Date of Award

8-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Member

Dr. Julia Sharp, advisor

Committee Member

Dr. William C. Bridges, Jr.

Committee Member

Dr. Patrick D. Gerard

Committee Member

Dr. Colin Gallagher

Abstract

In this paper, we discuss the impact of predictor omission in light of the omitted predictor's relationship with other predictors that were included in the model. Predictor omission in linear regression models (LMs) has been discussed by various sources in the literature. Our approach involves studying the impact of predictor omission for a wider range of omitted predictors than previously studied and extends the existing literature by considering the interaction status of an omitted predictor in addition to its correlation status. Results from models with uncentered predictors and models with centered predictors are considered. The mathematical implications of predictor omission are discussed in context of the LM, and simulated results are presented for both linear and logistic regression models. Overall, the impact of predictor omission varies among cases of interaction and correlation. A workflow for distinguishing types of model misspecification in LMs using residual plots and partial residual plots is proposed. Results from a case study using the techniques proposed to distinguish types of misspecification are presented.

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