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Full-Text Articles in Physical Sciences and Mathematics
Approximations To Continuous Processes In Hierarchical Models, Amanda Cangelosi
Approximations To Continuous Processes In Hierarchical Models, Amanda Cangelosi
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous-time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty ( …
Small Sample Methods For The Analysis Of Clustered Binary Data, Lawrence J. Cook
Small Sample Methods For The Analysis Of Clustered Binary Data, Lawrence J. Cook
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
There are several solutions for analysis of clustered binary data. However, the two most common tools in use today, generalized estimating equations and random effects or mixed models, rely heavily on asymptotic theory. However, in many situations, such as small or sparse samples, asymptotic assumptions may not be met. For this reason we explore the utility of the quadratic exponential model and conditional analysis to estimate the effect size of a trend parameter in small sample and sparse data settings. Further we explore the computational efficiency of two methods for conducting conditional analysis, the network algorithm and Markov chain Monte …