cultural clusters. The theoretical framework for this study was built from studies in non-military contexts and adapted to fit the military environment.

This research relies on historical data from one of the largest multinational …

Testing Longitudinal Data By Logarithmic Quantiles, Manfred Denker, Lucia Tabacu

Mathematics & Statistics Faculty Publications

The shoulder tip pain study of Lumley [13] is re-investigated. It is shown that the new logarithmic quantile estimation (LQE) technique in [9] applies and behaves well under singular covariance structure and small sample sizes as in the shoulder tip pain study. The findings in [6] can be assured under weaker assumptions using a combination of LQE and an ANOVA type statistic. © 2014, Institute of Mathematical Statistics.

Modelling Locally Changing Variance Structured Time Series Data By Using Breakpoints Bootstrap Filtering, Rajan Lamichhane

Mathematics & Statistics Theses & Dissertations

Stochastic processes have applications in many areas such as oceanography and engineering. Special classes of such processes deal with time series of sparse data. Studies in such cases focus in the analysis, construction and prediction in parametric models. Here, we assume several non-linear time series with additive noise components, and the model fitting is proposed in two stages. The first stage identifies the density using all the clusters information, without specifying any prior knowledge of the underlying distribution function of the time series. The effect of covariates is controlled by fitting the linear regression model with serially correlated errors. In …

Analysis Of Continuous Longitudinal Data With Arma(1, 1) And Antedependence Correlation Structures, Sirisha Mushti

Mathematics & Statistics Theses & Dissertations

Longitudinal or repeated measure data are common in biomedical and clinical trials. These data are often collected on individuals at scheduled times resulting in dependent responses. Inference methods for studying the behavior of responses over time as well as methods to study the association with certain risk factors or covariates taking into account the dependencies are of great importance. In this research we focus our study on the analysis of continuous longitudinal data. To model the dependencies of the responses over time, we consider appropriate correlation structures generated by the stationary and non-stationary time-series models. We develop new estimation procedures …

Canonical Correlation Analysis For Longitudinal Data, Raymond Mccollum

Mathematics & Statistics Theses & Dissertations

Data (multivariate data) on two sets of vectors commonly occur in applications. Statistical analysis of these data is usually done using a canonical correlation analysis (CCA). Occurrence of these data at multiple occasions or conditions leads to longitudinal multivariate data for a CCA. We address the problem of canonical correlation analysis on longitudinal data when the data have a Kronecker product covariance structure. Using structured correlation matrices we model the dependency of repeatedly observed data. Recent work of Srivastava, Nahtman, and von Rosen (2008) developed an iterative algorithm to determine the maximum likelihood estimate of the Kronecker product covariance structure …

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …

Time Valuation Of Risk: A Delayed-Bang Approach, Abhishek Pathak

Engineering Management & Systems Engineering Theses & Dissertations

The subject of this thesis is the combined use of engineering economics and survival analysis in estimating time-value of risk-related resources. The discussion includes (1) the need for sustainable risk management, (2) the importance of time-valuation of risk related resources in the allocation or selection among competing risk mitigation alternatives, (3) the convergence of deterministic engineering economics, survivability analysis, and probabilistic analysis, and (4) results and examples of application in the context of prevention of risk event or mitigation of its consequences.

The significance of this thesis is in how three topics: engineering economics, survivability analysis, and probability theory can …

Canonical Correlation And Correspondence Analysis Of Longitudinal Data, Jayesh Srivastava

Mathematics & Statistics Theses & Dissertations

Assessing the relationship between two sets of multivariate vectors is an important problem in statistics. Canonical correlation coefficients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. When the variables are qualitative (categorical), a technique called correspondence analysis (CA) is used. Canonical correspondence analysis (CCPA) is used to deal with the case when one set of variables is categorical and the other set is quantitative. By exploiting the interrelationships between these three techniques we first provide a theoretical basis for …

Statistical Analysis Of Longitudinal And Multivariate Discrete Data, Deepak Mav

Mathematics & Statistics Theses & Dissertations

Correlated multivariate Poisson and binary variables occur naturally in medical, biological and epidemiological longitudinal studies. Modeling and simulating such variables is difficult because the correlations are restricted by the marginal means via Fréchet bounds in a complicated way. In this dissertation we will first discuss partially specified models and methods for estimating the regression and correlation parameters. We derive the asymptotic distributions of these parameter estimates. Using simulations based on extensions of the algorithm due to Sim (1993, Journal of Statistical Computation and Simulation, 47, pp. 1–10), we study the performance of these estimates using infeasibility, coverage probabilities of the …

Estimation Of Parameters In Replicated Time Series Regression Models, Genming Shi

Mathematics & Statistics Theses & Dissertations

The time series regression model was widely studied in the literature by several authors. However, statistical analysis of replicated time series regression models has received little attention. In this thesis, we study the application of quasi-least squares, a relatively new method, to estimate the parameters in replicated time series models with general ARMA( p, q) correlation structure. We also study several established methods for estimating the parameters in those models, including the maximum likelihood, method of moments, and the GEE method. Asymptotic comparisons of the methods are made bV fixing the number of repeated measurements in each series, and …