Doctor of Philosophy, The Ohio State University, 2023, Statistics

Exponential family PCA (Collins et al., 2001) is a widely used dimension reduction tool for capturing a low-dimensional latent structure of exponential family data such as binary data or count data. As an extension of principal component analysis (PCA), it imposes a low-rank structure on the natural parameter matrix, which can be factorized into two matrices, namely, the principal component loadings matrix and scores matrix. These loadings and scores share the same interpretation and functionality as those in PCA. Loadings enable exploration of associations among variables, scores can be utilized as low-dimensional data embeddings, and estimated natural parameters can impute missing data entries. Despite the popularity of exponential family PCA, we find several statistical issues associated with this method. We investigate these issues from a statistical perspective and propose remedies in this dissertation. Our primary concern arises from the joint estimation of loadings and scores through the maximum likelihood method. As in the well-known incidental parameter problem, this formulation with scores as separate parameters may result in inconsistency in the estimation of loadings under the classical asymptotic setting where the data dimension is fixed. We examine the population version of this formulation and show that it lacks Fisher consistency in loadings. Additionally, estimating scores can be viewed as performing a generalized linear model with loadings as covariates. Maximum likelihood estimation (MLE) bias is naturally involved in this process but is often ignored. Upon identifying two major sources of bias in the estimation process, we propose a bias correction procedure to reduce their effects. First, we deal with the discrepancy between true loadings and their estimates under a limited sample size. We use the iterative bootstrap method to debias loadings estimates. Then, we account for sampling errors in loadings by treating them as covariates with me (open full item for complete abstract)

Committee: Yoonkyung Lee (Advisor); Asuman Turkmen (Committee Member); YunZhang Zhu (Committee Member) Subjects: Statistics

PhD, University of Cincinnati, 2019, Education, Criminal Justice, and Human Services: Educational Studies

Multilevel study designs are well suited for research in hierarchically structured educational settings. However, this structure, limited resources, and complex theories of teaching and learning limit the ability of educational researchers to feasibly conduct adequate studies. This three-article dissertation increases the feasibility of multilevel studies through improvements in study design and advancements in analytic approaches. The totality of this work expands the capacity of educational researchers to conduct multilevel studies. First, I extend the partial posterior predictive distribution method (p3 method) to test multilevel mediation. A variety of inferential tests are available for single and multilevel mediation but most come with notable limitations that balance tradeoffs between power and Type I error. The p3 method is a contemporary resampling-based composite approach specifically suited for complex null hypotheses. I develop the p3 method and investigate its performance within the context of two-level cluster-randomized multilevel mediation studies. The p3 method performed well relative to other mediation tests because it provides a more judicious balance of the Type I error rate and power. The method serves as a powerful alternative tool for researchers investigating multilevel mediation. Next, I investigate the robustness of statistical power under an optimal sampling framework to misspecified parameter values in cluster-randomized designs with cluster- or individual-level mediators. When planning cluster-randomized studies probing mediation, effective and efficient sample allocation is governed by several parameters. In the design stage, these parameters are typically approximated using information from prior research and these approximations are likely to deviate from the true values eventually realized in the study. The results suggest that estimates of statistical power are robust to misspecified parameter values across a variet (open full item for complete abstract)

Committee: Benjamin Kelcey Ph.D. (Committee Chair); Amy Farley Ph.D. (Committee Member); Jessaca Spybrook Ph.D. (Committee Member); Christopher Swoboda Ph.D. (Committee Member) Subjects: Psychological Tests

Master of Science (MS), Bowling Green State University, 2016, Communication Disorders

Studies in airflow during speech production typically use a pneumotachographic mask system placed upon the face to measure the expired airflows. Accurate measures of airflow require mask calibration and a complete seal of the mask rim to the face. Literature frequently cites mask rim leaks as causing flow measure inaccuracies, but quantitative studies of inaccuracies are needed. The purpose of this study was to determine the degree of inaccuracy of flow measurement using a Glottal Enterprises aerodynamic system for a variety of leak sizes. The primary hypothesis was that the greater the air leak cross sectional area at the rim of the mask, the greater the reduction in measured flows through the mask (and therefore the greater the error in measuring the upstream airflow). A range of airflows was both pushed and pulled through the Glottal Enterprises mask system with leaks being simulated by metal tubes of various cross-sectional areas. Two leak locations (bridge-of-nose and corner-of-mouth), single vs. multiple leaks, and two different leak geometries (rectangular and elliptical) were studied. Results suggest the following conclusions: (1) As leak area increases, the amount of leak flow increases; (2) the amount of flow leak is not independent of location; (3) given equivalent leak area, multiple leak locations provide more airflow resistance and less leak flow; (4) elliptical tubes were found to be more resistive to airflow than rectangular tubes. A general equation was obtained that relates the amount of flow reduction (the leak flow) to the rim leak cross sectional area and the upstream flow: Leak(cc/s) = 0.4125*Area(cm2)*Flow(cc/s), for airway flow in the range of ±2000 cc/s. This equation may provide researchers and clinicians in the field with a tool for generalizing airflow leak effects. 

Committee: Ronald Scherer PhD (Advisor); Alexander Goberman PhD (Committee Member); Jason Whitfield PhD (Committee Member) Subjects: Fluid Dynamics; Speech Therapy

PhD, University of Cincinnati, 2011, Arts and Sciences: Mathematical Sciences

The Cox proportional hazards model is commonly used to analyze the exposure-response relationship in occupational cohort studies. This analysis involves identifying cases (those who experience the outcome of interest) and forming risk-sets for each case. The risk-set for a case is the set of cohort members whose failure times are at least as large as the case's failure time and are under observation immediately before the case's failure time. Thomas proposed the idea of randomly sampling controls from each risk-set to use for analysis, which results in a nested case-control study. It has been shown that the analysis using the full risk-sets and the analysis using the sampled risk-sets produce asymptotically unbiased results. Also, the asymptotic relative efficiency between analyzing the full risk-sets and using Thomas' estimator to analyze the sampled risk-sets (sampling m controls per case) is m/(m+1) when there is no exposure-response relationship. A simulation study investigated the non-asymptotic properties of the nested case-control study design and found that the relative efficiency decreased as the number of cases in the cohort decreased, the true exposure-response parameter increased, and the skewness of the exposure distribution of the risk-sets increased. There also appeared to be some bias in a nested case-control study and this bias tended to be away from the null, however, this was not a major issue. In fact, when 10 or more controls were matched with each case, the bias was never more than 10%. A second simulation study compared the estimates obtained from a nested case-control analysis for a given cohort to the estimate obtained from analyzing the full cohort with Cox proportional hazards regression. The nested case-control estimate generally overestimated the full cohort estimate and the size of this discrepancy varied from cohort to cohort. Also, the sample variance of the estimates from a nested case-control study for a given cohort decreased d (open full item for complete abstract)

Committee: James Deddens PhD (Committee Chair); Misty Hein PhD (Committee Member); Mary Schubauer-Berigan PhD (Committee Member); Paul Horn PhD (Committee Member); Siva Sivaganesan PhD (Committee Member); Seongho Song PhD (Committee Member) Subjects: Statistics

MS, University of Cincinnati, 2005, Engineering : Industrial Engineering

Spherical components are an integral part of many industrial products. These components have to be manufactured and inspected with strict dimensional and geometric controls. Heavily loaded spherical components such as ball bearings when used with geometric imperfection may result in large amount of heat, wear, vibration and in turn will result in reduction in life. These geometric imperfections or deviations can be found by applying appropriate algorithms that conforms ANSI standards on the data obtained from CMM. There are a number of procedures to evaluate spherical deviations. Broadly these procedures can be divided into numerical optimization techniques and computational geometric techniques. The computational geometric technique yield accurate results but are time consuming and computationally intensive.This thesis presents a novel way to calculate the spherical error or sphericity of a component by combining both optimization and intrinsic geometric property of the feature. The spherical error formulation based on the minimum zone criterion is a non-linear and non-convex problem. This work presents a verification method which involves solving a sequence of linear programs that converges to a local optimal solution. At each stage the number of constraints on the linear program is function of number of data points. By using intrinsic geometric properties of the spherical feature, these constraints can be reduced. The data points, which form the constraints, are chosen using a heuristic procedure. Thus a non-linear optimization problem for calculation of sphericity error is solved through a sequence of linear programs with reduced constraints, which gives faster and accurate results.

Committee: Anand Sundararaman (Advisor) Subjects: Engineering, Industrial

PhD, University of Cincinnati, 2004, Arts and Sciences : Mathematics

In this dissertation, we use Bayesian methods to estimate parameters in measurement error models and in the two-period crossover trial. The reference prior approach is used to estimate parameters in the measurement error models, including simple normal structural models, Berkson models, structural models with replicates, and the hybrid models. Reference priors are derived. Jeffreys prior is obtained as a special case of reference priors. The posterior properties are studied. Simulation-based comparisons are made between the reference prior approach and the maximum likelihood method. A fractional Bayes factor (FBF) approach is used to estimate the treatment effect in the two-period crossover trial. The reference priors and the FBF are derived. The FBF is used to combine the carryover-effect model and the no-carryover-effect model. Markov chain Monte Carlo simulation is used to implement the Bayesian analysis.

Committee: Dr. Siva Sivaganesan (Advisor) Subjects: Mathematics; Statistics

Doctor of Philosophy, Case Western Reserve University, 2005, Statistics

In this dissertation we provide analysis strategies for two research areas: spatial-temporal data mining and measurement error problems. Motivated by analyzing data from a "Neuromuscular Electrical Stimulation" experiment we develop an efficient procedure for mining spatial-temporal data which combines the following modern and newly developed components: data segmentation and registration, statistical smoothing mapping for identifying "activated" regions and a semiparametric model for detecting spatial-temporal similarities/trends from "large-p-small-n" data sets. For measurement error problems we provide new density and regression estimators for nonparametric errors-in-variables models. The errors can be either homogeneous or nonhomogeneous. In contrast to most existing procedures our new estimators are stable, easy to compute and do not depend on a Fourier transform. The asymptotics of the new estimators is investigated. Our procedures have the potential to become powerful new tools in the image analysis and other fields.

Committee: Jiayang Sun (Advisor) Subjects: Statistics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2009, Mathematics/Mathematical Statistics

Predictor variables are often contaminated with measurement errors in statistical practice. This may be the case due to bad measurement apparatus or just because the true value of the variable cannot be measured precisely. In the framework of general regression models, measurement errors or misclassifications have very serious consequences in many cases as they lead to bias in the estimated parameters that does not disappear as the sample size goes to infinity. In most cases the estimated effect of the contaminated covariate is attenuated. There are some techniques, regression calibration, simulation extrapolation (SIMEX), and the score function method for correcting effect estimates in the presence of measurement error. These widely used approaches have some restricted applications in many situations, for example, SIMEX is a useful tool for correcting effect estimates in the presences of additive measurement error. The method is especially helpful for complex models with a simple measurement error structure. Score function method is employed only for linear measurement error models. In this dissertation, an inference method has been proposed that accounts for the presence of measurement error in the explanatory variables in both linear and nonlinear models. This approach relies on the consideration of the mean and variance function of the observed data and application of the empirical likelihood approach to those functions, which is referred to as quasi likelihood and variance function (QVF). This proposed approach provides the confidence intervals with high inclusion probability of the unknown regression parameters. Moreover, this method is computationally easy to employ to any measurement error model for correcting bias. In addition, general descriptions and comparisons of the existing methods and the suggested estimation framework with some applications in real life data are discussed. A simulation study is conducted to show the performance of the proposed estim (open full item for complete abstract)

Committee: Hanfeng Chen PhD (Advisor); Christopher Rump PhD (Committee Member); Barbara Moses PhD (Committee Member); John Chen PhD (Committee Member); Wei Ning PhD (Committee Member) Subjects: Statistics