Physical Sciences and Mathematics Commons^™

Dietary Patterns And Cognitive Decline In Aged Populations, Austin J. Bowles

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In this paper, we discuss distinctive features of longitudinal studies, and illustrate two regression-based methods for the analysis of longitudinal data. A study of dietary patterns and cognitive decline (Cache County Memory Study) is used to motivate our discussion and analysis. Cognitive decline is a risk factor for Alzheimer’s disease, the sixth leading cause of all deaths among Americans. The study attempted to identify dietary patterns associated with reduced risk of age-related cognitive decline in elderly populations. Higher levels of adherence to the Dietary Approaches to Stop Hypertension (DASH) and/or Mediterranean diets were found to be associated with increased cognitive …

Stressors Across The Lifespan And Dementia Risk: A Statistical Method Analysis, Megan Platt Borrowman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Cache Lifespan Stressors and Alzheimer's Disease (LSAD) study has access to data from the Cache County Study on Memory Health and Aging (CCS) that have been linked to the extensive genealogical and vital records from the Utah Population Database (UPDB). Information about stressful life events experienced by the original 5092 CCS participants has been extracted objectively from the UPDB, without the possibility of recall bias. This information was then statistically analyzed to look for relationships between key stressors and dementia risk. The LSAD study made it possible to examine the correlation between stressors as well as look at patterns …

Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able …

Climate Change And Community Dynamics: A Hierarchical Bayesian Model Of Resource-Driven Changes In A Desert Rodent Community, Glenda M. Yenni

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Predicting effects of climate change on species persistence often assumes that those species are responding to abiotic effects alone. However, biotic interactions between community members may affect species’ ability to respond to abiotic changes. Latent Gaussian models of resource availability using precipitation and NDVI and accounting for spatial autocorrelation and rodent group-level uncertainty in the process are developed to detect differences in seasons, groups, and the experimental removal of one group. Precipitation and NDVI have overall positive effects on rodent energy use as expected, but meaningful differences were detected. Differences in the importance of seasonality when the dominant group was …

Estimation Of Beta In A Simple Functional Capital Asset Pricing Model For High Frequency Us Stock Data, Yan Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project applies the methods of functional data analysis (FDA) to intra-daily returns of US corporations. It focuses on an extension of the Capital Asset Pricing Model (CAPM) to such returns. The CAPM is essentially a linear regression with the slope coefficient β. Returns of an asset are regressed on index return. We compare the estimates of β obtained for the daily and intra-daily returns. The variability of these estimates is assessed by two bootstrap methods. All computations are performed using statistical software R. Customized functions are developed to process the raw data, estimate the parameters and assess their variability. …

Controlling Error Rates With Multiple Positively-Dependent Tests, Abdullah Al Masud

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

It is a typical feature of high dimensional data analysis, for example a microarray study, that a researcher allows thousands of statistical tests at a time. All inferences for the tests are determined using the p-values; a smaller p-value than the α-level of the test signifies a statistically significant test. As the number of tests increases, the chance of observing some small p-values is very high even when all null hypotheses are true. Consequently, we make wrong conclusions on the hypotheses. This type of potential problem frequently happens when we test several hypotheses simultaneously, i.e., the multiple testing problem. …

Examining Child Sexual Abuse And Future Parenting: An Application Of Latent Class Modeling, Kimberly W. D'Zatko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This study was designed to empirically derive latent classes of mothers who were sexually abused during childhood and to assess the association between depression, alcohol/drug use, supportive intimate partner, and specific classes.

One hundred six women between the ages of 20 and 44 years (M = 27) who reported having been sexually abused during childhood (CSA) and 158 non-CSA mothers between the ages of 20 and 43 years (M = 23) were interviewed and assessed along six parenting dimensions. Logistic regression models evaluated the association between psychoemotional variables and specific classes.

The final model consisted of three classes—53.2%, …

On The Use Of Log-Transformation Vs. Nonlinear Regression For Analyzing Biological Power-Laws, Xiao Xiao

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Power-law relationships are among the most well-studied functional relationships in biology . Recently the common practice of fitting power-laws using linear regression on log-transformed data (LR) has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations we demonstrate that the error distribution determines which method performs better, with LR better characterizing data with multiplicative lognormal error and NLR better characterizing data with additive normal error. Analysis of 471 biological power-laws shows that both …

Development And Implementation Of A Bayesian Model For Sediment Transport In Fluvial Systems, Mark Schmelter

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Recent studies in the field of fluvial sediment transport underscore the difficulty in reliably estimating transport model parameters, collecting accurate observations, and making predictions due to measurement error and conceptual model uncertainty. There is a pressing need to develop models that can account for measurement error, conceptual model uncertainty, and natural variability while providing probability-based predictions as well as a means for conceptual model discrimination. The model presented in this research employs an excess shear sediment transport equation for a uni-size sediment bed developed in a Bayesian statistical framework. This statistical model provides a means to rigorously estimate distributions of …