Date of Award

6-14-2019

Publication Type

Doctoral Thesis

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Paul, S.R.

Keywords

Beta binomial, measurement error, Missing Value

Rights

info:eu-repo/semantics/openAccess

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Abstract

Discrete, binary data with over-dispersion and zero-inflation can arise in toxicology and other similar fields. In studies where the litter is an experimental unit, there is a ``litter effect" which means that the litter mates respond more alike than animals from other litters. In experimental data, foetuses in the same litter have similar responses to the treatment. The probability of ``success" may not remain constant throughout the litters. In regression analysis of such data another problem that may arise in practice is that some responses may be missing or/and some covariates may have measurement error. In this dissertation we develop an estimation procedure for the parameters of a zero-inflated over-dispersed binomial model in the presence of missing responses without/with considering covariate measurement errors. A weighted expectation maximization algorithm is used for the maximum likelihood (ML) estimation of the parameters involved. Extensive simulations are conducted to study the properties of the estimates in terms of average estimates (AE), relative bias (RB), variance (VAR), mean squared error (MSE) and coverage probability (CP) of estimates. Simulations show much superior properties of the estimates obtained using the weighted expectation maximization algorithm. Some illustrative examples and a discussion are given.

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