Statistical Methodology Commons^™

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 …

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 …

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 …

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) …

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 …

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 …

Comparison Of Hazard, Odds And Risk Ratio In The Two-Sample Survival Problem, Benedict P. Dormitorio

Dissertations

Cox proportional hazards is the standard method for analyzing treatment efficacy when time-to-event data is available. In the absence of time-to-event, investigators may use logistic regression which only requires relative frequencies of events, or Poisson regression which requires only interval-summarized frequency tables of time-to-event. When event frequencies are used instead of time-to-events, does it always result in a loss in power?

We investigate the relative performance of the three methods. In particular, we compare the power of tests based on the respective effect-size estimates (1)hazard ratio (HR), (2)odds ratio (OR), and (3)risk ratio (RR). We use a variety of survival …

Harnessing Complexity: Analysis Methodology And Ethical Framework To Facilitate Utilization Of Video Data In Evaluations, Kurt A. Wilson

Dissertations

Most evaluations in the nonprofit and international development sectors are conducted in contexts of complexity; the specific intervention being evaluated is but one of many interrelated factors influencing the desired outcome. Video data, especially when directly generated by program participants, can provide both exceptionally rich qualitative data as well as contextually-relevant feedback within complex systems. Despite these unique strengths and opportunities, video data is underutilized in the field of evaluation. This dissertation addresses specific barriers associated with video data through three inter-related papers: Papers one and two (Chapters II and III) present the findings from two interrelated studies of an …

Improving The Design Of Cluster-Randomized Trials In Education: Informing The Selection Of Variance Design Parameter Values For Science Achievement Studies, Carl D. Westine

Dissertations

The purpose of this three-essay dissertation is to provide practical guidance to evaluators planning cluster-randomized trials (CRTs) of science achievement. In an educational setting, interventions are often administered at the cluster level, while outcomes are typically measured at the student level through standardized achievement testing. When evaluating an intervention, a CRT is appropriate because it allows for treatment to be modeled at a different level than the unit of analysis, and properly accounts for the violation of independence that occurs due to nesting. Accurately designing a CRT involves estimating variance parameters (i.e., intraclass correlations [ICCs] and percent of variance explained …

Robust Residuals And Diagnostics In Autoregressive Time Series, Kirk W. Anderson

Dissertations

One of the goals of model diagnostics is outlier detection. In particular, we would like to use the residuals, appropriately standardized, to “flag” outliers. Hopefully, our (robust) procedure has yielded a fit that resists undue influence by outlying points, while simultaneously drawing attention to these interesting points via residual analysis. In this study we consider several different methods of standardizing the residuals resulting from autoregression. A large sample approximation for the variance of rank-based first order autoregressive time series residuals is developed. This provides studentized residuals, specific to the time series model and estimation procedure. Simulation studies are presented that …

New Statitstical Methods For The Estimation Of The Mean And Standard Deviation From Normally Distributed Censored Samples, Abou El-Makarim Abd El-Alim Aboueissa

Dissertations

The main objective of this dissertation is to estimate the mean /x and standard deviation cr of a normal population from left-censored samples. We have developed new methods for calculating estimates for the mean and standard deviation of a normal population from left-censored samples. Some of these methods based on traditional estimating procedures. A new method of obtaining the Cohen maximum likelihood estimates for fx and cr without the aid of an auxiliary table will be introduced. This new method will be used to extend Cohen table of estimating the Cohen A-parameter that is required for calculating the maximum likelihood …