All ETDs from UAB

Advisory Committee Chair

Timothy M Beasley

Advisory Committee Members

Justin L Blackburn

Virginia J Howard

Charles R Katholi

Document Type

Dissertation

Date of Award

2016

Degree Name by School

Doctor of Philosophy (PhD) School of Public Health

Abstract

Ordinary Least Squares Optimization is one of the most widely used methods in statistical analysis to estimate the parameters of a general linear model. Yet, when the assumption of homoskedastic errors is violated, the statistical model is incorrectly specified and alteration of both Type I and Type II error rates occurs. We examine different heteroskedasticity consistent covariance matrix estimators (HCCM) under various heteroskedastic analysis of covariance (ANCOVA) models with orthogonal predictors, and find that under the test of group differences, MacKinnon and White’s HC2 and Davidson and MacKinnon’s HC3 perform reasonably well in terms of Type I error control; and under the test of covariate, none of the HCCM estimators did well at maintaining Type I error rate control. Cai and Hayes’s estimator is conservative under both the test of group differences and the test of covariate. When we force the predictors in the ANCOVA models to be non-orthogonal, we get similar results to the ANCOVA with orthogonal predictors. In an applied analysis, examining the association between log transformed C-reactive protein (CRP) and smoking, controlling for waist circumference (WC) and race, we find that when heteroskedasticity is present, but ignored, there is significant evidence to suggest an association between log(CRP) and smoking, controlling for WC and race. Yet, when we adjust for heterskedasticity using a HCCM estimator, we find no significant evidence to suggest an association between log(CRP) and smoking, controlling for WC and race. We recommend using HCCM estimators to estimate the variance of a regression model regardless of the degree of heteroskedasticity. Moreover, in the presence of high leverage values, it may be more appropriate to use Cai and Hayes’s estimator.

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