Publication Date
2022
Document Type
Dissertation
Committee Members
Yang Liu, Ph.D. (Committee Chair); William Romine, Ph.D. (Committee Member); Shuxia Sun, Ph.D. (Committee Member); Weizhen Wang, Ph.D. (Committee Member)
Degree Name
Doctor of Philosophy (PhD)
Abstract
Data with excess zeros are common in many applications. Failure to account for the extra zeros may lead to biased estimates and misleading inference when analyzing this data type. To investigate the association between a set of predictor variables and an outcome variable with excess zeros, two kinds of regression models, the hurdle model and the zero-inflated model, are commonly used. In these models, the traditional tests, such as the likelihood-ratio test and the Wald test, can only be used to detect the fixed effects in association analysis. Recently, several random-effects or mixed-effects tests have been proposed for association analysis, such as the sequence kernel association test and the mixed-effects score test. But these tests are designed for continuous and binary data, which can not be used to analyze data with excess zeros. In this dissertation, a flexible framework is proposed to detect the mixed effects of analyzing data with excess zeroes. A normal hurdle model is applied when analyzing continuous data with extra zeros. Some score-type statistics are derived for testing both fixed and random effects in this model, and their asymptotic properties are established. Then, Fisher's and Tipptte's procedures are adopted to combine these statistics for the global test. A zero-inflated Poisson model with mixed effects is developed when analyzing count data with excess zeros. Due to the complicated forms of the test statistics in this model, we further propose a resampling method to estimate the covariance of the statistics, and a Cauchy p-value combination method is used to calculate the final p-values of the test. We conduct extensive simulation studies for these two models and apply the proposed method to several real data applications. These studies demonstrate that the proposed method can significantly improve statistical power compared to competing approaches, especially when mixed effects are presented in the analysis.
Page Count
132
Department or Program
Department of Mathematics and Statistics
Year Degree Awarded
2022
Copyright
Copyright 2022, some rights reserved. My ETD may be copied and distributed only for non-commercial purposes and may not be modified. All use must give me credit as the original author.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
ORCID ID
0000-0003-4636-3221
