Date of Completion

6-21-2013

Embargo Period

12-22-2013

Major Advisor

Dipak Dey

Associate Advisor

Kent Holsinger

Associate Advisor

Jun Yan

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Campus Access

Abstract

Binary or binomial response data are often encountered in biology studies. These types of data are usually modeled under the framework of generalized linear models, where the latent probability of ”success” is modeled by a linear function of covariates through a link function. Typically, standard link functions such as logit, probit or complementary log-log (cloglog) are adopted. However, these standard links are prone to link misspecification because of there fixed skewness. This research proposes a new class of flexible link functions called the symmetric power link family. By introducing a power parameter into the cdf corresponding to a symmetric link function and its mirror reflection, greater flexibility in skewness can be achieved in both positive and negative directions.

We establish the advantage of symmetric power links against standard link functions in the case of independent binary response data through simulated data examples. We then extend the models to binomial geostatistical spatial data by modeling the species co-occurrence of members of the genus Protea in the Cape Floristic Region of southwestern Africa. Symmetric power link models are implemented to this data under Baeysian framework using Markov Chain Monte Carlo (MCMC) methods, it is then compared with standard link functions as well as other flexible link models.

The symmetric power link models are also extended to the context of state space models (SSM) for binary time series data. We compare the performance of symmetric power link models with other standard and flexible link functions in SSM. The flexibility of the propose model is illustrated to measure effects of deep brain stimulation (DBS) on attention of a macaque monkey performing a reaction-time task.

Ordinal response data are also commonly encountered in biology studies. We extend our proposed symmetric power link function to the context of ordinal response model through a latent variable approach. Empirical results on the survey data of Invasive Plant Atlas of New England (IPANE) show that the proposed symmetric power logit model outperforms traditional standard link functions in terms of model fitting and predictive power.

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