Date of Award

6-2024

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Duy Ngo, Ph.D.

Second Advisor

Dr. Joshua Naranjo, Ph.D.

Third Advisor

Dr. Kevin Lee, Ph.D.

Fourth Advisor

Dr. Sangwoo Lee, Ph.D.

Abstract

Spatial analysis is essential for comprehending the spatial distribution of diseases and various phenomena across geographic regions. This study investigates the utilization of alternative adjacency matrices in spatial analysis, with a specific focus on implementing Poisson regression models. This study intricately explores the methodology behind constructing alternative weight matrices, specifying weight matrices, and comparing the performance of Poisson models using five different weight matrices.

The popular Poisson model model is described, and five different definitions of weight matrices are defined, which are the following: binary weight matrix, inverse distance weight matrix using Euclidean distance, Graph distance matrix, Path matrix, and the combination matrix of Graph distance matrix and Path matrix. The first two weight matrices are commonly used in spatial analysis, and the last three weight matrices are introduced in the study.

In particular, we introduce three new weight matrices for spatially correlated random effects; Graph distance matrix, Path matrix, and the combination of Graph distance matrix and Path matrix. We investigate the performance of these new weight matrices via simulation study. Using the generated spatially correlated random effects, the three different kinds of data sets are generated, each representing a different underlying spatial structure. The models are evaluated using the standard error and the mean square error of estimated parameters. In result, Graph distance matrix, Path matrix, and the combination matrix of Graph distance matrix and Path matrix perform well and the models using these new weight matrices have better performance than binary weight matrix and inverse distance weight matrix using Euclidean distance in the simulated data. We also apply new weight matrices for the real data analysis. The opioid-related drug overdose deaths data collected by the Michigan Death Certificates are used for the real data analysis. In result of the real data analysis, the Poisson model with the combination matrix of Graph distance matrix and Path matrix has the best fit. In conclusion, the specification of the spatial weight matrices significantly influences both model fit and parameter estimation. The simulation results provide some evidence that all weight matrices that generated in the study have a good fit of the simulated data and the combination matrix of Graph distance matrix and Path matrix is the best choice for the real data analysis.

Access Setting

Dissertation-Open Access

Download

Share

COinS