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Topic

AdaptVarLM: A Linear Regression Model for Covariate-Dependent Non-Constant Error Variance

Department of Mathematics and Statistics

Date & location

• Friday, August 16, 2024
• 11:00 A.M.
• Virtual Defence

Examining Committee

Supervisory Committee

• Dr. Xuekui Zhang, Department of Mathematics and Statistics, ·¬ÇÑÉçÇø (Supervisor)
• Dr. Li Xing, Department of Mathematics and Statistics, UVic (Member)
• Dr. Xiaojian Shao, Department of Mathematics and Statistics, UVic (Member)

External Examiner

• Dr. Ke Xu, Department of Economics, UVic

Chair of Oral Examination

• Dr. Amanda Bates, Department of Biology, UVic

Abstract

In biological research, traditional multiple regression models assume homoscedasticity—constant variance of error terms—an assumption that is difficult to maintain in complex biological data. This thesis introduces AdaptVarLM, a novel linear regression model specialized in dealing with non-constant error variance dependent on one covariate. AdaptVarLM integrates an auxiliary linear relationship between the logarithmic variance of the error term and a specific explanatory variable, and uses maximum likelihood estimation (MLE) in the iterative updating process to improve the parameter estimation accuracy. By modelling non-constant error variance, AdaptVarLM outperforms the traditional regression model in capturing the complex variability inherent in biological data. Applying to the study of Alzheimer’s disease, AdaptVarLM detects genetically linked genes associated with the disease and error variance. The results of analyzing both bulk and single-cell data validate the effectiveness of AdaptVarLM in detecting significant genes.