Type of Document	Dissertation
Author	Thompson, Warren Robert
Author's Email Address	thompson@stat.fsu.edu
URN	etd-08222009-111751
Title	Variable Selection Of Correlated Predictors In Logistic Regression: Investigating The Diet-Heart Hypothesis
Degree	Doctor of Philosophy
Department	Statistics, Department of
Advisory Committee	Advisor Name Title Daniel McGee Committee Chair Debajyoti Sinha Committee Member Fred Huffer Committee Member Yiyuan She Committee Member Isaac Eberstein Outside Committee Member
Keywords	Logistic Regression Bootstrap Lasso Ridge Regression Bayesian Model Averaging Diet-Heart Hypothesis
Date of Defense	2009-08-10
Availability	unrestricted
Abstract Variable selection is an important aspect of modeling. Its aim is to distinguish between the authentic variables which are important in predicting outcome, and the noise variables which possess little to no predictive value. In other words, the goal is to find the variables that (collectively) best explains and predicts changes in the outcome variable. The variable selection problem is exacerbated when correlated variables are included in the covariate set. This dissertation examines the variable selection problem in the context of logistic regression. Specifically, we investigated the merits of the bootstrap, ridge regression, the lasso and Bayesian model averaging (BMA) as variable selection techniques when highly correlated predictors and a dichotomous outcome are considered. This dissertation also contributes to the literature on the diet-heart hypothesis. The diet-heart hypothesis has been around since the early twentieth century. Since then, researchers have attempted to isolate the nutrients in diet that promote coronary heart disease (CHD). After a century of research, there is still no consensus. In our current research, we used some of the more recent statistical methodologies (mentioned above) to investigate the effect of twenty dietary variables on the incidence of coronary heart disease. Logistic regression models were generated for the data from the Honolulu Heart Program - a study of CHD incidence in men of Japanese descent. Our results were largely method-specific. However, regardless of method considered, there was strong evidence to suggest that alcohol consumption has a strong protective effect on the risk of coronary heart disease. Of the variables considered, dietary cholesterol and caffeine were the only variables that, at best, exhibited a moderately strong harmful association with CHD incidence. Further investigation that includes a broader array of food groups is recommended.
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