Statistics and Probability Commons^™

Using Stability To Select A Shrinkage Method, Dean Dustin

Department of Statistics: Dissertations, Theses, and Student Work

Shrinkage methods are estimation techniques based on optimizing expressions to find which variables to include in an analysis, typically a linear regression. The general form of these expressions is the sum of an empirical risk plus a complexity penalty based on the number of parameters. Many shrinkage methods are known to satisfy an ‘oracle’ property meaning that asymptotically they select the correct variables and estimate their coefficients efficiently. In Section 1.2, we show oracle properties in two general settings. The first uses a log likelihood in place of the empirical risk and allows a general class of penalties. The second …

Optimal Design For A Causal Structure, Zaher Kmail

Department of Statistics: Dissertations, Theses, and Student Work

Linear models and mixed models are important statistical tools. But in many natural phenomena, there is more than one endogenous variable involved and these variables are related in a sophisticated way. Structural Equation Modeling (SEM) is often used to model the complex relationships between the endogenous and exogenous variables. It was first implemented in research to estimate the strength and direction of direct and indirect effects among variables and to measure the relative magnitude of each causal factor.

Historically, traditional optimal design theory focuses on univariate linear, nonlinear, and mixed models. There is no current literature on the subject of …

Best Practice Recommendations For Data Screening, Justin A. Desimone, Peter D. Harms, Alice J. Desimone

Department of Management: Faculty Publications

Survey respondents differ in their levels of attention and effort when responding to items. There are a number of methods researchers may use to identify respondents who fail to exert sufficient effort in order to increase the rigor of analysis and enhance the trustworthiness of study results. Screening techniques are organized into three general categories, which differ in impact on survey design and potential respondent awareness. Assumptions and considerations regarding appropriate use of screening techniques are discussed along with descriptions of each technique. The utility of each screening technique is a function of survey design and administration. Each technique has …

A Reduced Bias Method Of Estimating Variance Components In Generalized Linear Mixed Models, Elizabeth A. Claassen

Department of Statistics: Dissertations, Theses, and Student Work

In small samples it is well known that the standard methods for estimating variance components in a generalized linear mixed model (GLMM), pseudo-likelihood and maximum likelihood, yield estimates that are biased downward. An important consequence of this is that inferences on fixed effects will have inflated Type I error rates because their precision is overstated. We introduce a new method for estimating parameters in GLMMs that applies a Firth bias adjustment to the maximum likelihood-based GLMM estimating algorithm. We apply this technique to one- and two-treatment logistic regression models with a single random effect. We show simulation results that demonstrate …

Sequence Comparison And Stochastic Model Based On Multi-Order Markov Models, Xiang Fang

Department of Statistics: Dissertations, Theses, and Student Work

This dissertation presents two statistical methodologies developed on multi-order Markov models. First, we introduce an alignment-free sequence comparison method, which represents a sequence using a multi-order transition matrix (MTM). The MTM contains information of multi-order dependencies and provides a comprehensive representation of the heterogeneous composition within a sequence. Based on the MTM, a distance measure is developed for pair-wise comparison of sequences. The new method is compared with the traditional maximum likelihood (ML) method, the complete composition vector (CCV) method and the improved version of the complete composition vector (ICCV) method using simulated sequences. We further illustrate the application of …