Year of Publication

2012

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Yanbing Zheng

Second Advisor

Dr. Richard Kryscio

Abstract

Spatial-temporal autologistic models are useful models for binary data that are measured repeatedly over time on a spatial lattice. They can account for effects of potential covariates and spatial-temporal statistical dependence among the data. However, the traditional parametrization of spatial-temporal autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, where its non-negative autocovariates could bias the realizations toward 1. In order to achieve interpretable parameters, a centered spatial-temporal autologistic regression model has been developed. Two efficient statistical inference approaches, expectation-maximization pseudo-likelihood approach (EMPL) and Monte Carlo expectation-maximization likelihood approach (MCEML), have been proposed. Also, Bayesian inference is considered and studied. Moreover, the performance and efficiency of these three inference approaches across various sizes of sampling lattices and numbers of sampling time points through both simulation study and a real data example have been studied. In addition, We consider the imputation of missing values is for spatial-temporal autologistic regression models. Most existing imputation methods are not admissible to impute spatial-temporal missing values, because they can disrupt the inherent structure of the data and lead to a serious bias during the inference or computing efficient issue. Two imputation methods, iteration-KNN imputation and maximum entropy imputation, are proposed, both of them are relatively simple and can yield reasonable results. In summary, the main contributions of this dissertation are the development of a spatial-temporal autologistic regression model with centered parameterization, and proposal of EMPL, MCEML, and Bayesian inference to obtain the estimations of model parameters. Also, iteration-KNN and maximum entropy imputation methods have been presented for spatial-temporal missing data, which generate reliable imputed values with the reasonable efficient imputation time.

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