Year

2026

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Dr. Yisu Jia

Second Advisor

Dr. Jasper Xu

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Peiyao Wang

Department Chair

Dr. Richard F. Patterson

College Dean

Dr. Kaveri Subrahmanyam

Abstract

This thesis presents a comparative study of logistic regression, Linear Discriminant Analy- sis (LDA), and Quadratic Discriminant Analysis (QDA) for binary classification in healthcare analytics, integrating theoretical derivation, simulation, and real-data application. A facto- rial simulation study crosses the covariance structure (equal vs. unequal), predictor correla- tion (ρ ∈ {0, 0.5, 0.9}), dimensionality (p ∈ {2, 5, 10}) and sample size (n ∈ {50, 100, 200}) across 54 scenarios with 1,000 Monte Carlo replicates each. Three main findings emerge. Logistic regression and LDA are nearly interchangeable when the assumption of equal-covariance holds. QDA achieves substantially better discrimi- nation when class-specific covariance matrices differ, with AUC gains of 0.05–0.07. However, QDA’s variance penalty makes it unreliable when sample sizes are small relative to dimen- sionality. These findings are validated using NHANES 2017–2018 diabetes data (n = 3,703), where the survey-weighted logistic regression achieves a concordance statistic of 0.806 and LDA outperforms QDA in the cross-validated error rate (0.287 vs. 0.300). The results provide practical guidance for classifier selection in healthcare settings based on covariance structure, sample size, and inferential goals.

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