Date of Award

May 2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Adewale Lukman

Abstract

In this study, we developed some hybrid estimators for variable selection in logistic regression by integrating the sparse local gradients (SLG) with some existing variable selection methods such as LASSO, Elastic net, SCAD, and MCP. The goal is to retain the flexibility of penalized likelihood estimation while improving the stability and interpretability of the selected model.

The finite-sample performance of the proposed methods is examined through a Monte Carlo simulation study covering low-, moderate-, and high-dimensional settings under different levels of predictor correlation. The simulation results show that incorporating SLG screening generally leads to more controlled model sizes and fewer falsely selected predictors than the corresponding penalized logistic regression methods without screening. These improvements are especially evident when the covariates are strongly correlated or when the dimension of the predictor space increases. Among the proposed hybrids, the combinations of SLG with nonconvex penalties tend to produce selected models that are closer to the true underlying sparsity pattern, while still maintaining competitive recovery of relevant signals.

The methods are also applied to three binary classification datasets from different domains: behavioral survey data on misophonia, sonar signal classification, and radar-based ionospheric classification. Across these applications, the SLG-based procedures select considerably smaller sets of predictors than standard penalized logistic regression methods. Importantly, this gain in parsimony is achieved with only limited changes in out-of-sample classification performance. These results indicate that SLG screening is most useful when the analysis prioritizes stable variable selection and interpretation, not prediction alone. In summary, the proposed hybrid methods provides a simple way to improve variable selection in binary classification.

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