Title

Simulation and Application of Binary Logic Regression Models

Document Type

Thesis

Degree

Master of Science (MS)

Department

Statistics

First Advisor's Name

Wensong Wu

First Advisor's Committee Title

Committee chair

Second Advisor's Name

Florence George

Third Advisor's Name

Golam Kibria

Keywords

Logic regression, simulation, repeated measures, bootstrapping, cross-validation.

Date of Defense

4-1-2016

Abstract

Logic regression (LR) is a methodology to identify logic combinations of binary predictors in the form of intersections (and), unions (or) and negations (not) that are linearly associated with an outcome variable. Logic regression uses the predictors as inputs and enables us to identify important logic combinations of independent variables using a computationally efficient tree-based stochastic search algorithm, unlike the classical regression models, which only consider pre-determined conventional interactions (the “and” rules). In the thesis, we focused on LR with a binary outcome in a logistic regression framework. Simulation studies were conducted to examine the performance of LR under the assumption of independent and correlated observations, respectively, for various characteristics of the data sets and LR search parameters. We found that the proportion of times that LR selected the correct logic rule was usually low when the signal and/or prevalence of the true logic rule were relatively low. The method performed satisfactorily under easy learning conditions such as high signal, simple logic rules and/or small numbers of predictors. Given the simulation characteristics and correlation structures tested, we found some but not significant difference in performance when LR was applied to dependent observations compared to the independent case. In addition to simulation studies, an advanced application method was proposed to integrate LR and resampling methods in order to enhance LR performance. The proposed method was illustrated using two simulated data sets as well as a data set from a real-life situation. The proposed method showed some evidence of being effective in discerning the correct logic rule, even for unfavorable learning conditions.

Identifier

FIDC000269

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