Year of Publication

2021

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department/School/Program

Statistics

First Advisor

Dr. Derek S. Young

Abstract

Despite its popularity in diverse disciplines, quantile regression methods are primarily designed for the continuous response setting and cannot be directly applied to the discrete (or count) response setting. There can also be challenges when modeling count responses, such as the presence of excess zero counts, formally known as zero-inflation. To address the aforementioned challenges, we propose a comprehensive model-aware strategy that synthesizes quantile regression methods with estimation of zero-inflated count regression models. Various competing computational routines are examined, while residual analysis and model selection procedures are included to validate our method. The performance of these methods is characterized through extensive Monte Carlo simulations. An application to the Oregon Health Insurance Experiment will also be discussed. We then extend our methods to the setting of longitudinal data with zero-inflated count responses, where the goal is to study identification and estimation of conditional quantile functions for such data. We first show that conditional quantile functions for discrete responses are identified in zero-inflated models with subject heterogeneity. Then, we develop a simple three-step approach to estimate the effects of covariates on the quantiles of the response variable. We present a simulation study to show the small sample performance of the estimator. Finally, we illustrate our model using the RAND Health Insurance Experiment data and the Combined Pharmacotherapies and Behavioral Interventions (COMBINE) data.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2021.188

Available for download on Sunday, May 28, 2023

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