Author

Xinxin Hu

Date of Award

Spring 2019

Document Type

Open Access Thesis

Department

Statistics

First Advisor

Xiaoyan Lin

Abstract

As pesticides are widely used in agriculture, more and more people who work at places like farm are exposed to the pesticides. According to enviroment re- searches [Villarejo; 2003; Reigart and Roberts; 1999], being exposed to some kind of pesticides like Organophosphorus (OP) insecticides has significantly effected the health of farmworkers and their family. The actual level of pesticides can be detected with some limitation for now. However, it is hard to detect when the level is below the limit of detection (LOD). Therefore, the goal of our research is to propose several different methods to analyze data with missing values below the LOD.

In Chapter 1, we apply two methods to analyze a variable with missing values below the LOD, we propose the zero-inflated lognormal to model the variable and apply the maximum likelihood method and the Bayesian Gibbs sampler method to analyze the data. In Chapter 2, we conduct the regression analysis with a predictor having missing values below the LOD. We propose four methods. Two naive methods include "delete missing values" method and "impute a fixed value to missing values" method. The other two methods are the "maximum likelihood method" and the "Bayesian Gibbs sampler" method.

Based on the estimation results, we find that the performance of the "Gibbs sam- pler" method is better than all other methods for each of the parameter. The "Gibbs sampler" method provides lower biases and standard errors, and better coverage prob- abilities. The performance may be due to the Bayesian hierarchical structure and the nature of the MCMC sampling, which allow to borrow all information from multiple levels to inform unknown quantities.

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