AdaptVarLM: A linear regression model for covariate-dependent non-constant error variance
| dc.contributor.author | Wang, Wanmeng | |
| dc.contributor.supervisor | Zhang, Xuekui | |
| dc.date.accessioned | 2024-09-04T21:24:55Z | |
| dc.date.available | 2024-09-04T21:24:55Z | |
| dc.date.issued | 2024 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science MSc | |
| dc.description.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. | |
| dc.description.embargo | 2025-08-20 | |
| dc.description.scholarlevel | Graduate | |
| dc.identifier.uri | https://hdl.handle.net/1828/20370 | |
| dc.language | English | eng |
| dc.language.iso | en | |
| dc.rights | Available to the World Wide Web | |
| dc.subject | statistics | |
| dc.subject | linear regression model | |
| dc.subject | non-constant error variance | |
| dc.title | AdaptVarLM: A linear regression model for covariate-dependent non-constant error variance | |
| dc.type | Thesis |