Term of Award

Spring 2019

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Stephen Carden

Committee Member 1

Arpita Chatterjee

Committee Member 2

Divine Wanduku

Committee Member 3

Nicolas Holtzman

Committee Member 3 Email



When considering statistical scenarios where one can sample from populations that are not of interest for the purposes of a study, bivariate mixture models can be used to study the effect that this missampling can have on parameter estimation. In this thesis, we will examine the behavior that bivariate mixture models have on two statistical constructs: Cronbach's alpha \cite{C51}, and Spearman's rho \cite{S04}. Chapter 1 will introduce notions of mixture models and the definition of bias under mixture models which will serve as the central concept of this thesis. Chapter 2 will investigate a particular psychometric issue known as insufficient effort responding (IER), which we model as a mixture model, while Chapter 3 will deal with mixture models in a more general setting. Chapter's 2 and 3 will demonstrate that the sign of the bias and the bias under bivariate mixture models for Cronbach's alpha and Spearman's rho, respectively, are polynomial functions in the mixing proportions of the underlying distributions. This will be followed in each chapter by simulation results and observations.

OCLC Number


Research Data and Supplementary Material