Date of Award

Summer 2023

Document Type

Open Access Dissertation



First Advisor

James W. Hardin


This dissertation focuses on theory and application of discrete data methods, particularly approaches to over- and underdispersion relative to the Poisson distribution and an application of random forest and logistic regression modeling. The first chapter derives a score test for over- and underdispersion in the heaped generalized Poisson distribution. Equi-, over-, and underdispersed heaped generalized Poisson and heaped negative binomial data are simulated to evaluate the performance of the score test by comparing the power it achieves to that of Wald and likelihood ratio tests. We find that the score test we derive performs comparably to both the Wald and likelihood ratio tests. The second chapter explores the application and limitations of a model for the dispersion parameter in the double Poisson distribution utilizing a logistic-like link function. Data are simulated under various dispersion structures and a set of models assuming different maximum dispersion values are estimated for each. Through the simulation and a case study, we assess the application of the proposed model and identify potential improvements to aid in its effective utilization. Finally, the third chapter evaluates the performance of, and identifies important items in, a screening and a diagnostic tool for tic disorders in children. We also compare their results in terms of their ability to correctly predict tics in children and determine that the random forest models are more effective at reducing Type II errors.


© 2023, Rebecca C. Wardrop

Included in

Biostatistics Commons